1
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Bornet G, Emperauger G, Chen C, Machado F, Chern S, Leclerc L, Gély B, Chew YT, Barredo D, Lahaye T, Yao NY, Browaeys A. Enhancing a Many-Body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls. PHYSICAL REVIEW LETTERS 2024; 132:263601. [PMID: 38996299 DOI: 10.1103/physrevlett.132.263601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2024] [Revised: 05/01/2024] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
We implement and characterize a protocol that enables arbitrary local controls in a dipolar atom array, where the degree of freedom is encoded in a pair of Rydberg states. Our approach relies on a combination of local addressing beams and global microwave fields. Using this method, we directly prepare two different types of three-atom entangled states, including a W state and a state exhibiting finite chirality. We verify the nature of the underlying entanglement by performing quantum state tomography. Finally, leveraging our ability to measure multibasis, multibody observables, we explore the adiabatic preparation of low-energy states in a frustrated geometry consisting of a pair of triangular plaquettes. By using local addressing to tune the symmetry of the initial state, we demonstrate the ability to prepare correlated states distinguished only by correlations of their chirality (a fundamentally six-body observable). Our protocol is generic, allowing for rotations on arbitrary sub-groups of atoms within the array at arbitrary times during the experiment; this extends the scope of capabilities for quantum simulations of the dipolar XY model.
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2
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Evered SJ, Bluvstein D, Kalinowski M, Ebadi S, Manovitz T, Zhou H, Li SH, Geim AA, Wang TT, Maskara N, Levine H, Semeghini G, Greiner M, Vuletić V, Lukin MD. High-fidelity parallel entangling gates on a neutral-atom quantum computer. Nature 2023; 622:268-272. [PMID: 37821591 PMCID: PMC10567572 DOI: 10.1038/s41586-023-06481-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 07/25/2023] [Indexed: 10/13/2023]
Abstract
The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.
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Affiliation(s)
- Simon J Evered
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Dolev Bluvstein
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Sepehr Ebadi
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Tom Manovitz
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Hengyun Zhou
- Department of Physics, Harvard University, Cambridge, MA, USA
- QuEra Computing Inc., Boston, MA, USA
| | - Sophie H Li
- Department of Physics, Harvard University, Cambridge, MA, USA
| | | | - Tout T Wang
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Nishad Maskara
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Harry Levine
- Department of Physics, Harvard University, Cambridge, MA, USA
- AWS Center for Quantum Computing, Pasadena, CA, USA
| | - Giulia Semeghini
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, MA, USA
| | - Vladan Vuletić
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
- Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, MA, USA.
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3
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Partial randomized benchmarking. Sci Rep 2022; 12:10129. [PMID: 35710571 PMCID: PMC9203587 DOI: 10.1038/s41598-022-13813-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 05/26/2022] [Indexed: 11/08/2022] Open
Abstract
In randomized benchmarking of quantum logical gates, partial twirling can be used for simpler implementation, better scaling, and higher accuracy and reliability. For instance, for two-qubit gates, single-qubit twirling is easier to realize than full averaging. We analyze such simplified, partial twirling and demonstrate that, unlike for the standard randomized benchmarking, the measured decay of fidelity is a linear combination of exponentials with different decay rates (3 for two qubits and single-bit twirling). The evolution with the sequence length is governed by an iteration matrix, whose spectrum gives the decay rates. For generic two-qubit gates one slowest exponential dominates and characterizes gate errors in three channels. Its decay rate is close, but different from that in the standard randomized benchmarking, and we find the leading correction. Using relations to the local invariants of two-qubit gates we identify all exceptional gates with several slow exponentials and analyze possibilities to extract their decay rates from the measured curves.
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4
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Ferraro E, De Michielis M. On the robustness of the hybrid qubit computational gates through simulated randomized benchmarking protocols. Sci Rep 2020; 10:17780. [PMID: 33082407 PMCID: PMC7575548 DOI: 10.1038/s41598-020-74817-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 09/28/2020] [Indexed: 11/09/2022] Open
Abstract
One of the main challenges in building a quantum processor is to characterize the environmental noise. Noise characterization can be achieved by exploiting different techniques, such as randomization where several sequences of random quantum gates are applied to the qubit under test to derive statistical characteristics about the affecting noises. A scalable and robust algorithm able to benchmark the full set of Clifford gates using randomization techniques is called randomized benchmarking. In this study, we simulated randomized benchmarking protocols in a semiconducting all-electrical three-electron double-quantum dot qubit, i.e. hybrid qubit, under different error models, that include quasi-static Gaussian and the more realistic 1/f noise model, for the input controls. The average error of specific quantum computational gates is extracted through interleaved randomized benchmarking obtained including Clifford gates between the gate of interest. It provides an estimate of the fidelity as well as theoretical bounds for the average error of the gate under test.
