1
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Surface code for low-density qubit array. Sci Rep 2022; 12:12946. [PMID: 35902709 PMCID: PMC9334604 DOI: 10.1038/s41598-022-17090-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2022] [Accepted: 07/20/2022] [Indexed: 11/20/2022] Open
Abstract
Surface code is a promising candidate for the quantum error corrections needed for fault-tolerant quantum computations because it can operate on a two-dimensional grid of qubits. However, the gates and control lines become dense as more and more qubits are integrated, making their design and control difficult. This problem can be alleviated if the surface code can operate on sparse qubit arrays. Here, we give an solution for an array in which qubits are placed on edges as well as on nodes of a two-dimensional grid. The qubits on the edges are divided into two groups: those in one group act as the deputies of data qubits; the others act as deputies of the syndrome qubits. Syndrome outputs are obtained by multiplying the measured values of the syndrome and edge qubits. The procedure for the quantum part is the same as that of the ordinary surface code, making the surface code applicable to sparse qubit arrays.
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2
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Jia Z, Fu Y, Cao Z, Cheng W, Zhao Y, Dou M, Duan P, Kong W, Cao G, Li H, Guo G. Superconducting and Silicon-Based Semiconductor Quantum Computers: A Review. IEEE NANOTECHNOLOGY MAGAZINE 2022. [DOI: 10.1109/mnano.2022.3175394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Zhilong Jia
- University of Science and Technology of China
| | - Yaobin Fu
- Hefei Origin Quantum Computing Technology
| | - Zhen Cao
- Hefei Origin Quantum Computing Technology
| | | | | | | | - Peng Duan
- University of Science and Technology of China
| | | | - Gang Cao
- University of Science and Technology of China
| | - Haiou Li
- University of Science and Technology of China
| | - Guoping Guo
- University of Science and Technology of China
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3
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Egan L, Debroy DM, Noel C, Risinger A, Zhu D, Biswas D, Newman M, Li M, Brown KR, Cetina M, Monroe C. Fault-tolerant control of an error-corrected qubit. Nature 2021; 598:281-286. [PMID: 34608286 DOI: 10.1038/s41586-021-03928-y] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2020] [Accepted: 08/18/2021] [Indexed: 02/08/2023]
Abstract
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system1,2. These extra degrees of freedom enable the detection and correction of errors, but also increase the control complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice3-6. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. In addition, we prepare magic states with fidelities that exceed the distillation threshold7, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
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Affiliation(s)
- Laird Egan
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA. .,Department of Physics, University of Maryland, College Park, MD, USA. .,IonQ, Inc, College Park, MD, USA.
| | - Dripto M Debroy
- Department of Physics, Duke University, Durham, NC, USA.,Google Research, Venice, CA, USA
| | - Crystal Noel
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA
| | - Andrew Risinger
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA.,Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA
| | - Daiwei Zhu
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA.,Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA
| | - Debopriyo Biswas
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA
| | - Michael Newman
- Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.,Google Research, Venice, CA, USA
| | - Muyuan Li
- School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA.,School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - Kenneth R Brown
- Department of Physics, Duke University, Durham, NC, USA.,Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.,School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA, USA.,School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA.,Department of Chemistry, Duke University, Durham, NC, USA
| | - Marko Cetina
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA
| | - Christopher Monroe
- Joint Quantum Institute, Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, USA.,Department of Physics, University of Maryland, College Park, MD, USA.,Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA.,Department of Physics, Duke University, Durham, NC, USA.,Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA.,IonQ, Inc, College Park, MD, USA
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4
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Jang W, Cho MK, Jang H, Kim J, Park J, Kim G, Kang B, Jung H, Umansky V, Kim D. Single-Shot Readout of a Driven Hybrid Qubit in a GaAs Double Quantum Dot. NANO LETTERS 2021; 21:4999-5005. [PMID: 34109799 DOI: 10.1021/acs.nanolett.1c00783] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We report a single-shot-based projective readout of a semiconductor hybrid qubit formed by three electrons in a GaAs double quantum dot. Voltage-controlled adiabatic transitions between the qubit operations and readout conditions allow high-fidelity mapping of quantum states. We show that a large ratio both in relaxation time vs tunneling time (≈50) and singlet-triplet splitting vs thermal energy (≈20) allows energy-selective tunneling-based spin-to-charge conversion with a readout visibility of ≈92.6%. Combined with ac driving, we demonstrate high visibility coherent Rabi and Ramsey oscillations of a hybrid qubit in GaAs. Further, we discuss the generality of the method for use in other materials, including silicon.
