1
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Rosenberg E, Andersen TI, Samajdar R, Petukhov A, Hoke JC, Abanin D, Bengtsson A, Drozdov IK, Erickson C, Klimov PV, Mi X, Morvan A, Neeley M, Neill C, Acharya R, Allen R, Anderson K, Ansmann M, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Bilmes A, Bortoli G, Bourassa A, Bovaird J, Brill L, Broughton M, Buckley BB, Buell DA, Burger T, Burkett B, Bushnell N, Campero J, Chang HS, Chen Z, Chiaro B, Chik D, Cogan J, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Debroy DM, Barba ADT, Demura S, Di Paolo A, Dunsworth A, Earle C, Faoro L, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, Garcia G, Genois É, Giang W, Gidney C, Gilboa D, Giustina M, Gosula R, Dau AG, Gross JA, Habegger S, Hamilton MC, Hansen M, Harrigan MP, Harrington SD, Heu P, Hill G, Hoffmann MR, Hong S, Huang T, Huff A, Huggins WJ, Ioffe LB, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Juhas P, Kafri D, Khattar T, Khezri M, Kieferová M, Kim S, Kitaev A, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lensky YD, Lester BJ, Lill AT, Liu W, Locharla A, Mandrà S, Martin O, Martin S, McClean JR, McEwen M, Meeks S, Miao KC, Mieszala A, Montazeri S, Movassagh R, Mruczkiewicz W, Nersisyan A, Newman M, Ng JH, Nguyen A, Nguyen M, Niu MY, O'Brien TE, Omonije S, Opremcak A, Potter R, Pryadko LP, Quintana C, Rhodes DM, Rocque C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schurkus HF, Schuster C, Shearn MJ, Shorter A, Shutty N, Shvarts V, Sivak V, Skruzny J, Smith WC, Somma RD, Sterling G, Strain D, Szalay M, Thor D, Torres A, Vidal G, Villalonga B, Heidweiller CV, White T, Woo BWK, Xing C, Yao ZJ, Yeh P, Yoo J, Young G, Zalcman A, Zhang Y, Zhu N, Zobrist N, Neven H, Babbush R, Bacon D, Boixo S, Hilton J, Lucero E, Megrant A, Kelly J, Chen Y, Smelyanskiy V, Khemani V, Gopalakrishnan S, Prosen T, Roushan P. Dynamics of magnetization at infinite temperature in a Heisenberg spin chain. Science 2024; 384:48-53. [PMID: 38574139 DOI: 10.1126/science.adi7877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 03/01/2024] [Indexed: 04/06/2024]
Abstract
Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.
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Affiliation(s)
- E Rosenberg
- Google Research, Mountain View, CA, USA
- Department of Physics, Cornell University, Ithaca, NY, USA
| | | | - R Samajdar
- Department of Physics, Princeton University, Princeton, NJ, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA
| | | | - J C Hoke
- Department of Physics, Stanford University, Stanford, CA, USA
| | - D Abanin
- Google Research, Mountain View, CA, USA
| | | | - I K Drozdov
- Google Research, Mountain View, CA, USA
- Department of Physics, University of Connecticut, Storrs, CT, USA
| | | | | | - X Mi
- Google Research, Mountain View, CA, USA
| | - A Morvan
- Google Research, Mountain View, CA, USA
| | - M Neeley
- Google Research, Mountain View, CA, USA
| | - C Neill
- Google Research, Mountain View, CA, USA
| | - R Acharya
- Google Research, Mountain View, CA, USA
| | - R Allen
- Google Research, Mountain View, CA, USA
| | | | - M Ansmann
- Google Research, Mountain View, CA, USA
| | - F Arute
- Google Research, Mountain View, CA, USA
| | - K Arya
- Google Research, Mountain View, CA, USA
| | - A Asfaw
- Google Research, Mountain View, CA, USA
| | - J Atalaya
- Google Research, Mountain View, CA, USA
| | - J C Bardin
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | - A Bilmes
- Google Research, Mountain View, CA, USA
| | - G Bortoli
- Google Research, Mountain View, CA, USA
| | | | - J Bovaird
- Google Research, Mountain View, CA, USA
| | - L Brill
- Google Research, Mountain View, CA, USA
| | | | | | - D A Buell
- Google Research, Mountain View, CA, USA
| | - T Burger
- Google Research, Mountain View, CA, USA
| | - B Burkett
- Google Research, Mountain View, CA, USA
| | | | - J Campero
- Google Research, Mountain View, CA, USA
| | - H-S Chang
- Google Research, Mountain View, CA, USA
| | - Z Chen
- Google Research, Mountain View, CA, USA
| | - B Chiaro
- Google Research, Mountain View, CA, USA
| | - D Chik
- Google Research, Mountain View, CA, USA
| | - J Cogan
- Google Research, Mountain View, CA, USA
| | - R Collins
- Google Research, Mountain View, CA, USA
| | - P Conner
- Google Research, Mountain View, CA, USA
| | | | - A L Crook
- Google Research, Mountain View, CA, USA
| | - B Curtin
- Google Research, Mountain View, CA, USA
| | | | | | - S Demura
- Google Research, Mountain View, CA, USA
| | | | | | - C Earle
- Google Research, Mountain View, CA, USA
| | - L Faoro
- Google Research, Mountain View, CA, USA
| | - E Farhi
- Google Research, Mountain View, CA, USA
| | - R Fatemi
- Google Research, Mountain View, CA, USA
| | | | | | - E Forati
- Google Research, Mountain View, CA, USA
| | | | - B Foxen
- Google Research, Mountain View, CA, USA
| | - G Garcia
- Google Research, Mountain View, CA, USA
| | - É Genois
- Google Research, Mountain View, CA, USA
| | - W Giang
- Google Research, Mountain View, CA, USA
| | - C Gidney
- Google Research, Mountain View, CA, USA
| | - D Gilboa
- Google Research, Mountain View, CA, USA
| | | | - R Gosula
- Google Research, Mountain View, CA, USA
| | | | - J A Gross
- Google Research, Mountain View, CA, USA
| | | | - M C Hamilton
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, Auburn University, Auburn, AL, USA
| | - M Hansen
- Google Research, Mountain View, CA, USA
| | | | | | - P Heu
- Google Research, Mountain View, CA, USA
| | - G Hill
- Google Research, Mountain View, CA, USA
| | | | - S Hong
- Google Research, Mountain View, CA, USA
| | - T Huang
- Google Research, Mountain View, CA, USA
| | - A Huff
- Google Research, Mountain View, CA, USA
| | | | - L B Ioffe
- Google Research, Mountain View, CA, USA
| | | | - J Iveland
- Google Research, Mountain View, CA, USA
| | - E Jeffrey
- Google Research, Mountain View, CA, USA
| | - Z Jiang
- Google Research, Mountain View, CA, USA
| | - C Jones
- Google Research, Mountain View, CA, USA
| | - P Juhas
- Google Research, Mountain View, CA, USA
| | - D Kafri
- Google Research, Mountain View, CA, USA
| | - T Khattar
- Google Research, Mountain View, CA, USA
| | - M Khezri
- Google Research, Mountain View, CA, USA
