1
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Rocca D, Cortes CL, Gonthier JF, Ollitrault PJ, Parrish RM, Anselmetti GL, Degroote M, Moll N, Santagati R, Streif M. Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization. J Chem Theory Comput 2024. [PMID: 38788209 DOI: 10.1021/acs.jctc.4c00352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.
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Affiliation(s)
- Dario Rocca
- QC Ware Corporation, Palo Alto, California 94306, United States
| | | | | | | | | | | | - Matthias Degroote
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | - Nikolaj Moll
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
| | | | - Michael Streif
- Quantum Lab, Boehringer Ingelheim, 55218 Ingelheim am Rhein, Germany
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2
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Liu J, Ma H, Shang H, Li Z, Yang J. Quantum-centric high performance computing for quantum chemistry. Phys Chem Chem Phys 2024. [PMID: 38787657 DOI: 10.1039/d4cp00436a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
High performance computing (HPC) is renowned for its capacity to tackle complex problems. Meanwhile, quantum computing (QC) provides a potential way to accurately and efficiently solve quantum chemistry problems. The emerging field of quantum-centric high performance computing (QCHPC), which merges these two powerful technologies, is anticipated to enhance computational capabilities for solving challenging problems in quantum chemistry. The implementation of QCHPC for quantum chemistry requires interdisciplinary research and collaboration across multiple fields, including quantum chemistry, quantum physics, computer science and so on. This perspective provides an introduction to the quantum algorithms that are suitable for deployment in QCHPC, focusing on conceptual insights rather than technical details. Parallel strategies to implement these algorithms on quantum-centric supercomputers are discussed. We also summarize high performance quantum emulating simulators, which are considered a viable tool to explore QCHPC. We conclude with challenges and outlooks in this field.
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Affiliation(s)
- Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
| | - Huan Ma
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
| | - Honghui Shang
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Zhenyu Li
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
| | - Jinlong Yang
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.
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3
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Patel S, Yen TC, Izmaylov AF. Extension of Exactly-Solvable Hamiltonians Using Symmetries of Lie Algebras. J Phys Chem A 2024; 128:4150-4159. [PMID: 38718293 DOI: 10.1021/acs.jpca.4c00993] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/24/2024]
Abstract
Exactly solvable Hamiltonians that can be diagonalized by using relatively simple unitary transformations are of great use in quantum computing. They can be employed for the decomposition of interacting Hamiltonians either in Trotter-Suzuki approximations of the evolution operator for the quantum phase estimation algorithm or in the quantum measurement problem for the variational quantum eigensolver. One of the typical forms of exactly solvable Hamiltonians is a linear combination of operators forming a modestly sized Lie algebra. Very frequently, such linear combinations represent noninteracting Hamiltonians and thus are of limited interest for describing interacting cases. Here, we propose an extension in which the coefficients in these combinations are substituted by polynomials of the Lie algebra symmetries. This substitution results in a more general class of solvable Hamiltonians, and for qubit algebras, it is related to the recently proposed noncontextual Pauli Hamiltonians. In fermionic problems, this substitution leads to Hamiltonians with eigenstates that are single Slater determinants but with different sets of single-particle states for different eigenstates. The new class of solvable Hamiltonians can be measured efficiently using quantum circuits with gates that depend on the result of a midcircuit measurement of the symmetries.
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Affiliation(s)
- Smik Patel
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Tzu-Ching Yen
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
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4
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Kono S, Pan J, Chegnizadeh M, Wang X, Youssefi A, Scigliuzzo M, Kippenberg TJ. Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 ms. Nat Commun 2024; 15:3950. [PMID: 38729959 PMCID: PMC11087564 DOI: 10.1038/s41467-024-48230-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 04/24/2024] [Indexed: 05/12/2024] Open
Abstract
Superconducting qubits are among the most advanced candidates for achieving fault-tolerant quantum computing. Despite recent significant advancements in the qubit lifetimes, the origin of the loss mechanism for state-of-the-art qubits is still subject to investigation. Furthermore, the successful implementation of quantum error correction requires negligible correlated errors between qubits. Here, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, averaging 0.2 ms and exceeding 0.4 ms - corresponding to quality factors above 5 million and 10 million, respectively. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of the qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments.
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Affiliation(s)
- Shingo Kono
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland.
| | - Jiahe Pan
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Mahdi Chegnizadeh
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Xuxin Wang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Amir Youssefi
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Marco Scigliuzzo
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland
| | - Tobias J Kippenberg
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, EPFL, Lausanne, Switzerland.
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5
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Koottandavida A, Tsioutsios I, Kargioti A, Smith CR, Joshi VR, Dai W, Teoh JD, Curtis JC, Frunzio L, Schoelkopf RJ, Devoret MH. Erasure Detection of a Dual-Rail Qubit Encoded in a Double-Post Superconducting Cavity. PHYSICAL REVIEW LETTERS 2024; 132:180601. [PMID: 38759169 DOI: 10.1103/physrevlett.132.180601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Accepted: 04/03/2024] [Indexed: 05/19/2024]
Abstract
Qubits with predominantly erasure errors present distinctive advantages for quantum error correction (QEC) and fault-tolerant quantum computing. Logical qubits based on dual-rail encoding that exploit erasure detection have been recently proposed in superconducting circuit architectures, with either coupled transmons or cavities. Here, we implement a dual-rail qubit encoded in a compact, double-post superconducting cavity. Using an auxiliary transmon, we perform erasure detection on the dual-rail subspace. We characterize the behavior of the code space by a novel method to perform joint-Wigner tomography. This is based on modifying the cross-Kerr interaction between the cavity modes and the transmon. We measure an erasure rate of 3.981±0.003 (ms)^{-1} and a residual, postselected dephasing error rate up to 0.17 (ms)^{-1} within the code space. This strong hierarchy of error rates, together with the compact and hardware-efficient nature of this novel architecture, holds promise in realizing QEC schemes with enhanced thresholds and improved scaling.
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Affiliation(s)
- Akshay Koottandavida
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Ioannis Tsioutsios
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Aikaterini Kargioti
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Cassady R Smith
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Vidul R Joshi
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Wei Dai
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - James D Teoh
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Jacob C Curtis
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Luigi Frunzio
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Robert J Schoelkopf
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
| | - Michel H Devoret
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA and Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
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6
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Ganjam S, Wang Y, Lu Y, Banerjee A, Lei CU, Krayzman L, Kisslinger K, Zhou C, Li R, Jia Y, Liu M, Frunzio L, Schoelkopf RJ. Surpassing millisecond coherence in on chip superconducting quantum memories by optimizing materials and circuit design. Nat Commun 2024; 15:3687. [PMID: 38693124 PMCID: PMC11063213 DOI: 10.1038/s41467-024-47857-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 04/12/2024] [Indexed: 05/03/2024] Open
Abstract
The performance of superconducting quantum circuits for quantum computing has advanced tremendously in recent decades; however, a comprehensive understanding of relaxation mechanisms does not yet exist. In this work, we utilize a multimode approach to characterizing energy losses in superconducting quantum circuits, with the goals of predicting device performance and improving coherence through materials, process, and circuit design optimization. Using this approach, we measure significant reductions in surface and bulk dielectric losses by employing a tantalum-based materials platform and annealed sapphire substrates. With this knowledge we predict the relaxation times of aluminum- and tantalum-based transmon qubits, and find that they are consistent with experimental results. We additionally optimize device geometry to maximize coherence within a coaxial tunnel architecture, and realize on-chip quantum memories with single-photon Ramsey times of 2.0 - 2.7 ms, limited by their energy relaxation times of 1.0 - 1.4 ms. These results demonstrate an advancement towards a more modular and compact coaxial circuit architecture for bosonic qubits with reproducibly high coherence.
