1
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Dobrautz W, Sokolov IO, Liao K, Ríos PL, Rahm M, Alavi A, Tavernelli I. Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method. J Chem Theory Comput 2024; 20:4146-4160. [PMID: 38723159 DOI: 10.1021/acs.jctc.4c00070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/29/2024]
Abstract
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.
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Affiliation(s)
- Werner Dobrautz
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Igor O Sokolov
- IBM Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Ke Liao
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Pablo López Ríos
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Martin Rahm
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Ali Alavi
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Ivano Tavernelli
- IBM Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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2
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Singh H, Majumder S, Mishra S. Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding. J Chem Phys 2024; 160:194106. [PMID: 38767256 DOI: 10.1063/5.0210597] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 05/01/2024] [Indexed: 05/22/2024] Open
Abstract
Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.
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Affiliation(s)
- Harshdeep Singh
- Center of Computational and Data Sciences, Indian Institute of Technology, Kharagpur, India
| | - Sonjoy Majumder
- Department of Physics, Indian Institute of Technology, Kharagpur, India
| | - Sabyashachi Mishra
- Department of Chemistry, Indian Institute of Technology, Kharagpur, India
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3
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Zhang T, Zhang Y, Liu L, Fang XX, Zhang QX, Yuan X, Lu H. Experimental Virtual Distillation of Entanglement and Coherence. PHYSICAL REVIEW LETTERS 2024; 132:180201. [PMID: 38759173 DOI: 10.1103/physrevlett.132.180201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2023] [Accepted: 03/18/2024] [Indexed: 05/19/2024]
Abstract
Noise is, in general, inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multiple copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, "virtual resource distillation," is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension four) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy Einstein-Podolsky-Rosen (EPR) pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware.
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Affiliation(s)
- Ting Zhang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| | - Yukun Zhang
- Center on Frontiers of Computing Studies, School of Computer Science, Peking University, Beijing 100871, China
| | - Lu Liu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| | - Xiao-Xu Fang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| | - Qian-Xi Zhang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, School of Computer Science, Peking University, Beijing 100871, China
| | - He Lu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China
- Shenzhen Research Institute of Shandong University, Shenzhen 518057, China
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4
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Qian Y, Wang X, Du Y, Wu X, Tao D. The Dilemma of Quantum Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024; 35:5603-5615. [PMID: 36191113 DOI: 10.1109/tnnls.2022.3208313] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bounds than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. In this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.
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5
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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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6
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Misiewicz J, Evangelista FA. Implementation of the Projective Quantum Eigensolver on a Quantum Computer. J Phys Chem A 2024; 128:2220-2235. [PMID: 38452262 PMCID: PMC10961848 DOI: 10.1021/acs.jpca.3c07429] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Revised: 01/29/2024] [Accepted: 02/20/2024] [Indexed: 03/09/2024]
Abstract
We study the performance of our previously proposed projective quantum eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H2, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both the stochastic error and the inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can prompt large parameter updates. For the 4-site transverse-field Ising model at its critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even after discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in a loss of accuracy despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.
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Affiliation(s)
| | - Francesco A. Evangelista
- Department of Chemistry and
Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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7
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Parzygnat AJ, Fullwood J, Buscemi F, Chiribella G. Virtual Quantum Broadcasting. PHYSICAL REVIEW LETTERS 2024; 132:110203. [PMID: 38563923 DOI: 10.1103/physrevlett.132.110203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 02/02/2024] [Indexed: 04/04/2024]
Abstract
The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show that, although quantum broadcasting cannot be achieved by any physical process, it can be achieved by a virtual process, described by a Hermitian-preserving trace-preserving map. This virtual process is canonical: it is the only map that broadcasts all quantum states, is covariant under unitary evolution, is invariant under permutations of the copies, and reduces to the classical broadcasting map when subjected to decoherence. We show that the optimal physical approximation to the canonical broadcasting map is the optimal universal quantum cloning, and we also show that virtual broadcasting can be achieved by a virtual measure-and-prepare protocol, where a virtual measurement is performed, and, depending on the outcomes, two copies of a virtual quantum state are generated. Finally, we use canonical virtual broadcasting to prove a uniqueness result for quantum states over time.
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Affiliation(s)
- Arthur J Parzygnat
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Experimental Study Group, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James Fullwood
- School of Mathematics and Statistics, Hainan University, Haikou, Hainan, 570228, China
- School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China
| | - Francesco Buscemi
- Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, United Kingdom
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada
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8
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Fauseweh B. Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges. Nat Commun 2024; 15:2123. [PMID: 38459040 PMCID: PMC10923891 DOI: 10.1038/s41467-024-46402-9] [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: 01/31/2023] [Accepted: 02/14/2024] [Indexed: 03/10/2024] Open
Abstract
Simulating quantum many-body systems is a key application for emerging quantum processors. While analog quantum simulation has already demonstrated quantum advantage, its digital counterpart has recently become the focus of intense research interest due to the availability of devices that aim to realize general-purpose quantum computers. In this perspective, we give a selective overview of the currently pursued approaches, review the advances in digital quantum simulation by comparing non-variational with variational approaches and identify hardware and algorithmic challenges. Based on this review, the question arises: What are the most promising problems that can be tackled with digital quantum simulation? We argue that problems of a qualitative nature are much more suitable for near-term devices then approaches aiming purely for a quantitative accuracy improvement.
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Affiliation(s)
- Benedikt Fauseweh
- Institute for Software Technology, German Aerospace Center (DLR), Linder Höhe, 51147, Cologne, Germany.
- Department of Physics, TU Dortmund University, Otto-Hahn-Str. 4, 44227, Dortmund, Germany.
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9
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Halder S, Dey A, Shrikhande C, Maitra R. Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware. Chem Sci 2024; 15:3279-3289. [PMID: 38425512 PMCID: PMC10901498 DOI: 10.1039/d3sc05807g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/16/2024] [Indexed: 03/02/2024] Open
Abstract
The development of various dynamic ansatz-constructing techniques has ushered in a new era, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
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Affiliation(s)
- Sonaldeep Halder
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Anish Dey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata West Bengal 741246 India
| | - Chinmay Shrikhande
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Rahul Maitra
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
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10
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Hassan M, Pavošević F, Wang DS, Flick J. Simulating Polaritonic Ground States on Noisy Quantum Devices. J Phys Chem Lett 2024; 15:1373-1381. [PMID: 38287217 DOI: 10.1021/acs.jpclett.3c02875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2024]
Abstract
The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon-coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H2 molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.