| | - M Kieferová
- Google Research, Mountain View, CA, USA
- QSI, Faculty of Engineering & Information Technology, University of Technology Sydney, Ultimo, NSW, Australia
| | - S Kim
- Google Research, Mountain View, CA, USA
| | - A Kitaev
- Google Research, Mountain View, CA, USA
| | - A R Klots
- Google Research, Mountain View, CA, USA
| | - A N Korotkov
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | | | - P Laptev
- Google Research, Mountain View, CA, USA
| | - K-M Lau
- Google Research, Mountain View, CA, USA
| | - L Laws
- Google Research, Mountain View, CA, USA
| | - J Lee
- Google Research, Mountain View, CA, USA
- Department of Chemistry, Columbia University, New York, NY, USA
| | - K W Lee
- Google Research, Mountain View, CA, USA
| | | | | | - A T Lill
- Google Research, Mountain View, CA, USA
| | - W Liu
- Google Research, Mountain View, CA, USA
| | | | - S Mandrà
- Google Research, Mountain View, CA, USA
| | - O Martin
- Google Research, Mountain View, CA, USA
| | - S Martin
- Google Research, Mountain View, CA, USA
| | | | - M McEwen
- Google Research, Mountain View, CA, USA
| | - S Meeks
- Google Research, Mountain View, CA, USA
| | - K C Miao
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - M Newman
- Google Research, Mountain View, CA, USA
| | - J H Ng
- Google Research, Mountain View, CA, USA
| | - A Nguyen
- Google Research, Mountain View, CA, USA
| | - M Nguyen
- Google Research, Mountain View, CA, USA
| | - M Y Niu
- Google Research, Mountain View, CA, USA
| | | | - S Omonije
- Google Research, Mountain View, CA, USA
| | | | - R Potter
- Google Research, Mountain View, CA, USA
| | - L P Pryadko
- Department of Physics and Astronomy, University of California, Riverside, CA, USA
| | | | | | - C Rocque
- Google Research, Mountain View, CA, USA
| | - N C Rubin
- Google Research, Mountain View, CA, USA
| | - N Saei
- Google Research, Mountain View, CA, USA
| | - D Sank
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - A Shorter
- Google Research, Mountain View, CA, USA
| | - N Shutty
- Google Research, Mountain View, CA, USA
| | - V Shvarts
- Google Research, Mountain View, CA, USA
| | - V Sivak
- Google Research, Mountain View, CA, USA
| | - J Skruzny
- Google Research, Mountain View, CA, USA
| | | | - R D Somma
- Google Research, Mountain View, CA, USA
| | | | - D Strain
- Google Research, Mountain View, CA, USA
| | - M Szalay
- Google Research, Mountain View, CA, USA
| | - D Thor
- Google Research, Mountain View, CA, USA
| | - A Torres
- Google Research, Mountain View, CA, USA
| | - G Vidal
- Google Research, Mountain View, CA, USA
| | | | | | - T White
- Google Research, Mountain View, CA, USA
| | - B W K Woo
- Google Research, Mountain View, CA, USA
| | - C Xing
- Google Research, Mountain View, CA, USA
| | | | - P Yeh
- Google Research, Mountain View, CA, USA
| | - J Yoo
- Google Research, Mountain View, CA, USA
| | - G Young
- Google Research, Mountain View, CA, USA
| | - A Zalcman
- Google Research, Mountain View, CA, USA
| | - Y Zhang
- Google Research, Mountain View, CA, USA
| | - N Zhu
- Google Research, Mountain View, CA, USA
| | - N Zobrist
- Google Research, Mountain View, CA, USA
| | - H Neven
- Google Research, Mountain View, CA, USA
| | - R Babbush
- Google Research, Mountain View, CA, USA
| | - D Bacon
- Google Research, Mountain View, CA, USA
| | - S Boixo
- Google Research, Mountain View, CA, USA
| | - J Hilton
- Google Research, Mountain View, CA, USA
| | - E Lucero
- Google Research, Mountain View, CA, USA
| | - A Megrant
- Google Research, Mountain View, CA, USA
| | - J Kelly
- Google Research, Mountain View, CA, USA
| | - Y Chen
- Google Research, Mountain View, CA, USA
| | | | - V Khemani
- Department of Physics, Stanford University, Stanford, CA, USA
| | | | - T Prosen
- Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
| | - P Roushan
- Google Research, Mountain View, CA, USA
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2
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Xiao X, Zhao H, Ren J, Fang WH, Li Z. Physics-Constrained Hardware-Efficient Ansatz on Quantum Computers That Is Universal, Systematically Improvable, and Size-Consistent. J Chem Theory Comput 2024; 20:1912-1922. [PMID: 38354395 DOI: 10.1021/acs.jctc.3c00966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2024]
Abstract
Variational wave function ansätze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach a certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than 10 qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.
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Affiliation(s)
- Xiaoxiao Xiao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Hewang Zhao
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Jiajun Ren
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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3
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Kim K, Lim S, Shin K, Lee G, Jung Y, Kyoung W, Rhee JKK, Rhee YM. Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections. Phys Chem Chem Phys 2024; 26:8390-8396. [PMID: 38406868 DOI: 10.1039/d3cp05570a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/27/2024]
Abstract
The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.
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Affiliation(s)
- Kyungmin Kim
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
| | - Sumin Lim
- Department of Physics, KAIST, Daejeon, 34141, Republic of Korea
| | - Kyujin Shin
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - Gwonhak Lee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
| | - Yousung Jung
- Department of Chemical Engineering, Seoul National University, Seoul, 08826, Republic of Korea
| | - Woomin Kyoung
- Materials Research & Engineering Center, CTO Division, Hyundai Motor Company, Uiwang 16082, Republic of Korea
| | - June-Koo Kevin Rhee
- School of Electrical Engineering, KAIST, Daejeon, 34141, Republic of Korea.
- KAIST ITRC of Quantum Computing for AI, KAIST, Daejeon, 34141, Republic of Korea
- KAIST Institute for IT Convergence, KAIST, Daejeon, 34141, Republic of Korea
| | - Young Min Rhee
- Department of Chemistry, KAIST, Daejeon, 34141, Republic of Korea.