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Affiliation(s)
- Suhas Ganjam
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA.
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA.
| | - Yanhao Wang
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Yao Lu
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Archan Banerjee
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Chan U Lei
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Lev Krayzman
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Kim Kisslinger
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, 11973, NY, USA
| | - Chenyu Zhou
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, 11973, NY, USA
| | - Ruoshui Li
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, 11973, NY, USA
| | - Yichen Jia
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, 11973, NY, USA
| | - Mingzhao Liu
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, 11973, NY, USA
| | - Luigi Frunzio
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA
| | - Robert J Schoelkopf
- Departments of Applied Physics and Physics, Yale University, New Haven, 06511, CT, USA.
- Yale Quantum Institute, Yale University, New Haven, 06511, CT, USA.
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7
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Réglade U, Bocquet A, Gautier R, Cohen J, Marquet A, Albertinale E, Pankratova N, Hallén M, Rautschke F, Sellem LA, Rouchon P, Sarlette A, Mirrahimi M, Campagne-Ibarcq P, Lescanne R, Jezouin S, Leghtas Z. Quantum control of a cat qubit with bit-flip times exceeding ten seconds. Nature 2024; 629:778-783. [PMID: 38710932 DOI: 10.1038/s41586-024-07294-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Accepted: 03/11/2024] [Indexed: 05/08/2024]
Abstract
Quantum bits (qubits) are prone to several types of error as the result of uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads1. One possible solution is to build qubits that are inherently protected against certain types of error, so the overhead required to correct the remaining errors is greatly reduced2-7. However, this strategy relies on one condition: any quantum manipulations of the qubit must not break the protection that has been so carefully engineered5,8. A type of qubit known as a cat qubit is encoded in the manifold of metastable states of a quantum dynamical system, and thereby acquires continuous and autonomous protection against bit-flips. Here, in a superconducting-circuit experiment, we implemented a cat qubit with bit-flip times exceeding 10 s. This is an improvement of four orders of magnitude over previously published cat-qubit implementations. We prepared and imaged quantum superposition states, and measured phase-flip times greater than 490 ns. Most importantly, we controlled the phase of these quantum superpositions without breaking the bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.
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Affiliation(s)
- U Réglade
- Alice & Bob, Paris, France
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - A Bocquet
- Alice & Bob, Paris, France
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - R Gautier
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | | | - A Marquet
- Alice & Bob, Paris, France
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Physique, Lyon, France
| | | | | | | | | | - L-A Sellem
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - P Rouchon
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - A Sarlette
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - M Mirrahimi
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | - P Campagne-Ibarcq
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France
| | | | | | - Z Leghtas
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS-PSL, CNRS, Sorbonne Université, Université Paris Cité, Centre Automatique et Systèmes, Mines Paris, Université PSL, Inria, Paris, France.
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8
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Rebello AM, Ruela LM, Moreto G, Klein NY, Martins E, Oliveira IS, Sinnecker JP, Rouxinol F. Optimizing Josephson Junction Reproducibility in 30 kV E-Beam Lithography: An Analysis of Backscattered Electron Distribution. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:783. [PMID: 38727377 PMCID: PMC11085180 DOI: 10.3390/nano14090783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Revised: 04/13/2024] [Accepted: 04/17/2024] [Indexed: 05/12/2024]
Abstract
This paper explores methods to enhance the reproducibility of Josephson junctions, which are crucial elements in superconducting quantum technologies, when employing the Dolan technique in 30 kV e-beam processes. The study explores the influence of dose distribution along the bridge area on reproducibility, addressing challenges related to fabrication sensitivity. Experimental methods include e-beam lithography, with electron trajectory simulations shedding light on the behavior of backscattered electrons. Wedescribe the fabrication of various Josephson junction geometries and analyze the correlation between the success rates of different lithography patterns and the simulated distribution of backscattered electrons. Our findings demonstrate a success rate of up to 96.3% for the double-resist 1-step low-energy e-beam lithography process. As a means of implementation strategy, we provide a geometric example that takes advantage of simulated stability regions to administer a controlled, uniform dose across the junction area, introducing novel features to overcome the difficulties associated with fabricating bridge-like structures.
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Affiliation(s)
- Arthur M. Rebello
- Coordenação de Matéria Condensada, Física Aplicada e Nanociência (COMAN), Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro 22290-180, RJ, Brazil; (A.M.R.); (N.Y.K.); (I.S.O.)
| | - Lucas M. Ruela
- Quantum Device Physics Laboratory, Universidade Estadual de Campinas (Unicamp), Instituto de Física Gleb Wataghin (IFGW), Campinas 13083-859, SP, Brazil; (L.M.R.); (G.M.)
| | - Gustavo Moreto
- Quantum Device Physics Laboratory, Universidade Estadual de Campinas (Unicamp), Instituto de Física Gleb Wataghin (IFGW), Campinas 13083-859, SP, Brazil; (L.M.R.); (G.M.)
| | - Naiara Y. Klein
- Coordenação de Matéria Condensada, Física Aplicada e Nanociência (COMAN), Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro 22290-180, RJ, Brazil; (A.M.R.); (N.Y.K.); (I.S.O.)
| | - Eldues Martins
- Leopoldo Américo Miguez de Mello Research, Development and Innovation Center (CENPES), Rio de Janeiro 21941-915, RJ, Brazil;
| | - Ivan S. Oliveira
- Coordenação de Matéria Condensada, Física Aplicada e Nanociência (COMAN), Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro 22290-180, RJ, Brazil; (A.M.R.); (N.Y.K.); (I.S.O.)
| | - João P. Sinnecker
- Coordenação de Matéria Condensada, Física Aplicada e Nanociência (COMAN), Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro 22290-180, RJ, Brazil; (A.M.R.); (N.Y.K.); (I.S.O.)
| | - Francisco Rouxinol
- Quantum Device Physics Laboratory, Universidade Estadual de Campinas (Unicamp), Instituto de Física Gleb Wataghin (IFGW), Campinas 13083-859, SP, Brazil; (L.M.R.); (G.M.)
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9
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Hiesmayr BC, Krzemień W, Bała M. Quantum error channels in high energetic photonic systems. Sci Rep 2024; 14:9672. [PMID: 38671255 DOI: 10.1038/s41598-024-60472-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Accepted: 04/23/2024] [Indexed: 04/28/2024] Open
Abstract
In medical applications-such as positron emission tomography (PET)-511 keV photons that experience Compton scattering are studied. We present a consistent framework based on quantum error-correction channels-intensively studied in quantum computing-to fully describe the quantum information-theoretic content of high energetic photons undergoing Compton scattering, characterized by the Klein-Nishina formula in unoriented matter. In this way, we can predict the expected spatial distribution of two or more, pure or mixed, polarization entangled or separable photons. This framework allows us to characterize the accessible and inaccessible information for different parameter ranges. It also answers the question of how to describe successive multi-photon scattering. In addition our formalism provides a complete framework for dealing with single and all multi-partite errors that can occur in the propagation, providing the basis for modeling future dedicated experiments that will then have applications in medicine, such as reducing errors in PET imaging or exploring possibilities for quantum-based diagnostic indicators.