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Affiliation(s)
- Mohammad Hassan
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
| | | | - Derek S Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Johannes Flick
- Department of Physics, City College of New York, New York, New York 10031, United States
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, United States
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, United States
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11
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Skogh M, Dobrautz W, Lolur P, Warren C, Biznárová J, Osman A, Tancredi G, Bylander J, Rahm M. The electron density: a fidelity witness for quantum computation. Chem Sci 2024; 15:2257-2265. [PMID: 38332826 PMCID: PMC10848700 DOI: 10.1039/d3sc05269a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Accepted: 12/19/2023] [Indexed: 02/10/2024] Open
Abstract
There is currently no combination of quantum hardware and algorithms that can provide an advantage over conventional calculations of molecules or materials. However, if or when such a point is reached, new strategies will be needed to verify predictions made using quantum devices. We propose that the electron density, obtained through experimental or computational means, can serve as a robust benchmark for validating the accuracy of quantum computation of chemistry. An initial exploration into topological features of electron densities, facilitated by quantum computation, is presented here as a proof of concept. Additionally, we examine the effects of constraining and symmetrizing measured one-particle reduced density matrices on noise-driven errors in the electron density distribution. We emphasize the potential benefits and future need for high-quality electron densities derived from diffraction experiments for validating classically intractable quantum computations of materials.
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Affiliation(s)
- Mårten Skogh
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology Gothenburg Sweden
- Data Science & Modelling, Pharmaceutical Science, R&D, AstraZeneca Gothenburg Sweden
| | - Werner Dobrautz
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology Gothenburg Sweden
| | - Phalgun Lolur
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology Gothenburg Sweden
| | - Christopher Warren
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology Gothenburg Sweden
| | - Janka Biznárová
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology Gothenburg Sweden
| | - Amr Osman
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology Gothenburg Sweden
| | - Giovanna Tancredi
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology Gothenburg Sweden
| | - Jonas Bylander
- Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology Gothenburg Sweden
| | - Martin Rahm
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology Gothenburg Sweden
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12
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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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13
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Yuan X, Regula B, Takagi R, Gu M. Virtual Quantum Resource Distillation. PHYSICAL REVIEW LETTERS 2024; 132:050203. [PMID: 38364147 DOI: 10.1103/physrevlett.132.050203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Revised: 09/26/2023] [Accepted: 11/27/2023] [Indexed: 02/18/2024]
Abstract
Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted "free" operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call "virtual resource distillation," provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.
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Affiliation(s)
- Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- School of Computer Science, Peking University, Beijing 100871, China
| | - Bartosz Regula
- Mathematical Quantum Information RIKEN Hakubi Research Team, RIKEN Cluster for Pioneering Research (CPR) and RIKEN Center for Quantum Computing (RQC), Wako, Saitama 351-0198, Japan
- Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Ryuji Takagi
- Department of Basic Science, The University of Tokyo, Tokyo 153-8902, Japan
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore
| | - Mile Gu
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore 117543, Singapore
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14
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Prasad VK, Cheng F, Fekl U, Jacobsen HA. Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry. Phys Chem Chem Phys 2024; 26:4071-4082. [PMID: 38225897 DOI: 10.1039/d3cp03523a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2024]
Abstract
The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.
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Affiliation(s)
- Viki Kumar Prasad
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Freeman Cheng
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
| | - Ulrich Fekl
- Department of Chemical and Physical Sciences, University of Toronto Mississauga, 3359 Mississauga Road, Mississauga, Ontario, Canada, L5L 1C6.
| | - Hans-Arno Jacobsen
- The Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, 10 Kings College Road, Toronto, Ontario, Canada, M5S 3G4. arno,
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada, M5S 2E4
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15
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Begušić T, Gray J, Chan GKL. Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance. SCIENCE ADVANCES 2024; 10:eadk4321. [PMID: 38232163 DOI: 10.1126/sciadv.adk4321] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2023] [Accepted: 12/19/2023] [Indexed: 01/19/2024]
Abstract
A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wave function-operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness.
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Affiliation(s)
- Tomislav Begušić
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Johnnie Gray
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
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16
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Charles C, Gustafson EJ, Hardt E, Herren F, Hogan N, Lamm H, Starecheski S, Van de Water RS, Wagman ML. Simulating Z_{2} lattice gauge theory on a quantum computer. Phys Rev E 2024; 109:015307. [PMID: 38366518 DOI: 10.1103/physreve.109.015307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 12/21/2023] [Indexed: 02/18/2024]
Abstract
The utility of quantum computers for simulating lattice gauge theories is currently limited by the noisiness of the physical hardware. Various quantum error mitigation strategies exist to reduce the statistical and systematic uncertainties in quantum simulations via improved algorithms and analysis strategies. We perform quantum simulations of Z_{2} gauge theory with matter to study the efficacy and interplay of different error mitigation methods: readout error mitigation, randomized compiling, rescaling, and dynamical decoupling. We compute Minkowski correlation functions in this confining gauge theory and extract the mass of the lightest spin-1 state from fits to their time dependence. Quantum error mitigation extends the range of times over which our correlation function calculations are accurate by a factor of 6 and is therefore essential for obtaining reliable masses.
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Affiliation(s)
- Clement Charles
- Department of Physics, The University of the West Indies, St. Augustine Campus, Trinidad and Tobago
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Erik J Gustafson
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, California 94035, USA
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
| | - Elizabeth Hardt
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Florian Herren
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Norman Hogan
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Henry Lamm
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Sara Starecheski
- Department of Physics, Sarah Lawrence College, Bronxville, New York 10708, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | - Michael L Wagman
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
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17
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Kumar A, Asthana A, Abraham V, Crawford TD, Mayhall NJ, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Response Properties in the NISQ Era. J Chem Theory Comput 2023; 19:9136-9150. [PMID: 38054645 DOI: 10.1021/acs.jctc.3c00731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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18
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Ghosh K, Kumar S, Rajan NM, Yamijala SSRKC. Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers. ACS OMEGA 2023; 8:48211-48220. [PMID: 38144092 PMCID: PMC10734038 DOI: 10.1021/acsomega.3c07364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/24/2023] [Revised: 11/07/2023] [Accepted: 11/10/2023] [Indexed: 12/26/2023]
Abstract
The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems in the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate iterative errors, albeit primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits.