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4
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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5
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Hoke JC, Ippoliti M, Rosenberg E, Abanin D, Acharya R, Andersen TI, Ansmann M, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Bengtsson A, Bortoli G, Bourassa A, Bovaird J, Brill L, Broughton M, Buckley BB, Buell DA, Burger T, Burkett B, Bushnell N, Chen Z, Chiaro B, Chik D, Cogan J, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Dau AG, Debroy DM, Del Toro Barba A, Demura S, Di Paolo A, Drozdov IK, Dunsworth A, Eppens D, Erickson C, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, Giang W, Gidney C, Gilboa D, Giustina M, Gosula R, Gross JA, Habegger S, Hamilton MC, Hansen M, Harrigan MP, Harrington SD, Heu P, Hoffmann MR, Hong S, Huang T, Huff A, Huggins WJ, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Juhas P, Kafri D, Kechedzhi K, Khattar T, Khezri M, Kieferová M, Kim S, Kitaev A, Klimov PV, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lensky YD, Lester BJ, Lill AT, Liu W, Locharla A, Martin O, McClean JR, McEwen M, Miao KC, Mieszala A, Montazeri S, Morvan A, Movassagh R, Mruczkiewicz W, Neeley M, Neill C, Nersisyan A, Newman M, Ng JH, Nguyen A, Nguyen M, Niu MY, O’Brien TE, Omonije S, Opremcak A, Petukhov A, Potter R, Pryadko LP, Quintana C, Rocque C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schurkus HF, Schuster C, Shearn MJ, Shorter A, Shutty N, Shvarts V, Skruzny J, Smith WC, Somma R, Sterling G, Strain D, Szalay M, Torres A, Vidal G, Villalonga B, Heidweiller CV, White T, Woo BWK, Xing C, Yao ZJ, Yeh P, Yoo J, Young G, Zalcman A, Zhang Y, Zhu N, Zobrist N, Neven H, Babbush R, Bacon D, Boixo S, Hilton J, Lucero E, Megrant A, Kelly J, Chen Y, Smelyanskiy V, Mi X, Khemani V, Roushan P. Measurement-induced entanglement and teleportation on a noisy quantum processor. Nature 2023; 622:481-486. [PMID: 37853150 PMCID: PMC10584681 DOI: 10.1038/s41586-023-06505-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Accepted: 08/01/2023] [Indexed: 10/20/2023]
Abstract
Measurement has a special role in quantum theory1: by collapsing the wavefunction, it can enable phenomena such as teleportation2 and thereby alter the 'arrow of time' that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time3-10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium11-13. For present-day noisy intermediate-scale quantum (NISQ) processors14, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping9,15-17 to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling3,4 to measurement-induced teleportation18. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors.
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6
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Choi JR. Dynamics of Dispersive Measurements of Flux-Qubit States: Energy-Level Splitting Connected to Quantum Wave Mechanics. Nanomaterials (Basel) 2023; 13:2395. [PMID: 37686903 PMCID: PMC10490274 DOI: 10.3390/nano13172395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Revised: 08/09/2023] [Accepted: 08/16/2023] [Indexed: 09/10/2023]
Abstract
Superconducting flux qubits have many advantages as a storage of quantum information, such as broad range tunability of frequency, small-size fabricability, and high controllability. In the flux qubit-oscillator, qubits are connected to SQUID resonators for the purpose of performing dispersive non-destructive readouts of qubit signals with high fidelity. In this work, we propose a theoretical model for analyzing quantum characteristics of a flux qubit-oscillator on the basis of quantum solutions obtained using a unitary transformation approach. The energy levels of the combined system (qubit + resonator) are analyzed in detail. Equally spaced each energy level of the resonator splits into two parts depending on qubit states. Besides, coupling of the qubit to the resonator brings about an additional modification in the split energy levels. So long as the coupling strength and the tunnel splitting are not zero but finite values, the energy-level splitting of the resonator does not disappear. We conclude that quantum nondemolition dispersive measurements of the qubit states are possible by inducing bifurcation of the resonator states through the coupling.
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Affiliation(s)
- Jeong Ryeol Choi
- School of Electronic Engineering, Kyonggi University, Yeongtong-gu, Suwon 16227, Gyeonggi-do, Republic of Korea
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7
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Shaib A, Naim MH, Fouda ME, Kanj R, Kurdahi F. Efficient noise mitigation technique for quantum computing. Sci Rep 2023; 13:3912. [PMID: 36890156 DOI: 10.1038/s41598-023-30510-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [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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8
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Abstract
Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10-6 logical error per cycle floor set by a single high-energy event (1.6 × 10-7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.
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9
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Luo K, Huang W, Tao Z, Zhang L, Zhou Y, Chu J, Liu W, Wang B, Cui J, Liu S, Yan F, Yung MH, Chen Y, Yan T, Yu D. Experimental Realization of Two Qutrits Gate with Tunable Coupling in Superconducting Circuits. Phys Rev Lett 2023; 130:030603. [PMID: 36763397 DOI: 10.1103/physrevlett.130.030603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multidimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this Letter, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low crosstalk between qutrits, thus being friendly for scaling up. Our Letter constitutes an important step toward scalable qutrit-based quantum computation.
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Affiliation(s)
- Kai Luo
- Department of Physics, Harbin Institute of Technology, Harbin 150001, China
- 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
| | - Wenhui Huang
- 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
| | - Ziyu Tao
- 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
| | - Libo 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
| | - Yuxuan Zhou
- 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
| | - Ji Chu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Wuxin Liu
- Central Research Institute, 2012 Labs, Huawei Technologies, Shenzhen, 518129, China
| | - Biying Wang
- Central Research Institute, 2012 Labs, Huawei Technologies, Shenzhen, 518129, China
| | - Jiangyu Cui
- Central Research Institute, 2012 Labs, Huawei Technologies, Shenzhen, 518129, China
| | - Song Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, China
| | - Fei Yan
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, 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
- Central Research Institute, 2012 Labs, Huawei Technologies, Shenzhen, 518129, China
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, China
| | - Yuanzhen Chen
- 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
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, China
| | - Tongxing Yan
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, China
| | - Dapeng Yu
- 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
- Guangdong Provincial Key Laboratory of 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
- International Quantum Academy, Shenzhen 518048, China
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10
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Horová N, Stárek R, Mičuda M, Kolář M, Fiurášek J, Filip R. Deterministic controlled enhancement of local quantum coherence. Sci Rep 2022; 12:22455. [PMID: 36575239 DOI: 10.1038/s41598-022-26450-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/14/2022] [Indexed: 12/28/2022] Open
Abstract
We investigate assisted enhancement of quantum coherence in a bipartite setting with control and target systems, which converts the coherence of the control qubit into the enhanced coherence of the target qubit. We assume that only incoherent operations and measurements can be applied locally and classical information can be exchanged. In addition, the two subsystems are also coupled by a fixed Hamiltonian whose interaction strength can be controlled. This coupling does not generate any local coherence from incoherent input states. We show that in this setting a measurement and feed-forward based protocol can deterministically enhance the coherence of the target system while fully preserving its purity. The protocol can be iterated and several copies of the control state can be consumed to drive the target system arbitrarily close to a maximally coherent state. We experimentally demonstrate this protocol with a photonic setup and observe the enhancement of coherence for up to five iterations of the protocol.