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Affiliation(s)
- B C Hiesmayr
- University of Vienna, Faculty of Physics, Währingerstrasse 17, 1090, Vienna, Austria.
| | - W Krzemień
- High Energy Physics Division, National Centre for Nuclear Research, Andrzeja Soltana 7, 05-400, Otwock, Swierk, Poland
| | - M Bała
- Department of Complex Systems, National Centre for Nuclear Research, Andrzeja Soltana 7, 05-400, Otwock, Swierk, Poland
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10
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Lachance-Quirion D, Lemonde MA, Simoneau JO, St-Jean L, Lemieux P, Turcotte S, Wright W, Lacroix A, Fréchette-Viens J, Shillito R, Hopfmueller F, Tremblay M, Frattini NE, Camirand Lemyre J, St-Jean P. Autonomous Quantum Error Correction of Gottesman-Kitaev-Preskill States. PHYSICAL REVIEW LETTERS 2024; 132:150607. [PMID: 38682990 DOI: 10.1103/physrevlett.132.150607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2023] [Accepted: 03/11/2024] [Indexed: 05/01/2024]
Abstract
The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum error correction of GKP states based on reservoir engineering of a superconducting device. Error correction is made fully autonomous through an unconditional reset of an auxiliary transmon qubit. We show that the lifetime of the logical qubit is increased from quantum error correction, therefore reaching the point at which more errors are corrected than generated.
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Affiliation(s)
| | | | | | | | | | | | - Wyatt Wright
- Nord Quantique, Sherbrooke, Québec J1J 2E2, Canada
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11
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Jones JA. Controlling NMR spin systems for quantum computation. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2024; 140-141:49-85. [PMID: 38705636 DOI: 10.1016/j.pnmrs.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 02/05/2024] [Indexed: 05/07/2024]
Abstract
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.
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Affiliation(s)
- Jonathan A Jones
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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12
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Koczor B, Morton JJL, Benjamin SC. Probabilistic Interpolation of Quantum Rotation Angles. PHYSICAL REVIEW LETTERS 2024; 132:130602. [PMID: 38613262 DOI: 10.1103/physrevlett.132.130602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 02/15/2024] [Indexed: 04/14/2024]
Abstract
Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2^{B} possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher B can greatly complexify hardware. Here, we explore an alternative: probabilistic angle interpolation (PAI). This effectively implements any desired, continuously parametrized rotation by randomly choosing one of three discretized gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that (a) the approach is optimal in the sense that PAI achieves the least possible overhead and (b) the overhead is remarkably modest even with thousands of parametrized gates and only seven bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even 5-6 bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late noisy intermediate-scale quantum era hardware, no more than nine bits will be necessary.
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Affiliation(s)
- Bálint Koczor
- Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - John J L Morton
- Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, United Kingdom
| | - Simon C Benjamin
- Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
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13
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Mi X, Michailidis AA, Shabani S, Miao KC, Klimov PV, Lloyd J, Rosenberg E, Acharya R, Aleiner I, Andersen TI, Ansmann M, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Bengtsson A, Bortoli G, Bourassa A, Bovaird J, Brill L, Broughton M, Buckley BB, Buell DA, Burger T, Burkett B, Bushnell N, Chen Z, Chiaro B, Chik D, Chou C, Cogan J, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Dau AG, Debroy DM, Del Toro Barba A, Demura S, Di Paolo A, Drozdov IK, Dunsworth A, Erickson C, Faoro L, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, Genois É, Giang W, Gidney C, Gilboa D, Giustina M, Gosula R, Gross JA, Habegger S, Hamilton MC, Hansen M, Harrigan MP, Harrington SD, Heu P, Hoffmann MR, Hong S, Huang T, Huff A, Huggins WJ, Ioffe LB, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Juhas P, Kafri D, Kechedzhi K, Khattar T, Khezri M, Kieferová M, Kim S, Kitaev A, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lensky YD, Lester BJ, Lill AT, Liu W, Locharla A, Malone FD, Martin O, McClean JR, McEwen M, Mieszala A, Montazeri S, Morvan A, Movassagh R, Mruczkiewicz W, Neeley M, Neill C, Nersisyan A, Newman M, Ng JH, Nguyen A, Nguyen M, Niu MY, O'Brien TE, Opremcak A, Petukhov A, Potter R, Pryadko LP, Quintana C, Rocque C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schurkus HF, Schuster C, Shearn MJ, Shorter A, Shutty N, Shvarts V, Skruzny J, Smith WC, Somma R, Sterling G, Strain D, Szalay M, Torres A, Vidal G, Villalonga B, Heidweiller CV, White T, Woo BWK, Xing C, Yao ZJ, Yeh P, Yoo J, Young G, Zalcman A, Zhang Y, Zhu N, Zobrist N, Neven H, Babbush R, Bacon D, Boixo S, Hilton J, Lucero E, Megrant A, Kelly J, Chen Y, Roushan P, Smelyanskiy V, Abanin DA. Stable quantum-correlated many-body states through engineered dissipation. Science 2024; 383:1332-1337. [PMID: 38513021 DOI: 10.1126/science.adh9932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 02/13/2024] [Indexed: 03/23/2024]
Abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Affiliation(s)
- X Mi
- Google Research, Mountain View, CA, USA
| | - A A Michailidis
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - S Shabani
- Google Research, Mountain View, CA, USA
| | - K C Miao
- Google Research, Mountain View, CA, USA
| | | | - J Lloyd
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | | | - R Acharya
- Google Research, Mountain View, CA, USA
| | - I Aleiner
- Google Research, Mountain View, CA, USA
| | | | - M Ansmann
- Google Research, Mountain View, CA, USA
| | - F Arute
- Google Research, Mountain View, CA, USA
| | - K Arya
- Google Research, Mountain View, CA, USA
| | - A Asfaw
- Google Research, Mountain View, CA, USA
| | - J Atalaya
- Google Research, Mountain View, CA, USA
| | - J C Bardin
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | | | - G Bortoli
- Google Research, Mountain View, CA, USA
| | | | - J Bovaird
- Google Research, Mountain View, CA, USA
| | - L Brill
- Google Research, Mountain View, CA, USA
| | | | | | - D A Buell
- Google Research, Mountain View, CA, USA
| | - T Burger
- Google Research, Mountain View, CA, USA
| | - B Burkett
- Google Research, Mountain View, CA, USA
| | | | - Z Chen
- Google Research, Mountain View, CA, USA
| | - B Chiaro
- Google Research, Mountain View, CA, USA
| | - D Chik
- Google Research, Mountain View, CA, USA
| | - C Chou
- Google Research, Mountain View, CA, USA
| | - J Cogan
- Google Research, Mountain View, CA, USA
| | - R Collins
- Google Research, Mountain View, CA, USA
| | - P Conner
- Google Research, Mountain View, CA, USA
| | | | - A L Crook
- Google Research, Mountain View, CA, USA
| | - B Curtin
- Google Research, Mountain View, CA, USA
| | - A G Dau
- Google Research, Mountain View, CA, USA
| | | | | | - S Demura
- Google Research, Mountain View, CA, USA
| | | | | | | | | | - L Faoro
- Google Research, Mountain View, CA, USA
| | - E Farhi
- Google Research, Mountain View, CA, USA
| | - R Fatemi
- Google Research, Mountain View, CA, USA
| | | | | | - E Forati
- Google Research, Mountain View, CA, USA
| | | | - B Foxen
- Google Research, Mountain View, CA, USA
| | - É Genois
- Google Research, Mountain View, CA, USA
| | - W Giang
- Google Research, Mountain View, CA, USA
| | - C Gidney
- Google Research, Mountain View, CA, USA
| | - D Gilboa
- Google Research, Mountain View, CA, USA
| | | | - R Gosula
- Google Research, Mountain View, CA, USA
| | - J A Gross
- Google Research, Mountain View, CA, USA
| | | | - M C Hamilton
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, USA
| | - M Hansen
- Google Research, Mountain View, CA, USA
| | | | | | - P Heu
- Google Research, Mountain View, CA, USA
| | | | - S Hong
- Google Research, Mountain View, CA, USA
| | - T Huang
- Google Research, Mountain View, CA, USA
| | - A Huff
- Google Research, Mountain View, CA, USA
| | | | - L B Ioffe
- Google Research, Mountain View, CA, USA
