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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Mi X, Michailidis AA, Shabani S, Miao KC, Klimov PV, Lloyd J, Rosenberg E, Acharya R, Aleiner I, 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, Chou C, 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, Erickson C, Faoro L, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, Genois É, 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, Ioffe LB, 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, 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, Malone FD, Martin O, McClean JR, McEwen M, 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, 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, Roushan P, Smelyanskiy V, Abanin DA. Stable quantum-correlated many-body states through engineered dissipation. Science 2024; 383:1332-1337. [PMID: 38513021 DOI: 10.1126/science.adh9932] [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: 03/27/2023] [Accepted: 02/13/2024] [Indexed: 03/23/2024]
Abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Affiliation(s)
- X Mi
- Google Research, Mountain View, CA, USA
| | - A A Michailidis
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - S Shabani
- Google Research, Mountain View, CA, USA
| | - K C Miao
- Google Research, Mountain View, CA, USA
| | | | - J Lloyd
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | | | - R Acharya
- Google Research, Mountain View, CA, USA
| | - I Aleiner
- 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
| | | | - 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
| | | | - Z Chen
- Google Research, Mountain View, CA, USA
| | - B Chiaro
- Google Research, Mountain View, CA, USA
| | - D Chik
- Google Research, Mountain View, CA, USA
| | - C Chou
- 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
| | - A G Dau
- Google Research, Mountain View, CA, USA
| | | | | | - S Demura
- 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
| | - 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
| | | | - 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
- Centre for Quantum Software and Information (QSI), Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, 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
| | | | | | - O Martin
- Google Research, Mountain View, CA, USA
| | | | - M McEwen
- 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
| | | | - 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
| | | | | | | | - R Potter
- Google Research, Mountain View, CA, USA
| | - L P Pryadko
- Google Research, Mountain View, CA, USA
- 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
| | - J Skruzny
- Google Research, Mountain View, CA, USA
| | - W C Smith
- Google Research, Mountain View, CA, USA
| | - R Somma
- Google Research, Mountain View, CA, USA
| | | | - D Strain
- Google Research, Mountain View, CA, USA
| | - M Szalay
- 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
| | - Z J Yao
- 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
| | - P Roushan
- Google Research, Mountain View, CA, USA
| | | | - D A Abanin
- Google Research, Mountain View, CA, USA
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
- Department of Physics, Princeton University, Princeton, NJ, USA
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3
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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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4
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Andersen TI, Lensky YD, Kechedzhi K, Drozdov IK, Bengtsson A, Hong S, Morvan A, Mi X, Opremcak A, Acharya R, Allen R, Ansmann M, Arute F, Arya K, Asfaw A, Atalaya J, Babbush R, Bacon D, Bardin JC, 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, Chou C, Cogan J, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Debroy DM, Del Toro Barba A, Demura S, Dunsworth A, Eppens D, Erickson C, Faoro L, Farhi E, Fatemi R, Ferreira VS, Burgos LF, Forati E, Fowler AG, Foxen B, 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, Hilton J, Hoffmann MR, 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, Klimov PV, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lester BJ, Lill AT, Liu W, Locharla A, Lucero E, Malone FD, Martin O, McClean JR, McCourt T, McEwen M, Miao KC, Mieszala A, Mohseni M, Montazeri S, Mount E, Movassagh R, Mruczkiewicz W, Naaman O, Neeley M, Neill C, Nersisyan A, Newman M, Ng JH, Nguyen A, Nguyen M, Niu MY, O’Brien TE, Omonije S, 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, Boixo S, Megrant A, Kelly J, Chen Y, Smelyanskiy V, Kim EA, Aleiner I, Roushan P. Non-Abelian braiding of graph vertices in a superconducting processor. Nature 2023; 618:264-269. [PMID: 37169834 DOI: 10.1038/s41586-023-05954-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 03/14/2023] [Indexed: 06/09/2023]
Abstract
Indistinguishability of particles is a fundamental principle of quantum mechanics1. For all elementary and quasiparticles observed to date-including fermions, bosons and Abelian anyons-this principle guarantees that the braiding of identical particles leaves the system unchanged2,3. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions4-8. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals9-22, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons9,10, we implement a generalized stabilizer code and unitary protocol23 to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.
