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Gu Y, Zhuang WF, Chai X, Liu DE. Benchmarking universal quantum gates via channel spectrum. Nat Commun 2023; 14:5880. [PMID: 37735170 PMCID: PMC10514318 DOI: 10.1038/s41467-023-41598-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Accepted: 09/12/2023] [Indexed: 09/23/2023] Open
Abstract
Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of global entangling gates and frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation.
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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.
| | - Wei-Feng Zhuang
- Beijing Academy of Quantum Information Sciences, Beijing, 100193, China
| | - Xudan Chai
- 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
| | - 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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2
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Characterizing large-scale quantum computers via cycle benchmarking. Nat Commun 2019; 10:5347. [PMID: 31767840 PMCID: PMC6877623 DOI: 10.1038/s41467-019-13068-7] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Accepted: 10/08/2019] [Indexed: 11/28/2022] Open
Abstract
Quantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on large-scale processors. Current characterization techniques are unable to adequately account for the exponentially large set of potential errors, including cross-talk and other correlated noise sources. Here we develop cycle benchmarking, a rigorous and practically scalable protocol for characterizing local and global errors across multi-qubit quantum processors. We experimentally demonstrate its practicality by quantifying such errors in non-entangling and entangling operations on an ion-trap quantum computer with up to 10 qubits, and total process fidelities for multi-qubit entangling gates ranging from \documentclass[12pt]{minimal}
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\begin{document}$$86(2)\%$$\end{document}86(2)% for 10 qubits. Furthermore, cycle benchmarking data validates that the error rate per single-qubit gate and per two-qubit coupling does not increase with increasing system size. Checking the quality of operations of quantum computers in a reliable and scalable way is still an open challenge. Here, the authors show how to characterise multi-qubit operations in a way that scales favourably with the system’s size, and demonstrate it on a 10-qubit ion-trap device.
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McKay DC, Sheldon S, Smolin JA, Chow JM, Gambetta JM. Three-Qubit Randomized Benchmarking. PHYSICAL REVIEW LETTERS 2019; 122:200502. [PMID: 31172740 DOI: 10.1103/physrevlett.122.200502] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 06/09/2023]
Abstract
As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate, for the first time, three-qubit randomized benchmarking (RB) on a quantum device consisting of three fixed-frequency transmon qubits with pairwise microwave-activated interactions (cross-resonance). We measure a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB-simultaneous one- and two-qubit RB-we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates, we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates the importance of multiqubit metrics, such as three-qubit RB, on evaluating overall device performance.
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Affiliation(s)
- David C McKay
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Sarah Sheldon
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - John A Smolin
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Jerry M Chow
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Jay M Gambetta
- IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
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4
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Wendin G. Quantum information processing with superconducting circuits: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:106001. [PMID: 28682303 DOI: 10.1088/1361-6633/aa7e1a] [Citation(s) in RCA: 107] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.
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Affiliation(s)
- G Wendin
- Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
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Xin T, Lu D, Klassen J, Yu N, Ji Z, Chen J, Ma X, Long G, Zeng B, Laflamme R. Quantum State Tomography via Reduced Density Matrices. PHYSICAL REVIEW LETTERS 2017; 118:020401. [PMID: 28128623 DOI: 10.1103/physrevlett.118.020401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2016] [Indexed: 06/06/2023]
Abstract
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However, it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work, we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally, we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results demonstrate the advantages and possible pitfalls of quantum state tomography with local measurements.
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Affiliation(s)
- Tao Xin
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Dawei Lu
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Joel Klassen
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
| | - Nengkun Yu
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia
- Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
| | - Zhengfeng Ji
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, New South Wales 2007, Australia
- State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, 100190 Beijing, China
| | - Jianxin Chen
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland, USA
| | - Xian Ma
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Bei Zeng
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Mathematics and Statistics, University of Guelph, Guelph, N1G 2W1 Ontario, Canada
- Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Canadian Institute for Advanced Research, Toronto, M5G 1Z8 Ontario, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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Stárek R, Mičuda M, Miková M, Straka I, Dušek M, Ježek M, Fiurášek J. Experimental investigation of a four-qubit linear-optical quantum logic circuit. Sci Rep 2016; 6:33475. [PMID: 27647176 PMCID: PMC5028834 DOI: 10.1038/srep33475] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2016] [Accepted: 08/30/2016] [Indexed: 11/24/2022] Open
Abstract
We experimentally demonstrate and characterize a four-qubit linear-optical quantum logic circuit. Our robust and versatile scheme exploits encoding of two qubits into polarization and path degrees of single photons and involves two crossed inherently stable interferometers. This approach allows us to design a complex quantum logic circuit that combines a genuine four-qubit C(3)Z gate and several two-qubit and single-qubit gates. The C(3)Z gate introduces a sign flip if and only if all four qubits are in the computational state |1〉. We verify high-fidelity performance of this central four-qubit gate using Hofmann bounds on quantum gate fidelity and Monte Carlo fidelity sampling. We also experimentally demonstrate that the quantum logic circuit can generate genuine multipartite entanglement and we certify the entanglement with the use of suitably tailored entanglement witnesses.
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Affiliation(s)
- R. Stárek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M. Mičuda
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M. Miková
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - I. Straka
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M. Dušek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - M. Ježek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - J. Fiurášek
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
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Lu D, Xin T, Yu N, Ji Z, Chen J, Long G, Baugh J, Peng X, Zeng B, Laflamme R. Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables. PHYSICAL REVIEW LETTERS 2016; 116:230501. [PMID: 27341217 DOI: 10.1103/physrevlett.116.230501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Indexed: 06/06/2023]
Abstract
Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.
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Affiliation(s)
- Dawei Lu
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
| | - Tao Xin
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Nengkun Yu
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007, Australia
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - Zhengfeng Ji
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
| | - Jianxin Chen
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jonathan Baugh
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
| | - Xinhua Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, China
| | - Bei Zeng
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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8
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Lu D, Li H, Trottier DA, Li J, Brodutch A, Krismanich AP, Ghavami A, Dmitrienko GI, Long G, Baugh J, Laflamme R. Experimental estimation of average fidelity of a Clifford gate on a 7-qubit quantum processor. PHYSICAL REVIEW LETTERS 2015; 114:140505. [PMID: 25910102 DOI: 10.1103/physrevlett.114.140505] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2014] [Indexed: 06/04/2023]
Abstract
One of the major experimental achievements in the past decades is the ability to control quantum systems to high levels of precision. To quantify the level of control we need to characterize the dynamical evolution. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10^{8} experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to at least 87.5% if the signal's decay due to decoherence is taken into account. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.
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Affiliation(s)
- Dawei Lu
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Hang Li
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Denis-Alexandre Trottier
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jun Li
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Aharon Brodutch
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Anthony P Krismanich
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Ahmad Ghavami
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Gary I Dmitrienko
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Jonathan Baugh
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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9
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Ferrie C. Self-guided quantum tomography. PHYSICAL REVIEW LETTERS 2014; 113:190404. [PMID: 25415889 DOI: 10.1103/physrevlett.113.190404] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Indexed: 06/04/2023]
Abstract
We introduce a self-learning tomographic technique in which the experiment guides itself to an estimate of its own state. Self-guided quantum tomography uses measurements to directly test hypotheses in an iterative algorithm which converges to the true state. We demonstrate through simulation on many qubits that Self-guided quantum tomography is a more efficient and robust alternative to the usual paradigm of taking a large amount of informationally complete data and solving the inverse problem of postprocessed state estimation.
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Affiliation(s)
- Christopher Ferrie
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA
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