| | | | - J Iveland
- Google Research, Mountain View, CA, USA
| | - E Jeffrey
- Google Research, Mountain View, CA, USA
| | - Z Jiang
- Google Research, Mountain View, CA, USA
| | - C Jones
- Google Research, Mountain View, CA, USA
| | - P Juhas
- Google Research, Mountain View, CA, USA
| | - D Kafri
- Google Research, Mountain View, CA, USA
| | | | - T Khattar
- Google Research, Mountain View, CA, USA
| | - M Khezri
- Google Research, Mountain View, CA, USA
| | - M Kieferová
- Google Research, Mountain View, CA, USA
- Centre for Quantum Software and Information (QSI), Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia
| | - S Kim
- Google Research, Mountain View, CA, USA
| | - A Kitaev
- Google Research, Mountain View, CA, USA
| | - A R Klots
- Google Research, Mountain View, CA, USA
| | - A N Korotkov
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | | | - P Laptev
- Google Research, Mountain View, CA, USA
| | - K-M Lau
- Google Research, Mountain View, CA, USA
| | - L Laws
- Google Research, Mountain View, CA, USA
| | - J Lee
- Google Research, Mountain View, CA, USA
- Department of Chemistry, Columbia University, New York, NY, USA
| | - K W Lee
- Google Research, Mountain View, CA, USA
| | | | | | - A T Lill
- Google Research, Mountain View, CA, USA
| | - W Liu
- Google Research, Mountain View, CA, USA
| | | | | | - O Martin
- Google Research, Mountain View, CA, USA
| | | | - M McEwen
- Google Research, Mountain View, CA, USA
| | | | | | - A Morvan
- Google Research, Mountain View, CA, USA
| | | | | | - M Neeley
- Google Research, Mountain View, CA, USA
| | - C Neill
- Google Research, Mountain View, CA, USA
| | | | - M Newman
- Google Research, Mountain View, CA, USA
| | - J H Ng
- Google Research, Mountain View, CA, USA
| | - A Nguyen
- Google Research, Mountain View, CA, USA
| | - M Nguyen
- Google Research, Mountain View, CA, USA
| | - M Y Niu
- Google Research, Mountain View, CA, USA
| | | | | | | | - R Potter
- Google Research, Mountain View, CA, USA
| | - L P Pryadko
- Google Research, Mountain View, CA, USA
- Department of Physics and Astronomy, University of California, Riverside, CA, USA
| | | | - C Rocque
- Google Research, Mountain View, CA, USA
| | - N C Rubin
- Google Research, Mountain View, CA, USA
| | - N Saei
- Google Research, Mountain View, CA, USA
| | - D Sank
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - A Shorter
- Google Research, Mountain View, CA, USA
| | - N Shutty
- Google Research, Mountain View, CA, USA
| | - V Shvarts
- Google Research, Mountain View, CA, USA
| | - J Skruzny
- Google Research, Mountain View, CA, USA
| | - W C Smith
- Google Research, Mountain View, CA, USA
| | - R Somma
- Google Research, Mountain View, CA, USA
| | | | - D Strain
- Google Research, Mountain View, CA, USA
| | - M Szalay
- Google Research, Mountain View, CA, USA
| | - A Torres
- Google Research, Mountain View, CA, USA
| | - G Vidal
- Google Research, Mountain View, CA, USA
| | | | | | - T White
- Google Research, Mountain View, CA, USA
| | - B W K Woo
- Google Research, Mountain View, CA, USA
| | - C Xing
- Google Research, Mountain View, CA, USA
| | - Z J Yao
- Google Research, Mountain View, CA, USA
| | - P Yeh
- Google Research, Mountain View, CA, USA
| | - J Yoo
- Google Research, Mountain View, CA, USA
| | - G Young
- Google Research, Mountain View, CA, USA
| | - A Zalcman
- Google Research, Mountain View, CA, USA
| | - Y Zhang
- Google Research, Mountain View, CA, USA
| | - N Zhu
- Google Research, Mountain View, CA, USA
| | - N Zobrist
- Google Research, Mountain View, CA, USA
| | - H Neven
- Google Research, Mountain View, CA, USA
| | - R Babbush
- Google Research, Mountain View, CA, USA
| | - D Bacon
- Google Research, Mountain View, CA, USA
| | - S Boixo
- Google Research, Mountain View, CA, USA
| | - J Hilton
- Google Research, Mountain View, CA, USA
| | - E Lucero
- Google Research, Mountain View, CA, USA
| | - A Megrant
- Google Research, Mountain View, CA, USA
| | - J Kelly
- Google Research, Mountain View, CA, USA
| | - Y Chen
- Google Research, Mountain View, CA, USA
| | - P Roushan
- Google Research, Mountain View, CA, USA
| | | | - D A Abanin
- Google Research, Mountain View, CA, USA
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
- Department of Physics, Princeton University, Princeton, NJ, USA
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14
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Eriksson AM, Sépulcre T, Kervinen M, Hillmann T, Kudra M, Dupouy S, Lu Y, Khanahmadi M, Yang J, Castillo-Moreno C, Delsing P, Gasparinetti S. Universal control of a bosonic mode via drive-activated native cubic interactions. Nat Commun 2024; 15:2512. [PMID: 38509084 PMCID: PMC10954688 DOI: 10.1038/s41467-024-46507-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 02/29/2024] [Indexed: 03/22/2024] Open
Abstract
Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which relies on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of polynomial quantum computing, in the continuous-variables notion originally introduced by Lloyd and Braunstein.
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Affiliation(s)
- Axel M Eriksson
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden.
| | - Théo Sépulcre
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Mikael Kervinen
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Timo Hillmann
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Marina Kudra
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Simon Dupouy
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Yong Lu
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
- Physikalisches Institut, University of Stuttgart, 70569, Stuttgart, Germany
| | - Maryam Khanahmadi
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Jiaying Yang
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Claudia Castillo-Moreno
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Per Delsing
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden
| | - Simone Gasparinetti
- Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96, Gothenburg, Sweden.
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15
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Chae E, Choi J, Kim J. An elementary review on basic principles and developments of qubits for quantum computing. NANO CONVERGENCE 2024; 11:11. [PMID: 38498068 PMCID: PMC10948723 DOI: 10.1186/s40580-024-00418-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 03/04/2024] [Indexed: 03/19/2024]
Abstract
An elementary review on principles of qubits and their prospects for quantum computing is provided. Due to its rapid development, quantum computing has attracted considerable attention as a core technology for the next generation and has demonstrated its potential in simulations of exotic materials, molecular structures, and theoretical computer science. To achieve fully error-corrected quantum computers, building a logical qubit from multiple physical qubits is crucial. The number of physical qubits needed depends on their error rates, making error reduction in physical qubits vital. Numerous efforts to reduce errors are ongoing in both existing and emerging quantum systems. Here, the principle and development of qubits, as well as the current status of the field, are reviewed to provide information to researchers from various fields and give insights into this promising technology.
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Affiliation(s)
- Eunmi Chae
- Department of Physics, Korea University, Seoul , 02841, Republic of Korea.
| | - Joonhee Choi
- Department of Electrical Engineering, Stanford University, Stanford, CA, 94305, USA.
| | - Junki Kim
- SKKU Advanced Institute of Nanotechnology (SAINT) & Department of Nano Science and Technology, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
- Department of Nano Engineering, Sungkyunkwan University, Suwon, 16419, Republic of Korea.
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16
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Klimov PV, Bengtsson A, Quintana C, Bourassa A, Hong S, Dunsworth A, Satzinger KJ, Livingston WP, Sivak V, Niu MY, Andersen TI, Zhang Y, Chik D, Chen Z, Neill C, Erickson C, Grajales Dau A, Megrant A, Roushan P, Korotkov AN, Kelly J, Smelyanskiy V, Chen Y, Neven H. Optimizing quantum gates towards the scale of logical qubits. Nat Commun 2024; 15:2442. [PMID: 38499541 PMCID: PMC10948820 DOI: 10.1038/s41467-024-46623-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Accepted: 03/04/2024] [Indexed: 03/20/2024] Open
Abstract
A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.