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11
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Ren W, Li W, Xu S, Wang K, Jiang W, Jin F, Zhu X, Chen J, Song Z, Zhang P, Dong H, Zhang X, Deng J, Gao Y, Zhang C, Wu Y, Zhang B, Guo Q, Li H, Wang Z, Biamonte J, Song C, Deng DL, Wang H. Experimental quantum adversarial learning with programmable superconducting qubits. Nat Comput Sci 2022; 2:711-717. [PMID: 38177368 DOI: 10.1038/s43588-022-00351-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 10/10/2022] [Indexed: 01/06/2024]
Abstract
Quantum computing promises to enhance machine learning and artificial intelligence. However, recent theoretical works show that, similar to traditional classifiers based on deep classical neural networks, quantum classifiers would suffer from adversarial perturbations as well. Here we report an experimental demonstration of quantum adversarial learning with programmable superconducting qubits. We train quantum classifiers, which are built on variational quantum circuits consisting of ten transmon qubits featuring average lifetimes of 150 μs, and average fidelities of simultaneous single- and two-qubit gates above 99.94% and 99.4%, respectively, with both real-life images (for example, medical magnetic resonance imaging scans) and quantum data. We demonstrate that these well-trained classifiers (with testing accuracy up to 99%) can be practically deceived by small adversarial perturbations, whereas an adversarial training process would substantially enhance their robustness to such perturbations.
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Affiliation(s)
- Wenhui Ren
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Weikang Li
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China
| | - Shibo Xu
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Ke Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Wenjie Jiang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China
| | - Feitong Jin
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Xuhao Zhu
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Jiachen Chen
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Zixuan Song
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Pengfei Zhang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Hang Dong
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Xu Zhang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Jinfeng Deng
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Yu Gao
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Chuanyu Zhang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Yaozu Wu
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Bing Zhang
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Qiujiang Guo
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Hekang Li
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Zhen Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Jacob Biamonte
- Beijing Institute of Mathematical Sciences and Applications, Beijing, China
| | - Chao Song
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China.
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China.
- Shanghai Qi Zhi Institute, Shanghai, China.
| | - H Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.
- Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China.
- State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, China.
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12
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Gyongyosi L. Adaptive Problem Solving Dynamics in Gate-Model Quantum Computers. Entropy (Basel) 2022; 24:1196. [PMID: 36141082 PMCID: PMC9498293 DOI: 10.3390/e24091196] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/17/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
Gate-model quantum computer architectures represent an implementable model used to realize quantum computations. The mathematical description of the dynamical attributes of adaptive problem solving and iterative objective function evaluation in a gate-model quantum computer is currently a challenge. Here, a mathematical model of adaptive problem solving dynamics in a gate-model quantum computer is defined. We characterize a canonical equation of adaptive objective function evaluation of computational problems. We study the stability of adaptive problem solving in gate-model quantum computers.
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Affiliation(s)
- Laszlo Gyongyosi
- Department of Networked Systems and Services, Budapest University of Technology and Economics, 1117 Budapest, Hungary;
- MTA-BME Information Systems Research Group, Hungarian Academy of Sciences, 1051 Budapest, Hungary
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13
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McGinley M, Roy S, Parameswaran SA. Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems. Phys Rev Lett 2022; 129:090404. [PMID: 36083640 DOI: 10.1103/physrevlett.129.090404] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 06/28/2022] [Indexed: 06/15/2023]
Abstract
We introduce a model of nonunitary quantum dynamics that exhibits infinitely long-lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. Ergodicity is evaded by combining a sequence of projective measurements with a local feedback rule that is inspired by Toom's "north-east-center" classical cellular automaton. The measurements in question only partially collapse the wave function of the system, allowing some quantum coherence to persist. We demonstrate our claims using numerical simulations of a Clifford circuit in two spatial dimensions which allows access to large system sizes, and also present results for more generic dynamics on modest system sizes. We also devise explicit experimental protocols realizing this dynamics using one- and two-qubit gates that are available on present-day quantum computing platforms.
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Affiliation(s)
- Max McGinley
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Sthitadhi Roy
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
- Physical and Theoretical Chemistry, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - S A Parameswaran
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
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14
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Yan B, Wei S, Jiang H, Wang H, Duan Q, Ma Z, Long GL. Fixed-point oblivious quantum amplitude-amplification algorithm. Sci Rep 2022; 12:14339. [PMID: 35995929 DOI: 10.1038/s41598-022-15093-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 06/17/2022] [Indexed: 11/24/2022] Open
Abstract
The quantum amplitude amplification algorithms based on Grover’s rotation operator need to perform phase flips for both the initial state and the target state. When the initial state is oblivious, the phase flips will be intractable, and we need to adopt oblivious amplitude amplification algorithm to handle. Without knowing exactly how many target items there are, oblivious amplitude amplification also suffers the “soufflé problem”, in which iterating too little “undercooks” the state and too much “overcooks” the state, both resulting in a mostly non-target final state. In this work, we present a fixed-point oblivious quantum amplitude-amplification (FOQA) algorithm by introducing damping based on methods proposed by A. Mizel. Moreover, we construct the quantum circuit to implement our algorithm under the framework of duality quantum computing. Our algorithm can avoid the “soufflé problem”, meanwhile keep the square speedup of quantum search, serving as a subroutine to improve the performance of quantum algorithms containing oblivious amplitude amplification procedure.
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15
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Abstract
Quantum optimal control (QOC) enables the realization of accurate operations, such as quantum gates, and supports the development of quantum technologies. To date, many QOC frameworks have been developed, but those remain only naturally suited to optimize a single targeted operation at a time. We extend this concept to optimal control with a continuous family of targets, and demonstrate that an optimization based on neural networks can find families of time-dependent Hamiltonians realizing desired classes of quantum gates in minimal time.