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Affiliation(s)
- Elena Ferraro
- CNR-IMM Agrate Unit, Via C. Olivetti 2, 20864, Agrate Brianza, MB, Italy.
| | - Marco De Michielis
- CNR-IMM Agrate Unit, Via C. Olivetti 2, 20864, Agrate Brianza, MB, Italy.
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5
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Hughes AC, Schäfer VM, Thirumalai K, Nadlinger DP, Woodrow SR, Lucas DM, Ballance CJ. Benchmarking a High-Fidelity Mixed-Species Entangling Gate. PHYSICAL REVIEW LETTERS 2020; 125:080504. [PMID: 32909787 DOI: 10.1103/physrevlett.125.080504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We implement a two-qubit logic gate between a ^{43}Ca^{+} hyperfine qubit and a ^{88}Sr^{+} Zeeman qubit. For this pair of ion species, the S-P optical transitions are close enough that a single laser of wavelength 402 nm can be used to drive the gate but sufficiently well separated to give good spectral isolation and low photon scattering errors. We characterize the gate by full randomized benchmarking, gate set tomography, and Bell state analysis. The latter method gives a fidelity of 99.8(1)%, comparable to that of the best same-species gates and consistent with known sources of error.
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Affiliation(s)
- A C Hughes
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - V M Schäfer
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - K Thirumalai
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D P Nadlinger
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S R Woodrow
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D M Lucas
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - C J Ballance
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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6
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Zhang S, Lu Y, Zhang K, Chen W, Li Y, Zhang JN, Kim K. Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system. Nat Commun 2020; 11:587. [PMID: 32001680 PMCID: PMC6992797 DOI: 10.1038/s41467-020-14376-z] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2019] [Accepted: 12/13/2019] [Indexed: 11/22/2022] Open
Abstract
Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from being affordable for near-term technologies. To alleviate the detrimental effects of errors on the estimation of expectation values, quantum error mitigation techniques have been proposed, which require no additional qubit resources. Here we benchmark the performance of a quantum error mitigation technique based on probabilistic error cancellation in a trapped-ion system. Our results clearly show that effective gate fidelities exceed physical fidelities, i.e., we surpass the break-even point of eliminating gate errors, by programming quantum circuits. The error rates are effectively reduced from (1.10 ± 0.12) × 10−3 to (1.44 ± 5.28) × 10−5 and from (0.99 ± 0.06) × 10−2 to (0.96 ± 0.10) × 10−3 for single- and two-qubit gates, respectively. Our demonstration opens up the possibility of implementing high-fidelity computations on a near-term noisy quantum device. Quantum error mitigation promises to improve expectation values’ estimation without the resource overhead of quantum error correction. Here, the authors test probabilistic error cancellation using trapped ions, decreasing single- and two-qubit gates’ error rates by two and one order of magnitude respectively.
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Affiliation(s)
- Shuaining Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Yao Lu
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Kuan Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.,MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Wentao Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China
| | - Ying Li
- Graduate School of China Academy of Engineering Physics, Beijing, 100193, China.
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China. .,Beijing Academy of Quantum Information Sciences, Beijing, 100193, China.
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, China.
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7
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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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8
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Zhang L, Yu Y, Zhu C, Pei C. Noise tailoring for quantum circuits via unitary 2t-design. Sci Rep 2019; 9:1790. [PMID: 30741965 PMCID: PMC6370869 DOI: 10.1038/s41598-018-38158-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2018] [Accepted: 12/20/2018] [Indexed: 11/09/2022] Open
Abstract
Because of environmental variations and imperfect operations, real-world quantum computers produce different coherent errors that are difficult to estimate. Here, we propose a method whereby the twirled noise over a unitary 2t-design (a set of unitary matrices that approximate the entire unitary group) for quantum circuits can be tailored into stochastic noise. Then, we prove that local random circuits for twirling separable noisy channel over the Clifford group can be used to construct a unitary 2t-design, which is easy to implement in experiments. Moreover, we prove that our method is robust to gate-dependent and gate-independent noise. The stochastic noise can be both estimated by average fidelity and directly obtained by randomized benchmarking via unitary 2t-designs. Obtaining such tailored noise is an important guarantee for achieving fault-tolerant quantum computation.