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Affiliation(s)
- Kalpak Ghosh
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
| | - Sumit Kumar
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
| | | | - Sharma S. R. K. C. Yamijala
- Department
of Chemistry, Indian Institute of Technology
Madras, Chennai, 600036, India
- Centre
for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai 600036, India
- Centre
for Molecular Materials and Functions, Indian
Institute of Technology Madras, Chennai 600036, India
- Centre
for Atomistic Modelling and Materials Design, Indian Institute of Technology Madras, Chennai 600036, India
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19
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Miguel-Ramiro J, Shi Z, Dellantonio L, Chan A, Muschik CA, Dür W. Superposed Quantum Error Mitigation. PHYSICAL REVIEW LETTERS 2023; 131:230601. [PMID: 38134783 DOI: 10.1103/physrevlett.131.230601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 11/06/2023] [Indexed: 12/24/2023]
Abstract
Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary states. We demonstrate, numerically and on the IBM Quantum Platform, that parallel applications of the same operation lead to significant noise mitigation when arbitrary noise processes are considered. We first design probabilistic implementations of our scheme that are plug and play, independent of the noise characteristic and require no postprocessing. We then enhance the success probability (up to deterministic) using adaptive corrections. We provide an analysis of our protocol performance and demonstrate that unit fidelity can be achieved asymptotically. Our approaches are suitable to both standard gate-based and measurement-based computational models.
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Affiliation(s)
- Jorge Miguel-Ramiro
- Universität Innsbruck, Institut für Theoretische Physik, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - Zheng Shi
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Luca Dellantonio
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom
| | - Albie Chan
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Christine A Muschik
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - Wolfgang Dür
- Universität Innsbruck, Institut für Theoretische Physik, Technikerstraße 21a, 6020 Innsbruck, Austria
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20
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Zeng X, Fan Y, Liu J, Li Z, Yang J. Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems. J Chem Theory Comput 2023. [PMID: 38044845 DOI: 10.1021/acs.jctc.3c00527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2023]
Abstract
The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.
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Affiliation(s)
- Xiongzhi Zeng
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China
| | - Yi Fan
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
| | - Jie Liu
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Zhenyu Li
- Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jinlong Yang
- Key Laboratory of Precision and Intelligent Chemistry, 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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21
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Ahn D. Non-Markovian cost function for quantum error mitigation with Dirac Gamma matrices representation. Sci Rep 2023; 13:20069. [PMID: 37973833 PMCID: PMC10654775 DOI: 10.1038/s41598-023-45053-y] [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: 06/17/2023] [Accepted: 10/15/2023] [Indexed: 11/19/2023] Open
Abstract
This paper investigates the non-Markovian cost function in quantum error mitigation (QEM) and employs Dirac Gamma matrices to illustrate two-qubit operators, significant in relativistic quantum mechanics. Amid the focus on error reduction in noisy intermediate-scale quantum (NISQ) devices, understanding non-Markovian noise, commonly found in solid-state quantum computers, is crucial. We propose a non-Markovian model for quantum state evolution and a corresponding QEM cost function, using simple harmonic oscillators as a proxy for environmental noise. Owing to their shared algebraic structure with two-qubit gate operators, Gamma matrices allow for enhanced analysis and manipulation of these operators. We evaluate the fluctuations of the output quantum state across various input states for identity and SWAP gate operations, and by comparing our findings with ion-trap and superconducting quantum computing systems' experimental data, we derive essential QEM cost function parameters. Our findings indicate a direct relationship between the quantum system's coupling strength with its environment and the QEM cost function. The research highlights non-Markovian models' importance in understanding quantum state evolution and assessing experimental outcomes from NISQ devices.
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Affiliation(s)
- Doyeol Ahn
- Department of Electrical and Computer Engineering, University of Seoul, 163 Seoulsiripdae-Ro, Tongdaimoon-Gu, Seoul, 02504, Republic of Korea.
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22
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Lee G, Hann CT, Puri S, Girvin SM, Jiang L. Error Suppression for Arbitrary-Size Black Box Quantum Operations. PHYSICAL REVIEW LETTERS 2023; 131:190601. [PMID: 38000438 DOI: 10.1103/physrevlett.131.190601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2022] [Accepted: 10/23/2023] [Indexed: 11/26/2023]
Abstract
Efficient suppression of errors without full error correction is crucial for applications with noisy intermediate-scale quantum devices. Error mitigation allows us to suppress errors in extracting expectation values without the need for any error correction code, but its applications are limited to estimating expectation values, and cannot provide us with high-fidelity quantum operations acting on arbitrary quantum states. To address this challenge, we propose to use error filtration (EF) for gate-based quantum computation, as a practical error suppression scheme without resorting to full quantum error correction. The result is a general-purpose error suppression protocol where the resources required to suppress errors scale independently of the size of the quantum operation, and does not require any logical encoding of the operation. The protocol provides error suppression whenever an error hierarchy is respected-that is, when the ancillary controlled-swap operations are less noisy than the operation to be corrected. We further analyze the application of EF to quantum random access memory, where EF offers hardware-efficient error suppression.
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Affiliation(s)
- Gideon Lee
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Connor T Hann
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA
- Yale Quantum Institute, New Haven, Connecticut 06520, USA
- AWS Center for Quantum Computing, Pasadena, California 91125, USA
- IQIM, California Institute of Technology, Pasadena, California 91125, USA
| | - Shruti Puri
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S M Girvin
- Department of Physics, Yale University, New Haven, Connecticut 06511, USA
- Yale Quantum Institute, New Haven, Connecticut 06520, USA
| | - Liang Jiang
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
- AWS Center for Quantum Computing, Pasadena, California 91125, USA
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23
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Sajjan M, Gupta R, Kale SS, Singh V, Kumaran K, Kais S. Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State. J Phys Chem A 2023; 127:8751-8764. [PMID: 37795926 DOI: 10.1021/acs.jpca.3c05172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/06/2023]
Abstract
Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model, a spin-1/2-unit cell of a Kagome antiferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques such as the density-matrix renormalization group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxiliary Hamiltonian with reduced measurables and also design an ansatz that is modular and gate-efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within 1% accuracy in energy. Since the protocol is linearly scaling O(n) in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices that can pave the way for efficient construction of spin-liquid ground states on a quantum device.