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Affiliation(s)
- Frédéric Sauvage
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Florian Mintert
- Physics Department, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom
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16
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Zhang X, Jiang W, Deng J, Wang K, Chen J, Zhang P, Ren W, Dong H, Xu S, Gao Y, Jin F, Zhu X, Guo Q, Li H, Song C, Gorshkov AV, Iadecola T, Liu F, Gong ZX, Wang Z, Deng DL, Wang H. Digital quantum simulation of Floquet symmetry-protected topological phases. Nature 2022; 607:468-473. [PMID: 35859194 PMCID: PMC9300455 DOI: 10.1038/s41586-022-04854-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 05/11/2022] [Indexed: 11/09/2022]
Abstract
Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1–8, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions9,10, solid-state spin systems11–15, ultracold atoms16,17 and superconducting qubits18–20. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors21. Signatures of non-equilibrium Floquet SPT phases with a programmable superconducting quantum processor are observed in which the discrete time translational symmetry only breaks at the boundaries and not in the bulk.
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Affiliation(s)
- Xu Zhang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Wenjie Jiang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China
| | - Jinfeng Deng
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Ke Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Jiachen Chen
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Pengfei Zhang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Wenhui Ren
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Hang Dong
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Shibo Xu
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Yu Gao
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Feitong Jin
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Xuhao Zhu
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China
| | - Qiujiang Guo
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.,Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Hekang Li
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.,Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Chao Song
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.,Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA
| | - Thomas Iadecola
- Department of Physics and Astronomy, Iowa State University, Ames, IA, USA.,Ames Laboratory, Ames, IA, USA
| | - Fangli Liu
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, University of Maryland and NIST, College Park, MD, USA.,QuEra Computing Inc., Boston, MA, USA
| | - Zhe-Xuan Gong
- Department of Physics, Colorado School of Mines, Golden, CO, USA.,National Institute of Standards and Technology, Boulder, CO, USA
| | - Zhen Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China. .,Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China.
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing, China. .,Shanghai Qi Zhi Institute, Shanghai, China.
| | - H Wang
- Department of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Interdisciplinary Center for Quantum Information, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou, China.,Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, Hangzhou, China
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17
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Green AM, Elben A, Alderete CH, Joshi LK, Nguyen NH, Zache TV, Zhu Y, Sundar B, Linke NM. Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature. Phys Rev Lett 2022; 128:140601. [PMID: 35476480 DOI: 10.1103/physrevlett.128.140601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2021] [Revised: 02/03/2022] [Accepted: 03/09/2022] [Indexed: 06/14/2023]
Abstract
Out-of-time-ordered correlators (OTOCs) are a key observable in a wide range of interconnected fields including many-body physics, quantum information science, and quantum gravity. Measuring OTOCs using near-term quantum simulators will extend our ability to explore fundamental aspects of these fields and the subtle connections between them. Here, we demonstrate an experimental method to measure OTOCs at finite temperatures and use the method to study their temperature dependence. These measurements are performed on a digital quantum computer running a simulation of the transverse field Ising model. Our flexible method, based on the creation of a thermofield double state, can be extended to other models and enables us to probe the OTOC's temperature-dependent decay rate. Measuring this decay rate opens up the possibility of testing the fundamental temperature-dependent bounds on quantum information scrambling.
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Affiliation(s)
- Alaina M Green
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - A Elben
- Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - C Huerta Alderete
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Lata Kh Joshi
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Nhung H Nguyen
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Torsten V Zache
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Yingyue Zhu
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Bhuvanesh Sundar
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
- JILA, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Norbert M Linke
- Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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18
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Miguel-tomé S, Sánchez-lázaro ÁL, Alonso-romero L. Fundamental Physics and Computation: The Computer-Theoretic Framework. Universe 2022; 8:40. [DOI: 10.3390/universe8010040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The central goal of this manuscript is to survey the relationships between fundamental physics and computer science. We begin by providing a short historical review of how different concepts of computer science have entered the field of fundamental physics, highlighting the claim that the universe is a computer. Following the review, we explain why computational concepts have been embraced to interpret and describe physical phenomena. We then discuss seven arguments against the claim that the universe is a computational system and show that those arguments are wrong because of a misunderstanding of the extension of the concept of computation. Afterwards, we address a proposal to solve Hempel’s dilemma using the computability theory but conclude that it is incorrect. After that, we discuss the relationship between the proposals that the universe is a computational system and that our minds are a simulation. Analysing these issues leads us to proposing a new physical principle, called the principle of computability, which claims that the universe is a computational system (not restricted to digital computers) and that computational power and the computational complexity hierarchy are two fundamental physical constants. On the basis of this new principle, a scientific paradigm emerges to develop fundamental theories of physics: the computer-theoretic framework (CTF). The CTF brings to light different ideas already implicit in the work of several researchers and provides a new view on the universe based on computer theoretic concepts that expands the current view. We address different issues regarding the development of fundamental theories of physics in the new paradigm. Additionally, we discuss how the CTF brings new perspectives to different issues, such as the unreasonable effectiveness of mathematics and the foundations of cognitive science.
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19
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Satzinger KJ, Liu YJ, Smith A, Knapp C, Newman M, Jones C, Chen Z, Quintana C, Mi X, Dunsworth A, Gidney C, Aleiner I, Arute F, Arya K, Atalaya J, Babbush R, Bardin JC, Barends R, Basso J, Bengtsson A, Bilmes A, Broughton M, Buckley BB, Buell DA, Burkett B, Bushnell N, Chiaro B, Collins R, Courtney W, Demura S, Derk AR, Eppens D, Erickson C, Faoro L, Farhi E, Fowler AG, Foxen B, Giustina M, Greene A, Gross JA, Harrigan MP, Harrington SD, Hilton J, Hong S, Huang T, Huggins WJ, Ioffe LB, Isakov SV, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Khattar T, Kim S, Klimov PV, Korotkov AN, Kostritsa F, Landhuis D, Laptev P, Locharla A, Lucero E, Martin O, McClean JR, McEwen M, Miao KC, Mohseni M, Montazeri S, Mruczkiewicz W, Mutus J, Naaman O, Neeley M, Neill C, Niu MY, O'Brien TE, Opremcak A, Pató B, Petukhov A, Rubin NC, Sank D, Shvarts V, Strain D, Szalay M, Villalonga B, White TC, Yao Z, Yeh P, Yoo J, Zalcman A, Neven H, Boixo S, Megrant A, Chen Y, Kelly J, Smelyanskiy V, Kitaev A, Knap M, Pollmann F, Roushan P. Realizing topologically ordered states on a quantum processor. Science 2021; 374:1237-1241. [PMID: 34855491 DOI: 10.1126/science.abi8378] [Citation(s) in RCA: 47] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
[Figure: see text].