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Affiliation(s)
- Linxi Zhang
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
- Science and Technology on Communication Networks Laboratory, Shijiazhuang, 050081, China
| | - Yan Yu
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China.
| | - Changhua Zhu
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
| | - Changxing Pei
- State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an, 710071, China
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9
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Reagor M, Osborn CB, Tezak N, Staley A, Prawiroatmodjo G, Scheer M, Alidoust N, Sete EA, Didier N, da Silva MP, Acala E, Angeles J, Bestwick A, Block M, Bloom B, Bradley A, Bui C, Caldwell S, Capelluto L, Chilcott R, Cordova J, Crossman G, Curtis M, Deshpande S, El Bouayadi T, Girshovich D, Hong S, Hudson A, Karalekas P, Kuang K, Lenihan M, Manenti R, Manning T, Marshall J, Mohan Y, O’Brien W, Otterbach J, Papageorge A, Paquette JP, Pelstring M, Polloreno A, Rawat V, Ryan CA, Renzas R, Rubin N, Russel D, Rust M, Scarabelli D, Selvanayagam M, Sinclair R, Smith R, Suska M, To TW, Vahidpour M, Vodrahalli N, Whyland T, Yadav K, Zeng W, Rigetti CT. Demonstration of universal parametric entangling gates on a multi-qubit lattice. SCIENCE ADVANCES 2018; 4:eaao3603. [PMID: 29423443 PMCID: PMC5804605 DOI: 10.1126/sciadv.aao3603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Accepted: 01/03/2018] [Indexed: 06/07/2023]
Abstract
We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gate set for a linear array of four superconducting qubits. An average process fidelity of ℱ = 93% is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity with the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all these permutations, an average fidelity of ℱ = 91.6 ± 2.6% is observed. These results thus offer a path to a scalable architecture with high selectivity and low cross-talk.
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10
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Kueng R, Long DM, Doherty AC, Flammia ST. Comparing Experiments to the Fault-Tolerance Threshold. PHYSICAL REVIEW LETTERS 2016; 117:170502. [PMID: 27824464 DOI: 10.1103/physrevlett.117.170502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2015] [Indexed: 06/06/2023]
Abstract
Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.
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Affiliation(s)
- Richard Kueng
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
- Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
- Institute for Physics and FDM, University of Freiburg, D-79104 Freiburg, Germany
| | - David M Long
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
| | - Andrew C Doherty
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
| | - Steven T Flammia
- Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia
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11
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Ballance CJ, Harty TP, Linke NM, Sepiol MA, Lucas DM. High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits. PHYSICAL REVIEW LETTERS 2016; 117:060504. [PMID: 27541450 DOI: 10.1103/physrevlett.117.060504] [Citation(s) in RCA: 117] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2015] [Indexed: 05/02/2023]
Abstract
We demonstrate laser-driven two-qubit and single-qubit logic gates with respective fidelities 99.9(1)% and 99.9934(3)%, significantly above the ≈99% minimum threshold level required for fault-tolerant quantum computation, using qubits stored in hyperfine ground states of calcium-43 ions held in a room-temperature trap. We study the speed-fidelity trade-off for the two-qubit gate, for gate times between 3.8 μs and 520 μs, and develop a theoretical error model which is consistent with the data and which allows us to identify the principal technical sources of infidelity.
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Affiliation(s)
- C J Ballance
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - T P Harty
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - N M Linke
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M A Sepiol
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D M Lucas
- Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
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12
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Gaebler JP, Tan TR, Lin Y, Wan Y, Bowler R, Keith AC, Glancy S, Coakley K, Knill E, Leibfried D, Wineland DJ. High-Fidelity Universal Gate Set for ^{9}Be^{+} Ion Qubits. PHYSICAL REVIEW LETTERS 2016; 117:060505. [PMID: 27541451 DOI: 10.1103/physrevlett.117.060505] [Citation(s) in RCA: 95] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2016] [Indexed: 06/06/2023]
Abstract
We report high-fidelity laser-beam-induced quantum logic gates on magnetic-field-insensitive qubits comprised of hyperfine states in ^{9}Be^{+} ions with a memory coherence time of more than 1 s. We demonstrate single-qubit gates with an error per gate of 3.8(1)×10^{-5}. By creating a Bell state with a deterministic two-qubit gate, we deduce a gate error of 8(4)×10^{-4}. We characterize the errors in our implementation and discuss methods to further reduce imperfections towards values that are compatible with fault-tolerant processing at realistic overhead.