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5
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Morvan A, Andersen TI, Mi X, Neill C, Petukhov A, Kechedzhi K, Abanin DA, Michailidis A, Acharya R, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Basso J, 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, Collins R, Conner P, Courtney W, Crook AL, Curtin B, Debroy DM, Del Toro Barba A, Demura S, Dunsworth A, Eppens D, Erickson C, Faoro L, Farhi E, Fatemi R, Flores Burgos L, Forati E, Fowler AG, Foxen B, Giang W, Gidney C, Gilboa D, Giustina M, Grajales Dau A, Gross JA, Habegger S, Hamilton MC, Harrigan MP, Harrington SD, Hoffmann M, Hong S, Huang T, Huff A, Huggins WJ, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Juhas P, Kafri D, Khattar T, Khezri M, Kieferová M, Kim S, Kitaev AY, Klimov PV, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Laws L, Lee J, Lee KW, Lester BJ, Lill AT, Liu W, Locharla A, Malone F, Martin O, McClean JR, McEwen M, Meurer Costa B, Miao KC, Mohseni M, Montazeri S, Mount E, Mruczkiewicz W, Naaman O, Neeley M, Nersisyan A, Newman M, Nguyen A, Nguyen M, Niu MY, O'Brien TE, Olenewa R, Opremcak A, Potter R, Quintana C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schurkus HF, Schuster C, Shearn MJ, Shorter A, Shvarts V, Skruzny J, Smith WC, Strain D, Sterling G, Su Y, Szalay M, Torres A, Vidal G, Villalonga B, Vollgraff-Heidweiller C, White T, Xing C, Yao Z, Yeh P, Yoo J, Zalcman A, Zhang Y, Zhu N, Neven H, Bacon D, Hilton J, Lucero E, Babbush R, Boixo S, Megrant A, Kelly J, Chen Y, Smelyanskiy V, Aleiner I, Ioffe LB, Roushan P. Formation of robust bound states of interacting microwave photons. Nature 2022; 612:240-245. [PMID: 36477133 PMCID: PMC9729104 DOI: 10.1038/s41586-022-05348-y] [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] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2022] [Accepted: 09/14/2022] [Indexed: 12/12/2022]
Abstract
Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.
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Affiliation(s)
- A Morvan
- Google Research, Mountain View, CA, USA
| | | | - X Mi
- Google Research, Mountain View, CA, USA
| | - C Neill
- Google Research, Mountain View, CA, USA
| | | | | | - D A Abanin
- Google Research, Mountain View, CA, USA
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - A Michailidis
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - R Acharya
- 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
| | - J Basso
- 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
| | | | - Z Chen
- Google Research, Mountain View, CA, USA
| | - B Chiaro
- 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
| | | | - D Eppens
- 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
| | - W Giang
- Google Research, Mountain View, CA, USA
| | - C Gidney
- Google Research, Mountain View, CA, USA
| | - D Gilboa
- Google Research, Mountain View, CA, USA
| | | | | | - J A Gross
- 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
| | | | | | - 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
- Centre for Quantum Computation and Communication Technology, Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, New South Wales, Australia
| | - S Kim
- Google Research, Mountain View, CA, USA
| | - A Y Kitaev
- Google Research, Mountain View, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, 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
| | - 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
| | | | - F Malone
- Google Research, Mountain View, CA, USA
| | - O Martin
- Google Research, Mountain View, CA, USA
| | | | - M McEwen
- Google Research, Mountain View, CA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | | | - K C Miao
- Google Research, Mountain View, CA, USA
| | - M Mohseni
- Google Research, Mountain View, CA, USA
| | | | - E Mount
- Google Research, Mountain View, CA, USA
| | | | - O Naaman
- Google Research, Mountain View, CA, USA
| | - M Neeley
- Google Research, Mountain View, CA, USA
| | | | - M Newman
- 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
| | | | - R Olenewa
- Google Research, Mountain View, CA, USA
| | | | - R Potter
- 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
| | - V Shvarts
- Google Research, Mountain View, CA, USA
| | - J Skruzny
- Google Research, Mountain View, CA, USA
| | - W C Smith
- Google Research, Mountain View, CA, USA
| | - D Strain
- Google Research, Mountain View, CA, USA
| | | | - Y Su
- Google Research, Mountain View, CA, USA
| | - M Szalay
- 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
| | - C Xing
- Google Research, Mountain View, CA, USA
| | - Z Yao
- Google Research, Mountain View, CA, USA
| | - P Yeh
- Google Research, Mountain View, CA, USA
| | - J Yoo
- 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
| | - H Neven
- Google Research, Mountain View, CA, USA
| | - D Bacon
- Google Research, Mountain View, CA, USA
| | - J Hilton
- Google Research, Mountain View, CA, USA
| | - E Lucero
- Google Research, Mountain View, CA, USA
| | - R Babbush
- Google Research, Mountain View, CA, USA
| | - S Boixo
- 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
| | | | - I Aleiner
- Google Research, Mountain View, CA, USA.