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Affiliation(s)
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Alexander N Korotkov
- Google AI, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | - Yu Chen
- Google AI, Mountain View, CA, USA
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17
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Goel S, Reynolds M, Girling M, McCutcheon W, Leedumrongwatthanakun S, Srivastav V, Jennings D, Malik M, Pachos JK. Unveiling the Non-Abelian Statistics of D(S_{3}) Anyons Using a Classical Photonic Simulator. PHYSICAL REVIEW LETTERS 2024; 132:110601. [PMID: 38563919 DOI: 10.1103/physrevlett.132.110601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 01/16/2024] [Accepted: 02/22/2024] [Indexed: 04/04/2024]
Abstract
Simulators can realize novel phenomena by separating them from the complexities of a full physical implementation. Here, we put forward a scheme that can simulate the exotic statistics of D(S_{3}) non-Abelian anyons with minimal resources. The qudit lattice representation of this planar code supports local encoding of D(S_{3}) anyons. As a proof-of-principle demonstration, we employ a classical photonic simulator to encode a single qutrit and manipulate it to perform the fusion and braiding properties of non-Abelian D(S_{3}) anyons. The photonic technology allows us to perform the required nonunitary operations with much higher fidelity than what can be achieved with current quantum computers. Our approach can be directly generalized to larger systems or to different anyonic models, thus enabling advances in the exploration of quantum error correction and fundamental physics alike.
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Affiliation(s)
- Suraj Goel
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Matthew Reynolds
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Matthew Girling
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - Will McCutcheon
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | | | - Vatshal Srivastav
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - David Jennings
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Mehul Malik
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Jiannis K Pachos
- School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom
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18
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Bengtsson A, Opremcak A, Khezri M, Sank D, Bourassa A, Satzinger KJ, Hong S, Erickson C, Lester BJ, Miao KC, Korotkov AN, Kelly J, Chen Z, Klimov PV. Model-Based Optimization of Superconducting Qubit Readout. PHYSICAL REVIEW LETTERS 2024; 132:100603. [PMID: 38518348 DOI: 10.1103/physrevlett.132.100603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 02/02/2024] [Indexed: 03/24/2024]
Abstract
Measurement is an essential component of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate model-based readout optimization achieving low measurement errors while avoiding detrimental side effects. For simultaneous and midcircuit measurements across 17 qubits, we observe 1.5% error per qubit with a 500 ns end-to-end duration and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions achieving a leakage rate limited by natural heating. This technique can scale to hundreds of qubits and be used to enhance the performance of error-correcting codes and near-term applications.
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Affiliation(s)
| | - Alex Opremcak
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | | | - Daniel Sank
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | | | | | - Sabrina Hong
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | | | | | - Kevin C Miao
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | - Alexander N Korotkov
- Google Quantum AI, Santa Barbara, 93111 California, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, 92521 California, USA
| | - Julian Kelly
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | - Zijun Chen
- Google Quantum AI, Santa Barbara, 93111 California, USA
| | - Paul V Klimov
- Google Quantum AI, Santa Barbara, 93111 California, USA
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19
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Bravyi S, Cross AW, Gambetta JM, Maslov D, Rall P, Yoder TJ. High-threshold and low-overhead fault-tolerant quantum memory. Nature 2024; 627:778-782. [PMID: 38538939 PMCID: PMC10972743 DOI: 10.1038/s41586-024-07107-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2023] [Accepted: 01/23/2024] [Indexed: 04/01/2024]
Abstract
The accumulation of physical errors1-3 prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction4 promises a solution by encoding k logical qubits onto a larger number n of physical qubits, such that the physical errors are suppressed enough to allow running a desired computation with tolerable fidelity. Quantum error correction becomes practically realizable once the physical error rate is below a threshold value that depends on the choice of quantum code, syndrome measurement circuit and decoding algorithm5. We present an end-to-end quantum error correction protocol that implements fault-tolerant memory on the basis of a family of low-density parity-check codes6. Our approach achieves an error threshold of 0.7% for the standard circuit-based noise model, on par with the surface code7-10 that for 20 years was the leading code in terms of error threshold. The syndrome measurement cycle for a length-n code in our family requires n ancillary qubits and a depth-8 circuit with CNOT gates, qubit initializations and measurements. The required qubit connectivity is a degree-6 graph composed of two edge-disjoint planar subgraphs. In particular, we show that 12 logical qubits can be preserved for nearly 1 million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of 0.1%, whereas the surface code would require nearly 3,000 physical qubits to achieve said performance. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.
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Affiliation(s)
- Sergey Bravyi
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Andrew W Cross
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Jay M Gambetta
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
| | - Dmitri Maslov
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA.
| | - Patrick Rall
- IBM Quantum, MIT-IBM Watson AI Laboratory, Cambridge, MA, USA
| | - Theodore J Yoder
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
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20
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Malnou M, Larson TFQ, Teufel JD, Lecocq F, Aumentado J. Low-noise cryogenic microwave amplifier characterization with a calibrated noise source. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2024; 95:034703. [PMID: 38451145 DOI: 10.1063/5.0193591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Accepted: 02/06/2024] [Indexed: 03/08/2024]
Abstract
Parametric amplifiers have become a workhorse in superconducting quantum computing; however, research and development of these devices has been hampered by inconsistent and, sometimes, misleading noise performance characterization methodologies. The concepts behind noise characterization are deceptively simple, and there are many places where one can make mistakes, either in measurement or in interpretation and analysis. In this article, we cover the basics of noise performance characterization and the special problems it presents in parametric amplifiers with limited power handling capability. We illustrate the issues with three specific examples: a high-electron mobility transistor amplifier, a Josephson traveling-wave parametric amplifier, and a Josephson parametric amplifier. We emphasize the use of a 50-Ω shot noise tunnel junction (SNTJ) as a broadband noise source, demonstrating its utility for cryogenic amplifier amplifications. These practical examples highlight the role of loss as well as the additional parametric amplifier "idler" input mode.
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Affiliation(s)
- M Malnou
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - T F Q Larson
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - J D Teufel
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - F Lecocq
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - J Aumentado
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
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21
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Chiesa A, Santini P, Garlatti E, Luis F, Carretta S. Molecular nanomagnets: a viable path toward quantum information processing? REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2024; 87:034501. [PMID: 38314645 DOI: 10.1088/1361-6633/ad1f81] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 01/17/2024] [Indexed: 02/06/2024]
Abstract
Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.
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Affiliation(s)
- A Chiesa
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - P Santini
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - E Garlatti
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
| | - F Luis
- Instituto de Nanociencia y Materiales de Aragon (INMA), CSIC, Universidad de Zaragoza, Zaragoza, Spain
- Departamento de Fısica de la Materia Condensada, Universidad de Zaragoza, Zaragoza, Spain
| | - S Carretta
- Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, I-43124 Parma, Italy
- INFN-Sezione di Milano-Bicocca, Gruppo Collegato di Parma, 43124 Parma, Italy
- UdR Parma, INSTM, I-43124 Parma, Italy
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22
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Terhal BM. Mobile atoms enable efficient computation with logical qubits. Nature 2024; 626:36-38. [PMID: 38287183 DOI: 10.1038/d41586-024-00075-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2024]
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23
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Bluvstein D, Evered SJ, Geim AA, Li SH, Zhou H, Manovitz T, Ebadi S, Cain M, Kalinowski M, Hangleiter D, Bonilla Ataides JP, Maskara N, Cong I, Gao X, Sales Rodriguez P, Karolyshyn T, Semeghini G, Gullans MJ, Greiner M, Vuletić V, Lukin MD. Logical quantum processor based on reconfigurable atom arrays. Nature 2024; 626:58-65. [PMID: 38056497 PMCID: PMC10830422 DOI: 10.1038/s41586-023-06927-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2023] [Accepted: 12/01/2023] [Indexed: 12/08/2023]
Abstract
Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy2-4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18 with up to 48 logical qubits entangled with hypercube connectivity19 with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.