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Affiliation(s)
- J P Gaebler
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T R Tan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Y Lin
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - Y Wan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - R Bowler
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - A C Keith
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - S Glancy
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - K Coakley
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - E Knill
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D J Wineland
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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13
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de Clercq LE, Lo HY, Marinelli M, Nadlinger D, Oswald R, Negnevitsky V, Kienzler D, Keitch B, Home JP. Parallel Transport Quantum Logic Gates with Trapped Ions. PHYSICAL REVIEW LETTERS 2016; 116:080502. [PMID: 26967401 DOI: 10.1103/physrevlett.116.080502] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2015] [Indexed: 06/05/2023]
Abstract
We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.
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Affiliation(s)
- Ludwig E de Clercq
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Hsiang-Yu Lo
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Matteo Marinelli
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - David Nadlinger
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Robin Oswald
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Vlad Negnevitsky
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Daniel Kienzler
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Ben Keitch
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - Jonathan P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
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14
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Xia T, Lichtman M, Maller K, Carr AW, Piotrowicz MJ, Isenhower L, Saffman M. Randomized benchmarking of single-qubit gates in a 2D array of neutral-atom qubits. PHYSICAL REVIEW LETTERS 2015; 114:100503. [PMID: 25815916 DOI: 10.1103/physrevlett.114.100503] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2015] [Indexed: 06/04/2023]
Abstract
We characterize single-qubit Clifford gate operations with randomized benchmarking in a 2D array of neutral-atom qubits and demonstrate global and site selected gates with high fidelity. An average fidelity of F2=0.9983(14) is measured for global microwave-driven gates applied to a 49-qubit array. Single-site gates are implemented with a focused laser beam to Stark shift the microwaves into resonance at a selected site. At Stark selected single sites we observe F2=0.9923(7) and an average spin-flip crosstalk error at other sites of 0.002(9).
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Affiliation(s)
- T Xia
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - M Lichtman
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - K Maller
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - A W Carr
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - M J Piotrowicz
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - L Isenhower
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
| | - M Saffman
- Department of Physics, University of Wisconsin, 1150 University Avenue, Madison, Wisconsin 53706, USA
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15
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Schwemmer C, Knips L, Richart D, Weinfurter H, Moroder T, Kleinmann M, Gühne O. Systematic errors in current quantum state tomography tools. PHYSICAL REVIEW LETTERS 2015; 114:080403. [PMID: 25768740 DOI: 10.1103/physrevlett.114.080403] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2013] [Indexed: 06/04/2023]
Abstract
Common tools for obtaining physical density matrices in experimental quantum state tomography are shown here to cause systematic errors. For example, using maximum likelihood or least squares optimization to obtain physical estimates for the quantum state, we observe a systematic underestimation of the fidelity and an overestimation of entanglement. Such strongly biased estimates can be avoided using linear evaluation of the data or by linearizing measurement operators yielding reliable and computational simple error bounds.
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Affiliation(s)
- Christian Schwemmer
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany and Department für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany
| | - Lukas Knips
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany and Department für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany
| | - Daniel Richart
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany and Department für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany
| | - Harald Weinfurter
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany and Department für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany
| | - Tobias Moroder
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
| | - Matthias Kleinmann
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
- Departamento de Matemtica, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, Minas Gerais 31270-901, Brazil
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
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16
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Gebert F, Frosz MH, Weiss T, Wan Y, Ermolov A, Joly NY, Schmidt PO, Russell PSJ. Damage-free single-mode transmission of deep-UV light in hollow-core PCF. OPTICS EXPRESS 2014; 22:15388-15396. [PMID: 24977799 DOI: 10.1364/oe.22.015388] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Transmission of UV light with high beam quality and pointing stability is desirable for many experiments in atomic, molecular and optical physics. In particular, laser cooling and coherent manipulation of trapped ions with transitions in the UV require stable, single-mode light delivery. Transmitting even ~2 mW CW light at 280 nm through silica solid-core fibers has previously been found to cause transmission degradation after just a few hours due to optical damage. We show that photonic crystal fiber of the kagomé type can be used for effectively single-mode transmission with acceptable loss and bending sensitivity. No transmission degradation was observed even after >100 hours of operation with 15 mW CW input power. In addition it is shown that implementation of the fiber in a trapped ion experiment increases the coherence time of the internal state transfer due to an increase in beam pointing stability.