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Affiliation(s)
- Wonjin Jang
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Min-Kyun Cho
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Hyeongyu Jang
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Jehyun Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Jaemin Park
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Gyeonghun Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Byoungwoo Kang
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
| | - Hwanchul Jung
- Department of Physics, Pusan National University, Busan 46241, Korea
| | - Vladimir Umansky
- Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Dohun Kim
- Department of Physics and Astronomy and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
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5
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Debroy DM, Li M, Newman M, Brown KR. Stabilizer Slicing: Coherent Error Cancellations in Low-Density Parity-Check Stabilizer Codes. PHYSICAL REVIEW LETTERS 2018; 121:250502. [PMID: 30608842 DOI: 10.1103/physrevlett.121.250502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2018] [Indexed: 06/09/2023]
Abstract
Coherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple technique for suppressing systematic coherent errors in low-density parity-check stabilizer codes, which we call stabilizer slicing. The essential idea is to slice low-weight stabilizers into two equally weighted Pauli operators and then apply them by rotating in opposite directions, causing their overrotations to interfere destructively on the logical subspace. With access to native gates generated by three-body Hamiltonians, we can completely eliminate purely coherent overrotation errors, and for overrotation noise of 0.99 unitarity we achieve a 135-fold improvement in the logical error rate of surface-17. For more conventional two-body ion trap gates, we observe an 89-fold improvement for Bacon-Shor-13 with purely coherent errors which should be testable in near-term fault-tolerance experiments. This second scheme takes advantage of the prepared gauge degrees of freedom, and to our knowledge is the first example in which the state of the gauge directly affects the robustness of a code's memory. This Letter demonstrates that coherent noise is preferable to stochastic noise within certain code and gate implementations when the coherence is utilized effectively.
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Affiliation(s)
- Dripto M Debroy
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Muyuan Li
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Michael Newman
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
- Departments of Electrical and Computer Engineering and Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Kenneth R Brown
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Departments of Electrical and Computer Engineering and Chemistry, Duke University, Durham, North Carolina 27708, USA
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6
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Rosenblum S, Reinhold P, Mirrahimi M, Jiang L, Frunzio L, Schoelkopf RJ. Fault-tolerant detection of a quantum error. Science 2018; 361:266-270. [PMID: 30026224 DOI: 10.1126/science.aat3996] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Accepted: 05/22/2018] [Indexed: 11/02/2022]
Abstract
A critical component of any quantum error-correcting scheme is detection of errors by using an ancilla system. However, errors occurring in the ancilla can propagate onto the logical qubit, irreversibly corrupting the encoded information. We demonstrate a fault-tolerant error-detection scheme that suppresses spreading of ancilla errors by a factor of 5, while maintaining the assignment fidelity. The same method is used to prevent propagation of ancilla excitations, increasing the logical qubit dephasing time by an order of magnitude. Our approach is hardware-efficient, as it uses a single multilevel transmon ancilla and a cavity-encoded logical qubit, whose interaction is engineered in situ by using an off-resonant sideband drive. The results demonstrate that hardware-efficient approaches that exploit system-specific error models can yield advances toward fault-tolerant quantum computation.
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Affiliation(s)
- S Rosenblum
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA. .,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - P Reinhold
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - M Mirrahimi
- Yale Quantum Institute, Yale University, New Haven, CT 06520, USA.,QUANTIC team, INRIA de Paris, 2 Rue Simone Iff, 75012 Paris, France
| | - Liang Jiang
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - L Frunzio
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
| | - R J Schoelkopf
- Departments of Applied Physics and Physics, Yale University, New Haven, CT 06511, USA.,Yale Quantum Institute, Yale University, New Haven, CT 06520, USA
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7
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Piedrafita Á, Renes JM. Reliable Channel-Adapted Error Correction: Bacon-Shor Code Recovery from Amplitude Damping. PHYSICAL REVIEW LETTERS 2017; 119:250501. [PMID: 29303301 DOI: 10.1103/physrevlett.119.250501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Indexed: 06/07/2023]
Abstract
We construct two simple error correction schemes adapted to amplitude damping noise for Bacon-Shor codes and investigate their prospects for fault-tolerant implementation. Both consist solely of Clifford gates and require far fewer qubits, relative to the standard method, to achieve exact correction to a desired order in the damping rate. The first, employing one-bit teleportation and single-qubit measurements, needs only one-fourth as many physical qubits, while the second, using just stabilizer measurements and Pauli corrections, needs only half. The improvements stem from the fact that damping events need only be detected, not corrected, and that effective phase errors arising due to undamped qubits occur at a lower rate than damping errors. For error correction that is itself subject to damping noise, we show that existing fault-tolerance methods can be employed for the latter scheme, while the former can be made to avoid potential catastrophic errors and can easily cope with damping faults in ancilla qubits.