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Affiliation(s)
- Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Madelyn Cain
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Dominik Hangleiter
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | | | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Iris Cong
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Xun Gao
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | | | - Giulia Semeghini
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Michael J Gullans
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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24
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Niu J, Li Y, Zhang L, Zhang J, Chu J, Huang J, Huang W, Nie L, Qiu J, Sun X, Tao Z, Wei W, Zhang J, Zhou Y, Chen Y, Hu L, Liu Y, Liu S, Zhong Y, Lu D, Yu D. Demonstrating Path-Independent Anyonic Braiding on a Modular Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2024; 132:020601. [PMID: 38277590 DOI: 10.1103/physrevlett.132.020601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Revised: 11/22/2023] [Accepted: 12/01/2023] [Indexed: 01/28/2024]
Abstract
Anyons, exotic quasiparticles in two-dimensional space exhibiting nontrivial exchange statistics, play a crucial role in universal topological quantum computing. One notable proposal to manifest the fractional statistics of anyons is the toric code model; however, scaling up its size through quantum simulation poses a serious challenge because of its highly entangled ground state. In this Letter, we demonstrate that a modular superconducting quantum processor enables hardware-pragmatic implementation of the toric code model. Through in-parallel control across separate modules, we generate a 10-qubit toric code ground state in four steps and realize six distinct braiding paths to benchmark the performance of anyonic statistics. The path independence of the anyonic braiding statistics is verified by correlation measurements in an efficient and scalable fashion. Our modular approach, serving as a hardware embodiment of the toric code model, offers a promising avenue toward scalable simulation of topological phases, paving the way for quantum simulation in a distributed fashion.
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Affiliation(s)
- Jingjing Niu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Branch, Hefei National Laboratory, Shenzhen 518048, China
| | - Yishan Li
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Libo Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiajian Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Ji Chu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiaxiang Huang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Wenhui Huang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Lifu Nie
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiawei Qiu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xuandong Sun
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Ziyu Tao
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Weiwei Wei
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jiawei Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yuxuan Zhou
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yuanzhen Chen
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Ling Hu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yang Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Song Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Branch, Hefei National Laboratory, Shenzhen 518048, China
| | - Youpeng Zhong
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Branch, Hefei National Laboratory, Shenzhen 518048, China
| | - Dawei Lu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- International Quantum Academy, Shenzhen 518048, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Branch, Hefei National Laboratory, Shenzhen 518048, China
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
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25
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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26
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Shirizly L, Misguich G, Landa H. Dissipative Dynamics of Graph-State Stabilizers with Superconducting Qubits. PHYSICAL REVIEW LETTERS 2024; 132:010601. [PMID: 38242658 DOI: 10.1103/physrevlett.132.010601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 11/21/2023] [Accepted: 11/29/2023] [Indexed: 01/21/2024]
Abstract
We study experimentally and numerically the noisy evolution of multipartite entangled states, focusing on superconducting qubit devices accessible via the cloud. We find that a valid modeling of the dynamics requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We introduce an approach modeling the charge-parity splitting using an extended Markovian environment. This approach is numerically scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Probing the continuous-time dynamics of increasingly larger and more complex initial states with up to 12 coupled qubits in a ring-graph state, we obtain a good agreement of the experiments and simulations. We show that the underlying many-body dynamics generate decays and revivals of stabilizers, which are used extensively in the context of quantum error correction. Furthermore, we demonstrate the mitigation of 2-qubit coherent interactions (crosstalk) using tailored dynamical decoupling sequences. Our noise model and the numerical approach can be valuable to advance the understanding of error correction and mitigation and invite further investigations of their dynamics.
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Affiliation(s)
- Liran Shirizly
- IBM Quantum, IBM Research - Israel, Haifa University Campus, Mount Carmel, Haifa 31905, Israel
| | - Grégoire Misguich
- Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France
| | - Haggai Landa
- IBM Quantum, IBM Research - Israel, Haifa University Campus, Mount Carmel, Haifa 31905, Israel
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27
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Waintal X. The quantum house of cards. Proc Natl Acad Sci U S A 2024; 121:e2313269120. [PMID: 38147549 PMCID: PMC10769848 DOI: 10.1073/pnas.2313269120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2023] Open
Abstract
Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.
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Affiliation(s)
- Xavier Waintal
- Université Grenoble Alpes, Quantum Photonics, Electronics and Engineering Laboratory, Alternative Energies and Atomic Energy Commission, Institut d’ingénierie et de management, Interdisciplinary Research Institute of Grenoble, Grenoble38000, France
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28
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Gupta RS, Sundaresan N, Alexander T, Wood CJ, Merkel ST, Healy MB, Hillenbrand M, Jochym-O'Connor T, Wootton JR, Yoder TJ, Cross AW, Takita M, Brown BJ. Encoding a magic state with beyond break-even fidelity. Nature 2024; 625:259-263. [PMID: 38200302 PMCID: PMC10781628 DOI: 10.1038/s41586-023-06846-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 11/07/2023] [Indexed: 01/12/2024]
Abstract
To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from noise1-8. We can complete a universal set of logic gates by producing special resources called magic states9-11. It is therefore important to produce high-fidelity magic states to conduct algorithms while introducing a minimal amount of noise to the computation. Here we propose and implement a scheme to prepare a magic state on a superconducting qubit array using error correction. We find that our scheme produces better magic states than those that can be prepared using the individual qubits of the device. This demonstrates a fundamental principle of fault-tolerant quantum computing12, namely, that we can use error correction to improve the quality of logic gates with noisy qubits. Moreover, we show that the yield of magic states can be increased using adaptive circuits, in which the circuit elements are changed depending on the outcome of mid-circuit measurements. This demonstrates an essential capability needed for many error-correction subroutines. We believe that our prototype will be invaluable in the future as it can reduce the number of physical qubits needed to produce high-fidelity magic states in large-scale quantum-computing architectures.
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Affiliation(s)
- Riddhi S Gupta
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
- IBM Quantum, Almaden Research Center, San Jose, CA, USA
| | | | - Thomas Alexander
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | | | - Seth T Merkel
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | - Michael B Healy
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | | | - Tomas Jochym-O'Connor
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
- IBM Quantum, Almaden Research Center, San Jose, CA, USA
| | | | - Theodore J Yoder
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | - Andrew W Cross
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | - Maika Takita
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA
| | - Benjamin J Brown
- IBM Quantum, T. J. Watson Research Center, Yorktown Heights, NY, USA.
- IBM Denmark, Brøndby, Denmark.
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29
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Wudarski F, Zhang Y, Dykman MI. Nonergodic Measurements of Qubit Frequency Noise. PHYSICAL REVIEW LETTERS 2023; 131:230201. [PMID: 38134761 DOI: 10.1103/physrevlett.131.230201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Revised: 09/26/2023] [Accepted: 11/13/2023] [Indexed: 12/24/2023]
Abstract
Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.