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Affiliation(s)
- Manas Sajjan
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Rishabh Gupta
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sumit Suresh Kale
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Vinit Singh
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Keerthi Kumaran
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sabre Kais
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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24
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Tian J, Sun X, Du Y, Zhao S, Liu Q, Zhang K, Yi W, Huang W, Wang C, Wu X, Hsieh MH, Liu T, Yang W, Tao D. Recent Advances for Quantum Neural Networks in Generative Learning. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023; 45:12321-12340. [PMID: 37126624 DOI: 10.1109/tpami.2023.3272029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Quantum computers are next-generation devices that hold promise to perform calculations beyond the reach of classical computers. A leading method towards achieving this goal is through quantum machine learning, especially quantum generative learning. Due to the intrinsic probabilistic nature of quantum mechanics, it is reasonable to postulate that quantum generative learning models (QGLMs) may surpass their classical counterparts. As such, QGLMs are receiving growing attention from the quantum physics and computer science communities, where various QGLMs that can be efficiently implemented on near-term quantum machines with potential computational advantages are proposed. In this paper, we review the current progress of QGLMs from the perspective of machine learning. Particularly, we interpret these QGLMs, covering quantum circuit Born machines, quantum generative adversarial networks, quantum Boltzmann machines, and quantum variational autoencoders, as the quantum extension of classical generative learning models. In this context, we explore their intrinsic relations and their fundamental differences. We further summarize the potential applications of QGLMs in both conventional machine learning tasks and quantum physics. Last, we discuss the challenges and further research directions for QGLMs.
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25
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Halder S, Shrikhande C, Maitra R. Development of zero-noise extrapolated projective quantum algorithm for accurate evaluation of molecular energetics in noisy quantum devices. J Chem Phys 2023; 159:114115. [PMID: 37724729 DOI: 10.1063/5.0166433] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 08/31/2023] [Indexed: 09/21/2023] Open
Abstract
The recently developed Projective Quantum Eigensolver (PQE) offers an elegant procedure to evaluate the ground state energies of molecular systems in quantum computers. However, the noise in available quantum hardware can result in significant errors in computed outcomes, limiting the realization of quantum advantage. Although PQE comes equipped with some degree of inherent noise resilience, any practical implementation with apposite accuracy would require additional routines to eliminate or mitigate the errors further. In this work, we propose a way to enhance the efficiency of PQE by developing an optimal framework for introducing Zero Noise Extrapolation (ZNE) in the nonlinear iterative procedure that outlines the PQE, leading to the formulation of ZNE-PQE. Moreover, we perform a detailed analysis of how various components involved in it affect the accuracy and efficiency of the reciprocated energy convergence trajectory. Additionally, we investigate the underlying mechanism that leads to the improvements observed in ZNE-PQE over conventional PQE by performing a comparative analysis of their residue norm landscape. This approach is expected to facilitate practical applications of quantum computing in fields related to molecular sciences, where it is essential to determine molecular energies accurately.
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Affiliation(s)
- Sonaldeep Halder
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Chinmay Shrikhande
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Rahul Maitra
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
- Centre of Excellence in Quantum Information, Computing, Science and Technology, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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26
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Rossini M, Maile D, Ankerhold J, Donvil BIC. Single-Qubit Error Mitigation by Simulating Non-Markovian Dynamics. PHYSICAL REVIEW LETTERS 2023; 131:110603. [PMID: 37774275 DOI: 10.1103/physrevlett.131.110603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Revised: 06/09/2023] [Accepted: 08/16/2023] [Indexed: 10/01/2023]
Abstract
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by completely positive (CP) maps, for which several quantum simulation schemes exist. Such maps, however, represent only a subset of a larger class of maps: the general dynamical maps which are linear, Hermitian preserving, and trace preserving but not necessarily positivity preserving. Here we present a simulation scheme for these general dynamical maps, which occur when the underlying system-reservoir model undergoes entangling (and thus non-Markovian) dynamics. Such maps also arise as the inverse of CP maps, which are commonly used in error mitigation. We illustrate our simulation scheme on an IBM quantum processor, demonstrating its ability to recover the initial state of a Lindblad evolution. This paves the way for a novel form of quantum error mitigation. Our scheme only requires one ancilla qubit as an overhead and a small number of one and two qubit gates. Consequently, we expect it to be of practical use in near-term quantum devices.
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Affiliation(s)
- Mirko Rossini
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Dominik Maile
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Joachim Ankerhold
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
| | - Brecht I C Donvil
- Institute for Complex Quantum Systems and IQST, Ulm University-Albert-Einstein-Allee 11, D-89069 Ulm, Germany
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27
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Shang ZX, Chen MC, Yuan X, Lu CY, Pan JW. Schrödinger-Heisenberg Variational Quantum Algorithms. PHYSICAL REVIEW LETTERS 2023; 131:060406. [PMID: 37625038 DOI: 10.1103/physrevlett.131.060406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 07/14/2023] [Indexed: 08/27/2023]
Abstract
Recent breakthroughs have opened the possibility of intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics. However, the high accuracy needed to surpass classical computers poses a critical demand on the circuit depth, which is severely limited by the non-negligible gate infidelity, currently around 0.1%-1%. The limited circuit depth places restrictions on the performance of variational quantum algorithms (VQA) and prevents VQAs from exploring desired nontrivial quantum states. To resolve this problem, we propose a paradigm of Schrödinger-Heisenberg variational quantum algorithms (SHVQA). Using SHVQA, the expectation values of operators on states that require very deep circuits to prepare can now be efficiently measured by rather shallow circuits. The idea is to incorporate a virtual Heisenberg circuit, which acts effectively on the measurement observables, into a real shallow Schrödinger circuit, which is implemented realistically on the quantum hardware. We choose a Clifford virtual circuit, whose effect on the Hamiltonian can be seen as efficient classical processing. Yet, it greatly enlarges the state's expressivity, realizing much larger unitary t designs. Our method enables accurate quantum simulation and computation that otherwise are only achievable with much deeper circuits or more accurate operations conventionally. This has been verified in our numerical experiments for a better approximation of random states, higher-fidelity solutions to the XXZ model, and the electronic structure Hamiltonians of small molecules. Thus, together with effective quantum error mitigation, our work paves the way for realizing accurate quantum computing algorithms with near-term quantum devices.