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Affiliation(s)
| | - Y-J Liu
- Department of Physics, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - A Smith
- Department of Physics, Technical University of Munich, 85748 Garching, Germany.,School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK.,Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, UK
| | - C Knapp
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA
| | - M Newman
- Google Quantum AI, Mountain View, CA, USA
| | - C Jones
- Google Quantum AI, Mountain View, CA, USA
| | - Z Chen
- Google Quantum AI, Mountain View, CA, USA
| | - C Quintana
- Google Quantum AI, Mountain View, CA, USA
| | - X Mi
- Google Quantum AI, Mountain View, CA, USA
| | | | - C Gidney
- Google Quantum AI, Mountain View, CA, USA
| | - I Aleiner
- Google Quantum AI, Mountain View, CA, USA
| | - F Arute
- Google Quantum AI, Mountain View, CA, USA
| | - K Arya
- Google Quantum AI, Mountain View, CA, USA
| | - J Atalaya
- Google Quantum AI, Mountain View, CA, USA
| | - R Babbush
- Google Quantum AI, Mountain View, CA, USA
| | - J C Bardin
- Google Quantum AI, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | - R Barends
- Google Quantum AI, Mountain View, CA, USA
| | - J Basso
- Google Quantum AI, Mountain View, CA, USA
| | | | - A Bilmes
- Google Quantum AI, Mountain View, CA, USA
| | | | | | - D A Buell
- Google Quantum AI, Mountain View, CA, USA
| | - B Burkett
- Google Quantum AI, Mountain View, CA, USA
| | - N Bushnell
- Google Quantum AI, Mountain View, CA, USA
| | - B Chiaro
- Google Quantum AI, Mountain View, CA, USA
| | - R Collins
- Google Quantum AI, Mountain View, CA, USA
| | - W Courtney
- Google Quantum AI, Mountain View, CA, USA
| | - S Demura
- Google Quantum AI, Mountain View, CA, USA
| | - A R Derk
- Google Quantum AI, Mountain View, CA, USA
| | - D Eppens
- Google Quantum AI, Mountain View, CA, USA
| | - C Erickson
- Google Quantum AI, Mountain View, CA, USA
| | - L Faoro
- Laboratoire de Physique Theorique et Hautes Energies, Sorbonne Université, 75005 Paris, France
| | - E Farhi
- Google Quantum AI, Mountain View, CA, USA
| | - A G Fowler
- Google Quantum AI, Mountain View, CA, USA
| | - B Foxen
- Google Quantum AI, Mountain View, CA, USA
| | - M Giustina
- Google Quantum AI, Mountain View, CA, USA
| | - A Greene
- Google Quantum AI, Mountain View, CA, USA.,Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - J A Gross
- Google Quantum AI, Mountain View, CA, USA
| | | | | | - J Hilton
- Google Quantum AI, Mountain View, CA, USA
| | - S Hong
- Google Quantum AI, Mountain View, CA, USA
| | - T Huang
- Google Quantum AI, Mountain View, CA, USA
| | | | - L B Ioffe
- Google Quantum AI, Mountain View, CA, USA
| | - S V Isakov
- Google Quantum AI, Mountain View, CA, USA
| | - E Jeffrey
- Google Quantum AI, Mountain View, CA, USA
| | - Z Jiang
- Google Quantum AI, Mountain View, CA, USA
| | - D Kafri
- Google Quantum AI, Mountain View, CA, USA
| | | | - T Khattar
- Google Quantum AI, Mountain View, CA, USA
| | - S Kim
- Google Quantum AI, Mountain View, CA, USA
| | - P V Klimov
- Google Quantum AI, Mountain View, CA, USA
| | - A N Korotkov
- Google Quantum AI, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | - D Landhuis
- Google Quantum AI, Mountain View, CA, USA
| | - P Laptev
- Google Quantum AI, Mountain View, CA, USA
| | - A Locharla
- Google Quantum AI, Mountain View, CA, USA
| | - E Lucero
- Google Quantum AI, Mountain View, CA, USA
| | - O Martin
- Google Quantum AI, Mountain View, CA, USA
| | | | - M McEwen
- Google Quantum AI, Mountain View, CA, USA.,Department of Physics, University of California, Santa Barbara, CA, USA
| | - K C Miao
- Google Quantum AI, Mountain View, CA, USA
| | - M Mohseni
- Google Quantum AI, Mountain View, CA, USA
| | | | | | - J Mutus
- Google Quantum AI, Mountain View, CA, USA
| | - O Naaman
- Google Quantum AI, Mountain View, CA, USA
| | - M Neeley
- Google Quantum AI, Mountain View, CA, USA
| | - C Neill
- Google Quantum AI, Mountain View, CA, USA
| | - M Y Niu
- Google Quantum AI, Mountain View, CA, USA
| | | | - A Opremcak
- Google Quantum AI, Mountain View, CA, USA
| | - B Pató
- Google Quantum AI, Mountain View, CA, USA
| | - A Petukhov
- Google Quantum AI, Mountain View, CA, USA
| | - N C Rubin
- Google Quantum AI, Mountain View, CA, USA
| | - D Sank
- Google Quantum AI, Mountain View, CA, USA
| | - V Shvarts
- Google Quantum AI, Mountain View, CA, USA
| | - D Strain
- Google Quantum AI, Mountain View, CA, USA
| | - M Szalay
- Google Quantum AI, Mountain View, CA, USA
| | | | - T C White
- Google Quantum AI, Mountain View, CA, USA
| | - Z Yao
- Google Quantum AI, Mountain View, CA, USA
| | - P Yeh
- Google Quantum AI, Mountain View, CA, USA
| | - J Yoo
- Google Quantum AI, Mountain View, CA, USA
| | - A Zalcman
- Google Quantum AI, Mountain View, CA, USA
| | - H Neven
- Google Quantum AI, Mountain View, CA, USA
| | - S Boixo
- Google Quantum AI, Mountain View, CA, USA
| | - A Megrant
- Google Quantum AI, Mountain View, CA, USA
| | - Y Chen
- Google Quantum AI, Mountain View, CA, USA
| | - J Kelly
- Google Quantum AI, Mountain View, CA, USA
| | | | - A Kitaev
- Google Quantum AI, Mountain View, CA, USA.,Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA
| | - M Knap
- Department of Physics, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany.,Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - F Pollmann
- Department of Physics, Technical University of Munich, 85748 Garching, Germany.,Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, 80799 München, Germany
| | - P Roushan
- Google Quantum AI, Mountain View, CA, USA
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20
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Mitchell BK, Naik RK, Morvan A, Hashim A, Kreikebaum JM, Marinelli B, Lavrijsen W, Nowrouzi K, Santiago DI, Siddiqi I. Hardware-Efficient Microwave-Activated Tunable Coupling between Superconducting Qubits. Phys Rev Lett 2021; 127:200502. [PMID: 34860047 DOI: 10.1103/physrevlett.127.200502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/31/2021] [Indexed: 06/13/2023]
Abstract
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
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Affiliation(s)
- Bradley K Mitchell
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Ravi K Naik
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Alexis Morvan
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Akel Hashim
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - John Mark Kreikebaum
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Brian Marinelli
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Wim Lavrijsen
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Kasra Nowrouzi
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - David I Santiago
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Irfan Siddiqi
- Quantum Nanoelectronics Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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21