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Affiliation(s)
- Filip Wudarski
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
| | - Yaxing Zhang
- Google Quantum AI, Santa Barbara, California 93111, USA
| | - M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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30
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Tejedor I, Urtizberea A, Natividad E, Martínez JI, Gascón I, Roubeau O. Dilute Gd hydroxycarbonate particles for localized spin qubit integration. MATERIALS HORIZONS 2023; 10:5214-5222. [PMID: 37725390 DOI: 10.1039/d3mh01201h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/21/2023]
Abstract
Molecular spins are considered as the quantum hardware to build hybrid quantum processors in which coupling to superconducting devices would provide the means to implement the necessary coherent manipulations. As an alternative to large magnetically-dilute crystals or concentrated nano-scale deposits of paramagnetic molecules that have been studied so far, the use of pre-formed sub-micronic spherical particles of a doped Gd@Y hydroxycarbonate is evaluated here. Particles with an adjustable number of spin carriers are prepared through the control of both particle size and doping. Bulk magnetic properties and continuous wave and time-domain-EPR spectroscopy show that the Gd spins in these particles are potential qubits with robust quantum coherence. Monolayers of densely-packed particles are then formed interfacially and transferred successfully to the surface of Nb superconducting resonators. Alternatively, these particles are disposed at controlled localizations as isolated groups of a few particles through Dip-Pen Nanolithography using colloidal organic dispersions as ink. Altogether, this study offers new material and methodologies relevant to the development of viable hybrid quantum processors.
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Affiliation(s)
- Inés Tejedor
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Plaza San Francisco s/n, 50009 Zaragoza, Spain
| | - Ainhoa Urtizberea
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Campus Río Ebro, María de Luna 3, 50018 Zaragoza, Spain.
| | - Eva Natividad
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Campus Río Ebro, María de Luna 3, 50018 Zaragoza, Spain.
| | - Jesús I Martínez
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Plaza San Francisco s/n, 50009 Zaragoza, Spain
| | - Ignacio Gascón
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Plaza San Francisco s/n, 50009 Zaragoza, Spain
| | - Olivier Roubeau
- Instituto de Nanociencia y Materiales de Aragón (INMA), CSIC and Universidad de Zaragoza, Plaza San Francisco s/n, 50009 Zaragoza, Spain
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31
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Teoh JD, Winkel P, Babla HK, Chapman BJ, Claes J, de Graaf SJ, Garmon JWO, Kalfus WD, Lu Y, Maiti A, Sahay K, Thakur N, Tsunoda T, Xue SH, Frunzio L, Girvin SM, Puri S, Schoelkopf RJ. Dual-rail encoding with superconducting cavities. Proc Natl Acad Sci U S A 2023; 120:e2221736120. [PMID: 37801473 PMCID: PMC10576063 DOI: 10.1073/pnas.2221736120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Accepted: 08/07/2023] [Indexed: 10/08/2023] Open
Abstract
The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.
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Affiliation(s)
- James D. Teoh
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Patrick Winkel
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Harshvardhan K. Babla
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Benjamin J. Chapman
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Jahan Claes
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Stijn J. de Graaf
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - John W. O. Garmon
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - William D. Kalfus
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Yao Lu
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Aniket Maiti
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Kaavya Sahay
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Neel Thakur
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Takahiro Tsunoda
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Sophia H. Xue
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Luigi Frunzio
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Steven M. Girvin
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Shruti Puri
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
| | - Robert J. Schoelkopf
- Department of Applied Physics, Yale University, New Haven, CT06511
- Department of Physics, Yale University, New Haven, CT06511
- Yale Quantum Institute, Yale University, New Haven, CT06511
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32
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Evered SJ, Bluvstein D, Kalinowski M, Ebadi S, Manovitz T, Zhou H, Li SH, Geim AA, Wang TT, Maskara N, Levine H, Semeghini G, Greiner M, Vuletić V, Lukin MD. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 2023; 622:268-272. [PMID: 37821591 PMCID: PMC10567572 DOI: 10.1038/s41586-023-06481-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/25/2023] [Indexed: 10/13/2023]
Abstract
The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.
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Affiliation(s)
- Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA
- AWS Center for Quantum Computing, Pasadena, CA, USA
| | - Giulia Semeghini
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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33
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Jin Z, Li S, Wang X, Liang F, Peng CZ. A co-simulation of superconducting qubit and control electronics for quantum computing. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2023; 94:104707. [PMID: 37815424 DOI: 10.1063/5.0163725] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 09/18/2023] [Indexed: 10/11/2023]
Abstract
As the number of qubits in quantum computing increases, the scalability of existing qubit circuit structures and control systems may become insufficient for large-scale expansion and high-fidelity control. To address this challenge, we propose a behavioral-level model of a superconducting qubit and its control electronics, followed by a co-simulation to evaluate their performance. In this paper, we present the modeling process, simulation procedure, and resulting design specifications for the qubit control system. Our co-simulation approach utilizes MATLAB and Simulink, enabling us to derive critical circuit design specifications, such as the required Digital-to-Analog Converter (DAC) resolution, which should be 8 bits or higher, to achieve high-fidelity control. By taking into account factors such as DAC sampling rates, integral and differential nonlinearities, and filter characteristics, we optimize the control system for efficient and accurate qubit manipulation. Our model and simulation approach offer a promising solution to the scalability challenges in quantum computing, providing valuable insights for the design of large-scale superconducting quantum computing systems.
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Affiliation(s)
- Zhanhong Jin
- Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shaowei Li
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xinzhe Wang
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Futian Liang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Cheng-Zhi Peng
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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34
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Liu FM, Wang C, Chen MC, Chen H, Li SW, Shang ZX, Ying C, Wang JW, Huo YH, Peng CZ, Zhu X, Lu CY, Pan JW. Quantum computer-aided design for advanced superconducting qubit: Plasmonium. Sci Bull (Beijing) 2023; 68:1625-1631. [PMID: 37453825 DOI: 10.1016/j.scib.2023.06.030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Revised: 05/14/2023] [Accepted: 06/25/2023] [Indexed: 07/18/2023]
Abstract
Complex quantum electronic circuits can be used to design noise-protected qubits, but their complexity may exceed the capabilities of classical simulation. In such cases, quantum computers are necessary for efficient simulation. In this work, we demonstrate the use of variational quantum computing on a transmon-based quantum processor to simulate a superconducting quantum electronic circuit and design a new type of qubit called "Plasmonium", which operates in the plasmon-transition regime. The fabricated Plasmonium qubits show a high two-qubit gate fidelity of 99.58(3)%, as well as a smaller physical size and larger anharmonicity compared to transmon qubits. These properties make Plasmonium a promising candidate for scaling up multi-qubit devices. Our results demonstrate the potential of using quantum computers to aid in the design of advanced quantum processors.
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Affiliation(s)
- Feng-Ming Liu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Can Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ming-Cheng Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China.
| | - He Chen
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Shao-Wei Li
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Zhong-Xia Shang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chong Ying
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wen Wang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yong-Heng Huo
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cheng-Zhi Peng
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiaobo Zhu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chao-Yang Lu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China.
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; Shanghai Branch CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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35
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Venn F, Behrends J, Béri B. Coherent-Error Threshold for Surface Codes from Majorana Delocalization. PHYSICAL REVIEW LETTERS 2023; 131:060603. [PMID: 37625066 DOI: 10.1103/physrevlett.131.060603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Accepted: 06/12/2023] [Indexed: 08/27/2023]
Abstract
Statistical mechanics mappings provide key insights on quantum error correction. However, existing mappings assume incoherent noise, thus ignoring coherent errors due to, e.g., spurious gate rotations. We map the surface code with coherent errors, taken as X or Z rotations (replacing bit or phase flips), to a two-dimensional (2D) Ising model with complex couplings, and further to a 2D Majorana scattering network. Our mappings reveal both commonalities and qualitative differences in correcting coherent and incoherent errors. For both, the error-correcting phase maps, as we explicitly show by linking 2D networks to 1D fermions, to a Z_{2}-nontrivial 2D insulator. However, beyond a rotation angle ϕ_{th}, instead of a Z_{2}-trivial insulator as for incoherent errors, coherent errors map to a Majorana metal. This ϕ_{th} is the theoretically achievable storage threshold. We numerically find ϕ_{th}≈0.14π. The corresponding bit-flip rate sin^{2}(ϕ_{th})≈0.18 exceeds the known incoherent threshold p_{th}≈0.11.