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Affiliation(s)
- Zhong-Xia Shang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 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 Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 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
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
- School of Computer Science, Peking University, Beijing 100871, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 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 Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 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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28
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Pyrkov A, Aliper A, Bezrukov D, Lin YC, Polykovskiy D, Kamya P, Ren F, Zhavoronkov A. Quantum computing for near-term applications in generative chemistry and drug discovery. Drug Discov Today 2023; 28:103675. [PMID: 37331692 DOI: 10.1016/j.drudis.2023.103675] [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: 02/17/2023] [Revised: 05/22/2023] [Accepted: 06/13/2023] [Indexed: 06/20/2023]
Abstract
In recent years, drug discovery and life sciences have been revolutionized with machine learning and artificial intelligence (AI) methods. Quantum computing is touted to be the next most significant leap in technology; one of the main early practical applications for quantum computing solutions is predicted to be in quantum chemistry simulations. Here, we review the near-term applications of quantum computing and their advantages for generative chemistry and highlight the challenges that can be addressed with noisy intermediate-scale quantum (NISQ) devices. We also discuss the possible integration of generative systems running on quantum computers into established generative AI platforms.
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Affiliation(s)
- Alexey Pyrkov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong.
| | - Alex Aliper
- Insilico Medicine AI Ltd, Masdar City, Abu Dhabi, United Arab Emirates
| | - Dmitry Bezrukov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong
| | - Yen-Chu Lin
- Insilico Medicine Taiwan Ltd, Taipei, Taiwan
| | | | | | - Feng Ren
- Insilico Medicine Shanghai Ltd, Shanghai, China
| | - Alex Zhavoronkov
- Insilico Medicine Hong Kong Ltd, Pak Shek Kok, New Territories, Hong Kong
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29
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Wang L, Sun Y, Zhang X. Quantum Adversarial Transfer Learning. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1090. [PMID: 37510037 PMCID: PMC10378263 DOI: 10.3390/e25071090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 06/09/2023] [Accepted: 07/08/2023] [Indexed: 07/30/2023]
Abstract
Adversarial transfer learning is a machine learning method that employs an adversarial training process to learn the datasets of different domains. Recently, this method has attracted attention because it can efficiently decouple the requirements of tasks from insufficient target data. In this study, we introduce the notion of quantum adversarial transfer learning, where data are completely encoded by quantum states. A measurement-based judgment of the data label and a quantum subroutine to compute the gradients are discussed in detail. We also prove that our proposal has an exponential advantage over its classical counterparts in terms of computing resources such as the gate number of the circuits and the size of the storage required for the generated data. Finally, numerical experiments demonstrate that our model can be successfully trained, achieving high accuracy on certain datasets.
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Affiliation(s)
- Longhan Wang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Yifan Sun
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Xiangdong Zhang
- Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics & Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China
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30
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Gu Y, Ma Y, Forcellini N, Liu DE. Noise-Resilient Phase Estimation with Randomized Compiling. PHYSICAL REVIEW LETTERS 2023; 130:250601. [PMID: 37418736 DOI: 10.1103/physrevlett.130.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2022] [Accepted: 06/01/2023] [Indexed: 07/09/2023]
Abstract
We develop an error mitigation method for the control-free phase estimation. We prove a theorem that under the first-order correction, the phases of a unitary operator are immune to the noise channels with only Hermitian Kraus operators, and therefore, certain benign types of noise for phase estimation are identified. By further incorporating the randomized compiling protocol, we can convert the generic noise in the phase estimation circuits into stochastic Pauli noise, which satisfies the condition of our theorem. Thus, we achieve a noise-resilient phase estimation without any quantum resource overhead. The simulated experiments show that our method can significantly reduce the estimation error of the phases by up to 2 orders of magnitude. Our method paves the way for the utilization of quantum phase estimation before the advent of fault-tolerant quantum computers.
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Affiliation(s)
- Yanwu Gu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Yunheng Ma
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Nicolò Forcellini
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Dong E Liu
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100184, China
- Hefei National Laboratory, Hefei 230088, China
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31
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Kim Y, Eddins A, Anand S, Wei KX, van den Berg E, Rosenblatt S, Nayfeh H, Wu Y, Zaletel M, Temme K, Kandala A. Evidence for the utility of quantum computing before fault tolerance. Nature 2023; 618:500-505. [PMID: 37316724 PMCID: PMC10266970 DOI: 10.1038/s41586-023-06096-3] [Citation(s) in RCA: 29] [Impact Index Per Article: 29.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 04/18/2023] [Indexed: 06/16/2023]
Abstract
Quantum computing promises to offer substantial speed-ups over its classical counterpart for certain problems. However, the greatest impediment to realizing its full potential is noise that is inherent to these systems. The widely accepted solution to this challenge is the implementation of fault-tolerant quantum circuits, which is out of reach for current processors. Here we report experiments on a noisy 127-qubit processor and demonstrate the measurement of accurate expectation values for circuit volumes at a scale beyond brute-force classical computation. We argue that this represents evidence for the utility of quantum computing in a pre-fault-tolerant era. These experimental results are enabled by advances in the coherence and calibration of a superconducting processor at this scale and the ability to characterize1 and controllably manipulate noise across such a large device. We establish the accuracy of the measured expectation values by comparing them with the output of exactly verifiable circuits. In the regime of strong entanglement, the quantum computer provides correct results for which leading classical approximations such as pure-state-based 1D (matrix product states, MPS) and 2D (isometric tensor network states, isoTNS) tensor network methods2,3 break down. These experiments demonstrate a foundational tool for the realization of near-term quantum applications4,5.
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Affiliation(s)
- Youngseok Kim
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA.
| | - Andrew Eddins
- IBM Quantum, IBM Research - Cambridge, Cambridge, MA, USA.
| | - Sajant Anand
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
| | - Ken Xuan Wei
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Ewout van den Berg
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Sami Rosenblatt
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Hasan Nayfeh
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Yantao Wu
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- RIKEN iTHEMS, Wako, Japan
| | - Michael Zaletel
- Department of Physics, University of California, Berkeley, Berkeley, CA, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Kristan Temme
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA
| | - Abhinav Kandala
- IBM Quantum, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA.