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Mi X, Roushan P, Quintana C, Mandrà S, Marshall J, Neill C, Arute F, Arya K, Atalaya J, Babbush R, Bardin JC, Barends R, Basso J, Bengtsson A, Boixo S, Bourassa A, Broughton M, Buckley BB, Buell DA, Burkett B, Bushnell N, Chen Z, Chiaro B, Collins R, Courtney W, Demura S, Derk AR, Dunsworth A, Eppens D, Erickson C, Farhi E, Fowler AG, Foxen B, Gidney C, Giustina M, Gross JA, Harrigan MP, Harrington SD, Hilton J, Ho A, Hong S, Huang T, Huggins WJ, Ioffe LB, Isakov SV, Jeffrey E, Jiang Z, Jones C, Kafri D, Kelly J, Kim S, Kitaev A, Klimov PV, Korotkov AN, Kostritsa F, Landhuis D, Laptev P, Lucero E, Martin O, McClean JR, McCourt T, McEwen M, Megrant A, Miao KC, Mohseni M, Montazeri S, Mruczkiewicz W, Mutus J, Naaman O, Neeley M, Newman M, Niu MY, O'Brien TE, Opremcak A, Ostby E, Pato B, Petukhov A, Redd N, Rubin NC, Sank D, Satzinger KJ, Shvarts V, Strain D, Szalay M, Trevithick MD, Villalonga B, White T, Yao ZJ, Yeh P, Zalcman A, Neven H, Aleiner I, Kechedzhi K, Smelyanskiy V, Chen Y. Information scrambling in quantum circuits. Science 2021; 374:1479-1483. [PMID: 34709938 DOI: 10.1126/science.abg5029] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
[Figure: see text].
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Affiliation(s)
- Xiao Mi
- Google Research, Mountain View, CA, USA
| | | | | | - Salvatore Mandrà
- QuAIL, NASA Ames Research Center, Moffett Field, CA, USA.,KBR, Inc., Houston, TX, USA
| | - Jeffrey Marshall
- QuAIL, NASA Ames Research Center, Moffett Field, CA, USA.,USRA Research Institute for Advanced Computer Science, Mountain View, CA, USA
| | | | | | | | | | | | - Joseph C Bardin
- Google Research, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | | | | | | | | | - Alexandre Bourassa
- Google Research, Mountain View, CA, USA.,Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Alan Ho
- Google Research, Mountain View, CA, USA
| | | | | | | | - L B Ioffe
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | | | - Seon Kim
- Google Research, Mountain View, CA, USA
| | - Alexei Kitaev
- Google Research, Mountain View, CA, USA.,Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA
| | | | - Alexander N Korotkov
- Google Research, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | | | | | | | | | | | - Matt McEwen
- Google Research, Mountain View, CA, USA.,Department of Physics, University of California, Santa Barbara, CA, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Ping Yeh
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - Yu Chen
- Google Research, Mountain View, CA, USA
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22
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Mugel S, Abad M, Bermejo M, Sánchez J, Lizaso E, Orús R. Hybrid quantum investment optimization with minimal holding period. Sci Rep 2021; 11:19587. [PMID: 34599213 DOI: 10.1038/s41598-021-98297-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2020] [Accepted: 09/01/2021] [Indexed: 11/27/2022] Open
Abstract
In this paper we propose a hybrid quantum-classical algorithm for dynamic portfolio optimization with minimal holding period. Our algorithm is based on sampling the near-optimal portfolios at each trading step using a quantum processor, and efficiently post-selecting to meet the minimal holding constraint. We found the optimal investment trajectory in a dataset of 50 assets spanning a 1 year trading period using the D-Wave 2000Q processor. Our method is remarkably efficient, and produces results much closer to the efficient frontier than typical portfolios. Moreover, we also show how our approach can easily produce trajectories adapted to different risk profiles, as typically offered in financial products. Our results are a clear example of how the combination of quantum and classical techniques can offer novel valuable tools to deal with real-life problems, beyond simple toy models, in current NISQ quantum processors.
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23
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Kandala A, Wei KX, Srinivasan S, Magesan E, Carnevale S, Keefe GA, Klaus D, Dial O, McKay DC. Demonstration of a High-Fidelity cnot Gate for Fixed-Frequency Transmons with Engineered ZZ Suppression. Phys Rev Lett 2021; 127:130501. [PMID: 34623861 DOI: 10.1103/physrevlett.127.130501] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 07/28/2021] [Indexed: 06/13/2023]
Abstract
Improving two-qubit gate performance and suppressing cross talk are major, but often competing, challenges to achieving scalable quantum computation. In particular, increasing the coupling to realize faster gates has been intrinsically linked to enhanced cross talk due to unwanted two-qubit terms in the Hamiltonian. Here, we demonstrate a novel coupling architecture for transmon qubits that circumvents the standard relationship between desired and undesired interaction rates. Using two fixed frequency coupling elements to tune the dressed level spacings, we demonstrate an intrinsic suppression of the static ZZ while maintaining large effective coupling rates. Our architecture reveals no observable degradation of qubit coherence (T_{1},T_{2}>100 μs) and, over a factor of 6 improvement in the ratio of desired to undesired coupling. Using the cross-resonance interaction, we demonstrate a 180 ns single-pulse controlled not (cnot) gate, and measure a cnot fidelity of 99.77(2)% from interleaved randomized benchmarking.
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Affiliation(s)
- A Kandala
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - K X Wei
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - S Srinivasan
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - E Magesan
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - S Carnevale
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - G A Keefe
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - D Klaus
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - O Dial
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - D C McKay
- IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
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24
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Stehlik J, Zajac DM, Underwood DL, Phung T, Blair J, Carnevale S, Klaus D, Keefe GA, Carniol A, Kumph M, Steffen M, Dial OE. Tunable Coupling Architecture for Fixed-Frequency Transmon Superconducting Qubits. Phys Rev Lett 2021; 127:080505. [PMID: 34477428 DOI: 10.1103/physrevlett.127.080505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
Implementation of high-fidelity 2-qubit operations is a key ingredient for scalable quantum error correction. In superconducting qubit architectures, tunable buses have been explored as a means to higher-fidelity gates. However, these buses introduce new pathways for leakage. Here we present a modified tunable bus architecture appropriate for fixed-frequency qubits in which the adiabaticity restrictions on gate speed are reduced. We characterize this coupler on a range of 2-qubit devices, achieving a maximum gate fidelity of 99.85%. We further show the calibration is stable over one day.