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Affiliation(s)
- Florian Venn
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
| | - Jan Behrends
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - Benjamin Béri
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, United Kingdom
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
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36
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Chiappina P, Banker J, Meesala S, Lake D, Wood S, Painter O. Design of an ultra-low mode volume piezo-optomechanical quantum transducer. OPTICS EXPRESS 2023; 31:22914-22927. [PMID: 37475390 DOI: 10.1364/oe.493532] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Accepted: 06/13/2023] [Indexed: 07/22/2023]
Abstract
Coherent transduction of quantum states from the microwave to the optical domain can play a key role in quantum networking and distributed quantum computing. We present the design of a piezo-optomechanical device formed in a hybrid lithium niobate on silicon platform, that is suitable for microwave-to-optical quantum transduction. Our design is based on acoustic hybridization of an ultra-low mode volume piezoacoustic cavity with an optomechanical crystal cavity. The strong piezoelectric nature of lithium niobate allows us to mediate transduction via an acoustic mode which only minimally interacts with the lithium niobate, and is predominantly silicon-like, with very low electrical and acoustic loss. We estimate that this transducer can realize an intrinsic conversion efficiency of up to 35% with <0.5 added noise quanta when resonantly coupled to a superconducting transmon qubit and operated in pulsed mode at 10 kHz repetition rate. The performance improvement gained in such hybrid lithium niobate-silicon transducers make them suitable for heralded entanglement of qubits between superconducting quantum processors connected by optical fiber links.
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37
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Li W, Allcock J, Cheng L, Zhang SX, Chen YQ, Mailoa JP, Shuai Z, Zhang S. TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era. J Chem Theory Comput 2023. [PMID: 37317520 DOI: 10.1021/acs.jctc.3c00319] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem's capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H2O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H2 molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.
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Affiliation(s)
- Weitang Li
- Tencent Quantum Lab, Shenzhen 518057, China
| | | | | | | | | | | | - Zhigang Shuai
- Department of Chemistry, Tsinghua University, Beijing, 100084, China
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, China
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38
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Ippoliti M, Li Y, Rakovszky T, Khemani V. Operator Relaxation and the Optimal Depth of Classical Shadows. PHYSICAL REVIEW LETTERS 2023; 130:230403. [PMID: 37354418 DOI: 10.1103/physrevlett.130.230403] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Accepted: 05/18/2023] [Indexed: 06/26/2023]
Abstract
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via "shallow shadows," a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. We show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing ("twirling") circuit-namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t∼log(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.
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Affiliation(s)
- Matteo Ippoliti
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Yaodong Li
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Tibor Rakovszky
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Vedika Khemani
- Department of Physics, Stanford University, Stanford, California 94305, USA
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39
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Domingo L, Carlo G, Borondo F. Taking advantage of noise in quantum reservoir computing. Sci Rep 2023; 13:8790. [PMID: 37258528 PMCID: PMC10232431 DOI: 10.1038/s41598-023-35461-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 05/18/2023] [Indexed: 06/02/2023] Open
Abstract
The biggest challenge that quantum computing and quantum machine learning are currently facing is the presence of noise in quantum devices. As a result, big efforts have been put into correcting or mitigating the induced errors. But, can these two fields benefit from noise? Surprisingly, we demonstrate that under some circumstances, quantum noise can be used to improve the performance of quantum reservoir computing, a prominent and recent quantum machine learning algorithm. Our results show that the amplitude damping noise can be beneficial to machine learning, while the depolarizing and phase damping noises should be prioritized for correction. This critical result sheds new light into the physical mechanisms underlying quantum devices, providing solid practical prescriptions for a successful implementation of quantum information processing in nowadays hardware.
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Affiliation(s)
- L Domingo
- Instituto de Ciencias Matemáticas (ICMAT), Campus de Cantoblanco; Nicolás Cabrera, 13-15, 28049, Madrid, Spain
- Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain
- Grupo de Sistemas ComplejosUniversidad Politécnica de Madrid, 28035, Madrid, Spain
| | - G Carlo
- Departamento de Física, Comisión Nacional de Energía Atómica, CONICET, Av. del Libertador 8250, 1429, Buenos Aires, Argentina
| | - F Borondo
- Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain.
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40
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Singh K, Bradley CE, Anand S, Ramesh V, White R, Bernien H. Mid-circuit correction of correlated phase errors using an array of spectator qubits. Science 2023:eade5337. [PMID: 37228222 DOI: 10.1126/science.ade5337] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 05/15/2023] [Indexed: 05/27/2023]
Abstract
Scaling up invariably error-prone quantum processors is a formidable challenge. Although quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting. In a complementary proposal, co-located, auxiliary 'spectator' qubits act as in-situ probes of noise, and enable real-time, coherent corrections of data qubit errors. We use an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. By combining in-sequence readout, data processing, and feed-forward operations, these correlated errors are suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms, and establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feed-forward, and coherent mid-circuit reloading of atomic qubits.
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Affiliation(s)
- K Singh
- Intelligence Community Postdoctoral Research Fellowship Program, Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
| | - C E Bradley
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
| | - S Anand
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
| | - V Ramesh
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - R White
- Department of Physics, University of Chicago, Chicago, IL 60637, USA
| | - H Bernien
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA
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41
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Wagner T, Kampermann H, Bruß D, Kliesch M. Learning Logical Pauli Noise in Quantum Error Correction. PHYSICAL REVIEW LETTERS 2023; 130:200601. [PMID: 37267535 DOI: 10.1103/physrevlett.130.200601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2022] [Accepted: 04/10/2023] [Indexed: 06/04/2023]
Abstract
The characterization of quantum devices is crucial for their practical implementation but can be costly in experimental effort and classical postprocessing. Therefore, it is desirable to measure only the information that is relevant for specific applications and develop protocols that require little additional effort. In this Letter, we focus on the characterization of quantum computers in the context of stabilizer quantum error correction. For arbitrary stabilizer codes, subsystem codes, and data syndrome codes, we prove that the logical error channel induced by Pauli noise can be estimated from syndrome data under minimal conditions. More precisely, for any such code, we show that the estimation is possible as long as the code can correct the noise.
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Affiliation(s)
- Thomas Wagner
- Institute for Theoretical Physics, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Hermann Kampermann
- Institute for Theoretical Physics, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Dagmar Bruß
- Institute for Theoretical Physics, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
| | - Martin Kliesch
- Institute for Theoretical Physics, Heinrich-Heine-University Düsseldorf, 40225 Düsseldorf, Germany
- Institute for Quantum-Inspired and Quantum Optimization, Hamburg University of Technology, 21079 Hamburg, Germany
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Chen Z, Sun L, Zou CL. Entering the error-corrected quantum era. Sci Bull (Beijing) 2023:S2095-9273(23)00293-1. [PMID: 37150630 DOI: 10.1016/j.scib.2023.04.039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Affiliation(s)
- Zijie Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Luyan Sun
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China; Hefei National Laboratory, Hefei 230088, China.
| | - Chang-Ling Zou
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China; Hefei National Laboratory, Hefei 230088, China.
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Giustina M. Superconducting qubits cover new distances. Nature 2023; 617:254-256. [PMID: 37165233 DOI: 10.1038/d41586-023-01488-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
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Castelvecchi D. Google's quantum computer hits key milestone by reducing errors. Nature 2023:10.1038/d41586-023-00536-w. [PMID: 36814025 DOI: 10.1038/d41586-023-00536-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
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