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32
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Wendin G, Bylander J. Quantum computer scales up by mitigating errors. Nature 2023; 618:462-463. [PMID: 37316716 DOI: 10.1038/d41586-023-01884-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
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33
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John M, Schuhmacher J, Barkoutsos P, Tavernelli I, Tacchino F. Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets. ENTROPY (BASEL, SWITZERLAND) 2023; 25:860. [PMID: 37372204 DOI: 10.3390/e25060860] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 05/24/2023] [Accepted: 05/24/2023] [Indexed: 06/29/2023]
Abstract
The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.
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Affiliation(s)
- Manuel John
- IBM Quantum, IBM Research Europe-Zurich, 8803 Rüschlikon, Switzerland
- Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
| | | | | | - Ivano Tavernelli
- IBM Quantum, IBM Research Europe-Zurich, 8803 Rüschlikon, Switzerland
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34
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Pokharel B, Lidar DA. Demonstration of Algorithmic Quantum Speedup. PHYSICAL REVIEW LETTERS 2023; 130:210602. [PMID: 37295120 DOI: 10.1103/physrevlett.130.210602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2022] [Accepted: 04/20/2023] [Indexed: 06/12/2023]
Abstract
Despite the development of increasingly capable quantum computers, an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant devices has remained elusive. Here, we unequivocally demonstrate such a speedup within the oracular model, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, using two different 27-qubit IBM Quantum superconducting processors. The speedup is observed on only one of the two processors when the quantum computation is protected by dynamical decoupling but not without it. The quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem in the setting of a game with an oracle and a verifier.
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Affiliation(s)
- Bibek Pokharel
- Department of Physics & Astronomy and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Departments of Electrical & Computer Engineering, Chemistry, and Physics & Astronomy, and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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35
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Li J, Jones BA, Kais S. Toward perturbation theory methods on a quantum computer. SCIENCE ADVANCES 2023; 9:eadg4576. [PMID: 37172088 PMCID: PMC10181180 DOI: 10.1126/sciadv.adg4576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Perturbation theory, used in a wide range of fields, is a powerful tool for approximate solutions to complex problems, starting from the exact solution of a related, simpler problem. Advances in quantum computing, especially over the past several years, provide opportunities for alternatives to classical methods. Here, we present a general quantum circuit estimating both the energy and eigenstates corrections that is far superior to the classical version when estimating second-order energy corrections. We demonstrate our approach as applied to the two-site extended Hubbard model. In addition to numerical simulations based on qiskit, results on IBM's quantum hardware are also presented. Our work offers a general approach to studying complex systems with quantum devices, with no training or optimization process needed to obtain the perturbative terms, which can be generalized to other Hamiltonian systems both in chemistry and physics.
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Affiliation(s)
- Junxu Li
- Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
- Department of Physics, College of Sciences, Northeastern University, Shenyang 110819, China
| | | | - Sabre Kais
- Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
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36
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Zhang Y, Niu D, Shabani A, Shapourian H. Quantum Volume for Photonic Quantum Processors. PHYSICAL REVIEW LETTERS 2023; 130:110602. [PMID: 37001084 DOI: 10.1103/physrevlett.130.110602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
Defining metrics for near-term quantum computing processors has been an integral part of the quantum hardware research and development efforts. Such quantitative characteristics are not only useful for reporting the progress and comparing different quantum platforms but also essential for identifying the bottlenecks and designing a technology road map. Most metrics such as randomized benchmarking and quantum volume were originally introduced for circuit-based quantum computers and were not immediately applicable to measurement-based quantum computing (MBQC) processors such as in photonic devices. In this Letter, we close this long-standing gap by presenting a framework to map physical noises and imperfections in MBQC processes to logical errors in equivalent quantum circuits, whereby enabling the well-known metrics to characterize MBQC. To showcase our framework, we study a continuous-variable cluster state based on the Gottesman-Kitaev-Preskill (GKP) encoding as a near-term candidate for photonic quantum computing, and derive the effective logical gate error channels and calculate the quantum volume in terms of the GKP squeezing and photon transmission rate.
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Affiliation(s)
- Yuxuan Zhang
- Cisco Quantum Lab, San Jose, California 95134, USA
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Daoheng Niu
- Cisco Quantum Lab, San Jose, California 95134, USA
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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37
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Huang B, Sheng N, Govoni M, Galli G. Quantum Simulations of Fermionic Hamiltonians with Efficient Encoding and Ansatz Schemes. J Chem Theory Comput 2023; 19:1487-1498. [PMID: 36791415 DOI: 10.1021/acs.jctc.2c01119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2023]
Abstract
We propose a computational protocol for quantum simulations of fermionic Hamiltonians on a quantum computer, enabling calculations on spin defect systems which were previously not feasible using conventional encodings and a unitary coupled-cluster ansatz of variational quantum eigensolvers. We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and in the number of required qubits, and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamonds and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.
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Affiliation(s)
- Benchen Huang
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States.,Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
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38
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Efficient noise mitigation technique for quantum computing. Sci Rep 2023; 13:3912. [PMID: 36890156 PMCID: PMC9995348 DOI: 10.1038/s41598-023-30510-5] [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: 09/09/2021] [Accepted: 02/24/2023] [Indexed: 03/10/2023] Open
Abstract
Quantum computers have enabled solving problems beyond the current machines' capabilities. However, this requires handling noise arising from unwanted interactions in these systems. Several protocols have been proposed to address efficient and accurate quantum noise profiling and mitigation. In this work, we propose a novel protocol that efficiently estimates the average output of a noisy quantum device to be used for quantum noise mitigation. The multi-qubit system average behavior is approximated as a special form of a Pauli Channel where Clifford gates are used to estimate the average output for circuits of different depths. The characterized Pauli channel error rates, and state preparation and measurement errors are then used to construct the outputs for different depths thereby eliminating the need for large simulations and enabling efficient mitigation. We demonstrate the efficiency of the proposed protocol on four IBM Q 5-qubit quantum devices. Our method demonstrates improved accuracy with efficient noise characterization. We report up to 88% and 69% improvement for the proposed approach compared to the unmitigated, and pure measurement error mitigation approaches, respectively.
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39
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Henderson JM, Podzorova M, Cerezo M, Golden JK, Gleyzer L, Viswanathan HS, O’Malley D. Quantum algorithms for geologic fracture networks. Sci Rep 2023; 13:2906. [PMID: 36805641 PMCID: PMC9938886 DOI: 10.1038/s41598-023-29643-4] [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: 11/01/2022] [Accepted: 02/08/2023] [Indexed: 02/20/2023] Open
Abstract
Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10-1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.