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17
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Barrett J, Cavalcanti EG, Lal R, Maroney OJE. No ψ-epistemic model can fully explain the indistinguishability of quantum states. PHYSICAL REVIEW LETTERS 2014; 112:250403. [PMID: 25014796 DOI: 10.1103/physrevlett.112.250403] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2013] [Indexed: 06/03/2023]
Abstract
According to a recent no-go theorem [M. Pusey, J. Barrett and T. Rudolph, Nat. Phys. 8, 475 (2012)], models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have the following feature: the distributions corresponding to distinct quantum states do not overlap. In such a model, it cannot coherently be maintained that the quantum state merely encodes information about underlying physical variables. The theorem, however, considers only models in which the physical variables corresponding to independently prepared systems are independent, and this has been used to challenge the conclusions of that work. Here we consider models that are defined for a single quantum system of dimension d, such that the independence condition does not arise, and derive an upper bound on the extent to which the probability distributions can overlap. In particular, models in which the quantum overlap between pure states is equal to the classical overlap between the corresponding probability distributions cannot reproduce the quantum predictions in any dimension d ≥ 3. Thus any ontological model for quantum theory must postulate some extra principle, such as a limitation on the measurability of physical variables, to explain the indistinguishability of quantum states. Moreover, we show that as d→∞, the ratio of classical and quantum overlaps goes to zero for a class of states. The result is noise tolerant, and an experiment is motivated to distinguish the class of models ruled out from quantum theory.
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Affiliation(s)
- Jonathan Barrett
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom
| | - Eric G Cavalcanti
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom and School of Physics, The University of Sydney, Sydney NSW 2016, Australia
| | - Raymond Lal
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, United Kingdom
| | - Owen J E Maroney
- Faculty of Philosophy, University of Oxford, Oxford OX2 6GG, United Kingdom
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18
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Tan TR, Gaebler JP, Bowler R, Lin Y, Jost JD, Leibfried D, Wineland DJ. Demonstration of a dressed-state phase gate for trapped ions. PHYSICAL REVIEW LETTERS 2013; 110:263002. [PMID: 23848869 DOI: 10.1103/physrevlett.110.263002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2013] [Indexed: 06/02/2023]
Abstract
We demonstrate a trapped-ion entangling-gate scheme proposed by Bermudez et al. [Phys. Rev. A 85, 040302 (2012)]. Simultaneous excitation of a strong carrier and a single-sideband transition enables deterministic creation of entangled states. The method works for magnetic field-insensitive states, is robust against thermal excitations, includes dynamical decoupling from qubit dephasing errors, and provides simplifications in experimental implementation compared to some other entangling gates with trapped ions. We achieve a Bell state fidelity of 0.974(4) and identify the main sources of error.
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Affiliation(s)
- T R Tan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA.
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19
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Warring U, Ospelkaus C, Colombe Y, Jördens R, Leibfried D, Wineland DJ. Individual-ion addressing with microwave field gradients. PHYSICAL REVIEW LETTERS 2013; 110:173002. [PMID: 23679718 DOI: 10.1103/physrevlett.110.173002] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2012] [Indexed: 06/02/2023]
Abstract
Individual-qubit addressing is a prerequisite for many instances of quantum information processing. We demonstrate this capability on trapped-ion qubits with microwave near fields delivered by electrode structures integrated into a microfabricated surface-electrode trap. We describe four approaches that may be used in quantum information experiments with hyperfine levels as qubits. We implement individual control on two 25Mg+ ions separated by 4.3 μm and find spin-flip crosstalk errors on the order of 10(-3).
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Affiliation(s)
- U Warring
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA.
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20
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Lin Y, Gaebler JP, Tan TR, Bowler R, Jost JD, Leibfried D, Wineland DJ. Sympathetic electromagnetically-induced-transparency laser cooling of motional modes in an ion chain. PHYSICAL REVIEW LETTERS 2013; 110:153002. [PMID: 25167259 DOI: 10.1103/physrevlett.110.153002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2012] [Indexed: 06/03/2023]
Abstract
We use electromagnetically-induced-transparency laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply electromagnetically-induced-transparency cooling on 24Mg+ ions to cool the axial modes of a 9Be+-24Mg+ ion pair and a 9Be+-24Mg+-24Mg+-9Be+ ion chain, thereby sympathetically cooling the 9Be+ ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required laser intensity.