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Affiliation(s)
- J Stehlik
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - D M Zajac
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - D L Underwood
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - T Phung
- IBM Quantum, IBM Almaden Research Center, San Jose, California 95120, USA
| | - J Blair
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - S Carnevale
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - D Klaus
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - G A Keefe
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - A Carniol
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - M Kumph
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - Matthias Steffen
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
| | - O E Dial
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
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25
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Abstract
Realizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits. Repetition codes running many cycles of quantum error correction achieve exponential suppression of errors with increasing numbers of qubits.
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26
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27
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McEwen M, Kafri D, Chen Z, Atalaya J, Satzinger KJ, Quintana C, Klimov PV, Sank D, Gidney C, Fowler AG, Arute F, Arya K, Buckley B, Burkett B, Bushnell N, Chiaro B, Collins R, Demura S, Dunsworth A, Erickson C, Foxen B, Giustina M, Huang T, Hong S, Jeffrey E, Kim S, Kechedzhi K, Kostritsa F, Laptev P, Megrant A, Mi X, Mutus J, Naaman O, Neeley M, Neill C, Niu M, Paler A, Redd N, Roushan P, White TC, Yao J, Yeh P, Zalcman A, Chen Y, Smelyanskiy VN, Martinis JM, Neven H, Kelly J, Korotkov AN, Petukhov AG, Barends R. Removing leakage-induced correlated errors in superconducting quantum error correction. Nat Commun 2021; 12:1761. [PMID: 33741936 PMCID: PMC7979694 DOI: 10.1038/s41467-021-21982-y] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 02/23/2021] [Indexed: 11/30/2022] Open
Abstract
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.
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Affiliation(s)
- M McEwen
- Department of Physics, University of California, Santa Barbara, CA, USA
- Google, Santa Barbara, CA, USA
| | | | - Z Chen
- Google, Santa Barbara, CA, USA
| | | | | | | | | | - D Sank
- Google, Santa Barbara, CA, USA
| | | | | | - F Arute
- Google, Santa Barbara, CA, USA
| | - K Arya
- Google, Santa Barbara, CA, USA
| | | | | | | | | | | | | | | | | | - B Foxen
- Google, Santa Barbara, CA, USA
| | | | - T Huang
- Google, Santa Barbara, CA, USA
| | - S Hong
- Google, Santa Barbara, CA, USA
| | | | - S Kim
- Google, Santa Barbara, CA, USA
| | | | | | | | | | - X Mi
- Google, Santa Barbara, CA, USA
| | - J Mutus
- Google, Santa Barbara, CA, USA
| | | | | | - C Neill
- Google, Santa Barbara, CA, USA
| | | | - A Paler
- Johannes Kepler University, Linz, Austria
- University of Texas at Dallas, Richardson, TX, USA
| | - N Redd
- Google, Santa Barbara, CA, USA
| | | | | | - J Yao
- Google, Santa Barbara, CA, USA
| | - P Yeh
- Google, Santa Barbara, CA, USA
| | | | - Yu Chen
- Google, Santa Barbara, CA, USA
| | | | - John M Martinis
- Department of Physics, University of California, Santa Barbara, CA, USA
| | - H Neven
- Google, Santa Barbara, CA, USA
| | - J Kelly
- Google, Santa Barbara, CA, USA
| | - A N Korotkov
- Google, Santa Barbara, CA, USA
- Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
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28
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Abstract
A scalable model for a distributed quantum computation is a challenging problem due to the complexity of the problem space provided by the diversity of possible quantum systems, from small-scale quantum devices to large-scale quantum computers. Here, we define a model of scalable distributed gate-model quantum computation in near-term quantum systems of the NISQ (noisy intermediate scale quantum) technology era. We prove that the proposed architecture can maximize an objective function of a computational problem in a distributed manner. We study the impacts of decoherence on distributed objective function evaluation.
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Affiliation(s)
- Laszlo Gyongyosi
- Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, 1117, Hungary.
- MTA-BME Information Systems Research Group, Hungarian Academy of Sciences, Budapest, 1051, Hungary.
| | - Sandor Imre
- Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, 1117, Hungary
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29
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Abstract
The quantum Internet enables networking based on the fundamentals of quantum mechanics. Here, methods and procedures of resource prioritization and resource balancing are defined for the quantum Internet. We define a model for resource consumption optimization in quantum repeaters, and a strongly-entangled network structure for resource balancing. We study the resource-balancing efficiency of the strongly-entangled structure. We prove that a strongly-entangled quantum network is two times more efficient in a resource balancing problem than a full-mesh network of the traditional Internet.
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Affiliation(s)
- Laszlo Gyongyosi
- Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, 1117, Hungary.
- MTA-BME Information Systems Research Group, Hungarian Academy of Sciences, Budapest, 1051, Hungary.
| | - Sandor Imre
- Department of Networked Systems and Services, Budapest University of Technology and Economics, Budapest, 1117, Hungary
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30
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Collodo MC, Herrmann J, Lacroix N, Andersen CK, Remm A, Lazar S, Besse JC, Walter T, Wallraff A, Eichler C. Implementation of Conditional Phase Gates Based on Tunable ZZ Interactions. Phys Rev Lett 2020; 125:240502. [PMID: 33412023 DOI: 10.1103/physrevlett.125.240502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2020] [Accepted: 10/12/2020] [Indexed: 06/12/2023]
Abstract
High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.
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Affiliation(s)
| | | | - Nathan Lacroix
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Ants Remm
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Stefania Lazar
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Theo Walter
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Andreas Wallraff
- Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
- Quantum Center, ETH Zurich, CH-8093 Zurich, Switzerland
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31
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Xu Y, Chu J, Yuan J, Qiu J, Zhou Y, Zhang L, Tan X, Yu Y, Liu S, Li J, Yan F, Yu D. High-Fidelity, High-Scalability Two-Qubit Gate Scheme for Superconducting Qubits. Phys Rev Lett 2020; 125:240503. [PMID: 33412065 DOI: 10.1103/physrevlett.125.240503] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2020] [Accepted: 10/12/2020] [Indexed: 06/12/2023]
Abstract
High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.
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Affiliation(s)
- Yuan Xu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Ji Chu
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Jiahao Yuan
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Jiawei Qiu
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Yuxuan Zhou
- Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Libo Zhang
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Xinsheng Tan
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, Jiangsu, 210093, China
| | - Song Liu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Jian Li
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Fei Yan
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China
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