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Affiliation(s)
- Jessie M. Henderson
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.263864.d0000 0004 1936 7929Southern Methodist University, Dallas, TX 75205 USA
| | - Marianna Podzorova
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.148313.c0000 0004 0428 3079Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.410443.60000 0004 0370 3414Department of Computer Science and Joint Center for Quantum Information and Computer Science, The University of Maryland, College Park, MD, 20742 USA
| | - M. Cerezo
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.148313.c0000 0004 0428 3079Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.148313.c0000 0004 0428 3079Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87544 USA
| | - John K. Golden
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.148313.c0000 0004 0428 3079Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
| | - Leonard Gleyzer
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA ,grid.40263.330000 0004 1936 9094Brown University, Providence, RI 02912 USA
| | - Hari S. Viswanathan
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA
| | - Daniel O’Malley
- grid.148313.c0000 0004 0428 3079Los Alamos National Laboratory, Los Alamos, NM 87545 USA
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40
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Cattan GH, Quemy A. Case-Based and Quantum Classification for ERP-Based Brain-Computer Interfaces. Brain Sci 2023; 13:brainsci13020303. [PMID: 36831846 PMCID: PMC9954540 DOI: 10.3390/brainsci13020303] [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: 12/20/2022] [Revised: 02/03/2023] [Accepted: 02/08/2023] [Indexed: 02/15/2023] Open
Abstract
Low transfer rates are a major bottleneck for brain-computer interfaces based on electroencephalography (EEG). This problem has led to the development of more robust and accurate classifiers. In this study, we investigated the performance of variational quantum, quantum-enhanced support vector, and hypergraph case-based reasoning classifiers in the binary classification of EEG data from a P300 experiment. On the one hand, quantum classification is a promising technology to reduce computational time and improve learning outcomes. On the other hand, case-based reasoning has an excellent potential to simplify the preprocessing steps of EEG analysis. We found that the balanced training (prediction) accuracy of each of these three classifiers was 56.95 (51.83), 83.17 (50.25), and 71.10% (52.04%), respectively. In addition, case-based reasoning performed significantly lower with a simplified (49.78%) preprocessing pipeline. These results demonstrated that all classifiers were able to learn from the data and that quantum classification of EEG data was implementable; however, more research is required to enable a greater prediction accuracy because none of the classifiers were able to generalize from the data. This could be achieved by improving the configuration of the quantum classifiers (e.g., increasing the number of shots) and increasing the number of trials for hypergraph case-based reasoning classifiers through transfer learning.
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Affiliation(s)
| | - Alexandre Quemy
- Faculty of Computer Sciences, Poznań University of Technology, 60-965 Poznań, Poland
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41
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Gonzales A, Shaydulin R, Saleem ZH, Suchara M. Quantum error mitigation by Pauli check sandwiching. Sci Rep 2023; 13:2122. [PMID: 36747037 PMCID: PMC9902625 DOI: 10.1038/s41598-023-28109-x] [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: 11/04/2022] [Accepted: 01/12/2023] [Indexed: 02/08/2023] Open
Abstract
We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.
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Affiliation(s)
- Alvin Gonzales
- Intelligence Community Postdoctoral Research Fellowship Program, Argonne National Laboratory, Lemont, IL, USA.
| | - Ruslan Shaydulin
- grid.466824.a0000 0001 2215 0980Global Technology Applied Research, JPMorgan Chase, New York, NY USA
| | - Zain H. Saleem
- grid.187073.a0000 0001 1939 4845Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL USA
| | - Martin Suchara
- grid.187073.a0000 0001 1939 4845Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL USA ,grid.467171.20000 0001 0316 7795Amazon Web Services, Amazon, Seattle, WS USA
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42
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Exploring finite temperature properties of materials with quantum computers. Sci Rep 2023; 13:1986. [PMID: 36737662 PMCID: PMC9898567 DOI: 10.1038/s41598-023-28317-5] [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: 08/17/2022] [Accepted: 01/17/2023] [Indexed: 02/05/2023] Open
Abstract
Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.
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43
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Lolur P, Skogh M, Dobrautz W, Warren C, Biznárová J, Osman A, Tancredi G, Wendin G, Bylander J, Rahm M. Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry. J Chem Theory Comput 2023; 19:783-789. [PMID: 36705548 PMCID: PMC9933421 DOI: 10.1021/acs.jctc.2c00807] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal postprocessing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver. Up to two orders-of-magnitude improvement in the computational accuracy of ground state energies of small molecules (H2, HeH+, and LiH) is demonstrated on superconducting quantum hardware. Simulations of noisy circuits with a depth exceeding 1000 two-qubit gates are used to demonstrate the scalability of the method.
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Affiliation(s)
- Phalgun Lolur
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, SE-412 96 Gothenburg, Sweden
| | - Mårten Skogh
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, SE-412 96 Gothenburg, Sweden,Data
Science & Modelling, Pharmaceutical Science, R&D, AstraZeneca, SE-431 83 Mölndal, Gothenburg, Sweden
| | - Werner Dobrautz
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, SE-412 96 Gothenburg, Sweden
| | - Christopher Warren
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Janka Biznárová
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Amr Osman
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Giovanna Tancredi
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Göran Wendin
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Jonas Bylander
- Department
of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Martin Rahm
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, SE-412 96 Gothenburg, Sweden,
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44
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Zhang ZJ, Sun J, Yuan X, Yung MH. Low-Depth Hamiltonian Simulation by an Adaptive Product Formula. PHYSICAL REVIEW LETTERS 2023; 130:040601. [PMID: 36763426 DOI: 10.1103/physrevlett.130.040601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Revised: 01/17/2022] [Accepted: 11/16/2022] [Indexed: 06/18/2023]
Abstract
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices. Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit. By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error. We numerically test the adaptive method with electronic Hamiltonians of the H_{2}O and H_{4} molecules, and the transverse field Ising model with random coefficients. Compared to the first-order Suzuki-Trotter product formula, our method can significantly reduce the circuit depth (specifically the number of two-qubit gates) by around two orders while maintaining the simulation accuracy. We show applications of the method in simulating many-body dynamics and solving energy spectra with the quantum Krylov algorithm. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
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Affiliation(s)
- Zi-Jian Zhang
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Jinzhao Sun
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Xiao Yuan
- Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China
| | - Man-Hong Yung
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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45
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Tammaro A, Galli DE, Rice JE, Motta M. N-Electron Valence Perturbation Theory with Reference Wave Functions from Quantum Computing: Application to the Relative Stability of Hydroxide Anion and Hydroxyl Radical. J Phys Chem A 2023; 127:817-827. [PMID: 36638358 DOI: 10.1021/acs.jpca.2c07653] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from nonvalence orbitals is demonstrated, through the integration of the variational quantum eigensolver and quantum subspace expansion methods in the workflow of N-electron valence perturbation theory, and shown to correctly predict the hydroxide anion to be more stable than the hydroxyl radical, provided that basis sets with diffuse orbitals are also employed. Finally, we calculate the electron affinity of the hydroxyl radical using an aug-cc-pVQZ basis on IBM's quantum devices.