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Affiliation(s)
- Álvaro Piedrafita
- Institut für Theoretische Physik, ETH Zurich, 8093 Zürich, Switzerland
- Qusoft and CWI, 1098 XG Amsterdam, The Netherlands
| | - Joseph M Renes
- Institut für Theoretische Physik, ETH Zurich, 8093 Zürich, Switzerland
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8
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Blume-Kohout R, Gamble JK, Nielsen E, Rudinger K, Mizrahi J, Fortier K, Maunz P. Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography. Nat Commun 2017; 8:ncomms14485. [PMID: 28198466 PMCID: PMC5330857 DOI: 10.1038/ncomms14485] [Citation(s) in RCA: 126] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2016] [Accepted: 01/04/2017] [Indexed: 01/14/2023] Open
Abstract
Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if-and only if-the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10-4).
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Affiliation(s)
- Robin Blume-Kohout
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - John King Gamble
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Erik Nielsen
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Kenneth Rudinger
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Jonathan Mizrahi
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Kevin Fortier
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Peter Maunz
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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9
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Kueng R, Long DM, Doherty AC, Flammia ST. Comparing Experiments to the Fault-Tolerance Threshold. PHYSICAL REVIEW LETTERS 2016; 117:170502. [PMID: 27824464 DOI: 10.1103/physrevlett.117.170502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2015] [Indexed: 06/06/2023]
Abstract
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.
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Affiliation(s)
- Richard Kueng
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
- Institute for Physics and FDM, University of Freiburg, D-79104 Freiburg, Germany
| | - David M Long
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
| | - Andrew C Doherty
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
| | - Steven T Flammia
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
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10
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Devitt SJ, Munro WJ, Nemoto K. Quantum error correction for beginners. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:076001. [PMID: 23787909 DOI: 10.1088/0034-4885/76/7/076001] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspects of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large-scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large-scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. The development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future.
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Affiliation(s)
- Simon J Devitt
- National Institute of Informatics, 2-1-2 Hitotsubashi Chiyoda-ku Tokyo, 101-8340, Japan.
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11
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Schindler P, Barreiro JT, Monz T, Nebendahl V, Nigg D, Chwalla M, Hennrich M, Blatt R. Experimental Repetitive Quantum Error Correction. Science 2011; 332:1059-61. [DOI: 10.1126/science.1203329] [Citation(s) in RCA: 221] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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12
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Kerckhoff J, Nurdin HI, Pavlichin DS, Mabuchi H. Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. PHYSICAL REVIEW LETTERS 2010; 105:040502. [PMID: 20867826 DOI: 10.1103/physrevlett.105.040502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2009] [Revised: 03/24/2010] [Indexed: 05/29/2023]
Abstract
We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits, providing an autonomous and "on-chip" quantum memory design requiring no external clocking or control logic.
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Affiliation(s)
- Joseph Kerckhoff
- Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA.
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13
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Oreshkov O. Holonomic quantum computation in subsystems. PHYSICAL REVIEW LETTERS 2009; 103:090502. [PMID: 19792771 DOI: 10.1103/physrevlett.103.090502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2009] [Indexed: 05/28/2023]
Abstract
We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show how fault-tolerant HQC can be realized via 2-local Hamiltonians with perturbative gadgets.
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Affiliation(s)
- Ognyan Oreshkov
- Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
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14
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Oreshkov O, Brun TA, Lidar DA. Fault-tolerant holonomic quantum computation. PHYSICAL REVIEW LETTERS 2009; 102:070502. [PMID: 19257652 DOI: 10.1103/physrevlett.102.070502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2008] [Indexed: 05/27/2023]
Abstract
We explain how to combine holonomic quantum computation (HQC) with fault-tolerant quantum error correction. This establishes the scalability of HQC, putting it on equal footing with other models of computation, while retaining the inherent robustness the method derives from its geometric nature.
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Affiliation(s)
- Ognyan Oreshkov
- Department of Physics, Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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15
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Lidar DA. Towards fault tolerant adiabatic quantum computation. PHYSICAL REVIEW LETTERS 2008; 100:160506. [PMID: 18518178 DOI: 10.1103/physrevlett.100.160506] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2007] [Revised: 11/04/2007] [Indexed: 05/26/2023]
Abstract
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes, and energy gaps. Corresponding error bounds are derived. As an example, I show how to perform decoherence-protected AQC against local noise using at most two-body interactions.
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Affiliation(s)
- Daniel A Lidar
- Department of Chemistry, Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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