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Affiliation(s)
- Y Lin
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - J P Gaebler
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - T R Tan
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - R Bowler
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - J D Jost
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D Leibfried
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - D J Wineland
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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21
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Bowler R, Warring U, Britton JW, Sawyer BC, Amini J. Arbitrary waveform generator for quantum information processing with trapped ions. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2013; 84:033108. [PMID: 23556808 DOI: 10.1063/1.4795552] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
Atomic ions confined in multi-electrode traps have been proposed as a basis for scalable quantum information processing. This scheme involves transporting ions between spatially distinct locations by use of time-varying electric potentials combined with laser or microwave pulses for quantum logic in specific locations. We report the development of a fast multi-channel arbitrary waveform generator for applying the time-varying electric potentials used for transport and for shaping quantum logic pulses. The generator is based on a field-programmable gate array controlled ensemble of 16-bit digital-to-analog converters with an update frequency of 50 MHz and an output range of ±10 V. The update rate of the waveform generator is much faster than relevant motional frequencies of the confined ions in our experiments, allowing diabatic control of the ion motion. Numerous pre-loaded sets of time-varying voltages can be selected with 40 ns latency conditioned on real-time signals. Here we describe the device and demonstrate some of its uses in ion-based quantum information experiments, including speed-up of ion transport and the shaping of laser and microwave pulses.
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Affiliation(s)
- R Bowler
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA.
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22
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Gambetta JM, Córcoles AD, Merkel ST, Johnson BR, Smolin JA, Chow JM, Ryan CA, Rigetti C, Poletto S, Ohki TA, Ketchen MB, Steffen M. Characterization of addressability by simultaneous randomized benchmarking. PHYSICAL REVIEW LETTERS 2012; 109:240504. [PMID: 23368295 DOI: 10.1103/physrevlett.109.240504] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2012] [Revised: 10/24/2012] [Indexed: 06/01/2023]
Abstract
The control and handling of errors arising from cross talk and unwanted interactions in multiqubit systems is an important issue in quantum information processing architectures. We introduce a benchmarking protocol that provides information about the amount of addressability present in the system and implement it on coupled superconducting qubits. The protocol consists of randomized benchmarking experiments run both individually and simultaneously on pairs of qubits. A relevant figure of merit for the addressability is then related to the differences in the measured average gate fidelities in the two experiments. We present results from two similar samples with differing cross talk and unwanted qubit-qubit interactions. The results agree with predictions based on simple models of the classical cross talk and Stark shifts.
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Affiliation(s)
- Jay M Gambetta
- IBM TJ Watson Research Center, Yorktown Heights, New York 10598, USA
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23
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Mari A, Eisert J. Positive Wigner functions render classical simulation of quantum computation efficient. PHYSICAL REVIEW LETTERS 2012; 109:230503. [PMID: 23368175 DOI: 10.1103/physrevlett.109.230503] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2012] [Indexed: 06/01/2023]
Abstract
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.
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Affiliation(s)
- A Mari
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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24
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Fowler AG. Proof of finite surface code threshold for matching. PHYSICAL REVIEW LETTERS 2012; 109:180502. [PMID: 23215261 DOI: 10.1103/physrevlett.109.180502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2012] [Indexed: 06/01/2023]
Abstract
The field of quantum computation currently lacks a formal proof of experimental feasibility. Qubits are fragile and sophisticated quantum error correction is required to achieve reliable quantum computation. The surface code is a promising quantum error correction code, requiring only a physically reasonable 2D lattice of qubits with nearest neighbor interactions. However, existing proofs that reliable quantum computation is possible using this code assume the ability to measure four-body operators and, despite making this difficult to realize assumption, require that the error rate of these operator measurements is less than 10(-9), an unphysically low target. High error rates have been proved tolerable only when assuming tunable interactions of strength and error rate independent of distance, which is also unphysical. In this work, given a 2D lattice of qubits with only nearest neighbor two-qubit gates, and single-qubit measurement, initialization, and unitary gates, all of which have error rate p, we prove that arbitrarily reliable quantum computation is possible provided p < 7.4 × 10(-4), a target that many experiments have already achieved. This closes a long-standing open problem, formally proving the experimental feasibility of quantum computation under physically reasonable assumptions.
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Affiliation(s)
- Austin G Fowler
- Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Melbourne, Victoria 3010, Australia
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