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Affiliation(s)
- Alessandro Tammaro
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Davide E Galli
- Dipartimento di Fisica "Aldo Pontremoli", Università degli Studi di Milano, via Celoria 16, I-20133Milano, Italy
| | - Julia E Rice
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden, 650 Harry Road, San Jose, California95120, United States
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46
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Weaving T, Ralli A, Kirby WM, Tranter A, Love PJ, Coveney PV. A Stabilizer Framework for the Contextual Subspace Variational Quantum Eigensolver and the Noncontextual Projection Ansatz. J Chem Theory Comput 2023; 19:808-821. [PMID: 36689668 PMCID: PMC9933439 DOI: 10.1021/acs.jctc.2c00910] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth.
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Affiliation(s)
- Tim Weaving
- Centre
for Computational Science, Department of Chemistry, University College London, LondonWC1H 0AJ, United Kingdom,E-mail:
| | - Alexis Ralli
- Centre
for Computational Science, Department of Chemistry, University College London, LondonWC1H 0AJ, United Kingdom
| | - William M. Kirby
- Department
of Physics and Astronomy, Tufts University, Medford, Massachusetts02155, United States
| | - Andrew Tranter
- Cambridge
Quantum Computing, 9a
Bridge Street, CambridgeCB2 1UB, United Kingdom
| | - Peter J. Love
- Department
of Physics and Astronomy, Tufts University, Medford, Massachusetts02155, United States,Computational
Science Initiative, Brookhaven National
Laboratory, Upton, New York11973, United
States
| | - Peter V. Coveney
- Centre
for Computational Science, Department of Chemistry, University College London, LondonWC1H 0AJ, United Kingdom,UCL
Centre for Advanced Research Computing, Gower Street, LondonWC1E 6BT, United Kingdom,Informatics
Institute, University of Amsterdam, Amsterdam1098 XH, the Netherlands,E-mail:
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47
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Ohtsuki Y, Mikami S, Ajiki T, Tannor DJ. Optimal control for maximally creating and maintaining a superposition state of a two‐level system under the influence of Markovian decoherence. J CHIN CHEM SOC-TAIP 2023. [DOI: 10.1002/jccs.202200451] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Affiliation(s)
- Yukiyoshi Ohtsuki
- Department of Chemistry, Graduate School of Science Tohoku University Sendai Japan
| | - Suicho Mikami
- Department of Chemistry, Graduate School of Science Tohoku University Sendai Japan
| | - Toru Ajiki
- Department of Chemistry, Graduate School of Science Tohoku University Sendai Japan
| | - David J. Tannor
- Department of Chemical Physics Weizmann Institute of Science Rehovot Israel
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48
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Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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49
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Gavreev MA, Kiktenko EO, Mastiukova AS, Fedorov AK. Suppressing Decoherence in Quantum State Transfer with Unitary Operations. ENTROPY (BASEL, SWITZERLAND) 2022; 25:67. [PMID: 36673212 PMCID: PMC9858199 DOI: 10.3390/e25010067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 12/25/2022] [Accepted: 12/27/2022] [Indexed: 06/17/2023]
Abstract
Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed approach for suppressing decoherence in the process of distributing a two-qubit state over remote physical qubits of a quantum processor.
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Affiliation(s)
- Maxim A. Gavreev
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
| | - Evgeniy O. Kiktenko
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
| | - Alena S. Mastiukova
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
| | - Aleksey K. Fedorov
- Russian Quantum Center, Skolkovo, Moscow 143025, Russia
- National University of Science and Technology “MISIS”, Moscow 119049, Russia
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50
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Yamamoto K, Endo S, Hakoshima H, Matsuzaki Y, Tokunaga Y. Error-Mitigated Quantum Metrology via Virtual Purification. PHYSICAL REVIEW LETTERS 2022; 129:250503. [PMID: 36608222 DOI: 10.1103/physrevlett.129.250503] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Revised: 07/13/2022] [Accepted: 08/11/2022] [Indexed: 06/17/2023]
Abstract
Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the viewpoint of reducing statistical errors under the assumption of perfect knowledge of a noise model. However, we cannot always obtain complete information about a noise model due to coherence time fluctuations, which are frequently observed in experiments. Such unknown fluctuating noise leads to systematic errors and nullifies the quantum advantages. Here, we propose an error-mitigated quantum metrology that can filter out unknown fluctuating noise with the aid of purification-based quantum error mitigation. We demonstrate that our protocol mitigates systematic errors and recovers superclassical scaling in a practical situation with time-inhomogeneous bias-inducing noise. Our result is the first demonstration to reveal the usefulness of purification-based error mitigation for unknown fluctuating noise, thus paving the way not only for practical quantum metrology but also for quantum computation affected by such noise.
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Affiliation(s)
- Kaoru Yamamoto
- NTT Computer and Data Science Laboratories, NTT Corporation, Musashino 180-8585, Japan
| | - Suguru Endo
- NTT Computer and Data Science Laboratories, NTT Corporation, Musashino 180-8585, Japan
- JST, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Hideaki Hakoshima
- Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
- Center for Quantum Information and Quantum Biology, Osaka University, 1-2 Machikaneyama, Toyonaka 560-0043, Japan
| | - Yuichiro Matsuzaki
- Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), Central2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
- NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan
| | - Yuuki Tokunaga
- NTT Computer and Data Science Laboratories, NTT Corporation, Musashino 180-8585, Japan
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