| | - L B Ioffe
- Google Research, Mountain View, CA, USA.
| | - P Roushan
- Google Research, Mountain View, CA, USA.
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6
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Mi X, Sonner M, Niu MY, Lee KW, Foxen B, Acharya R, Aleiner I, Andersen TI, Arute F, Arya K, Asfaw A, Atalaya J, Bardin JC, Basso J, Bengtsson A, Bortoli G, Bourassa A, Brill L, Broughton M, Buckley BB, Buell DA, Burkett B, Bushnell N, Chen Z, Chiaro B, Collins R, Conner P, Courtney W, Crook AL, Debroy DM, Demura S, Dunsworth A, Eppens D, Erickson C, Faoro L, Farhi E, Fatemi R, Flores L, Forati E, Fowler AG, Giang W, Gidney C, Gilboa D, Giustina M, Dau AG, Gross JA, Habegger S, Harrigan MP, Hoffmann M, Hong S, Huang T, Huff A, Huggins WJ, Ioffe LB, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Kafri D, Kechedzhi K, Khattar T, Kim S, Kitaev AY, Klimov PV, Klots AR, Korotkov AN, Kostritsa F, Kreikebaum JM, Landhuis D, Laptev P, Lau KM, Lee J, Laws L, Liu W, Locharla A, Martin O, McClean JR, McEwen M, Meurer Costa B, Miao KC, Mohseni M, Montazeri S, Morvan A, Mount E, Mruczkiewicz W, Naaman O, Neeley M, Neill C, Newman M, O’Brien TE, Opremcak A, Petukhov A, Potter R, Quintana C, Rubin NC, Saei N, Sank D, Sankaragomathi K, Satzinger KJ, Schuster C, Shearn MJ, Shvarts V, Strain D, Su Y, Szalay M, Vidal G, Villalonga B, Vollgraff-Heidweiller C, White T, Yao Z, Yeh P, Yoo J, Zalcman A, Zhang Y, Zhu N, Neven H, Bacon D, Hilton J, Lucero E, Babbush R, Boixo S, Megrant A, Chen Y, Kelly J, Smelyanskiy V, Abanin DA, Roushan P. Noise-resilient edge modes on a chain of superconducting qubits. Science 2022; 378:785-790. [DOI: 10.1126/science.abq5769] [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: 11/18/2022]
Abstract
Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with
ℤ
2
parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.
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Affiliation(s)
- X. Mi
- Google Research, Mountain View, CA, USA
| | - M. Sonner
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
| | - M. Y. Niu
- Google Research, Mountain View, CA, USA
| | - K. W. Lee
- Google Research, Mountain View, CA, USA
| | - B. Foxen
- 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. C. Bardin
- Google Research, Mountain View, CA, USA
- Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | - J. Basso
- Google Research, Mountain View, CA, USA
| | | | | | | | - L. Brill
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - Z. Chen
- Google Research, Mountain View, CA, USA
| | - B. Chiaro
- Google Research, Mountain View, CA, USA
| | | | - P. Conner
- Google Research, Mountain View, CA, USA
| | | | | | | | - S. Demura
- Google Research, Mountain View, CA, USA
| | | | - D. Eppens
- 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
| | - L. Flores
- Google Research, Mountain View, CA, USA
| | - E. Forati
- 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
| | | | - A. G. Dau
- 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
| | | | | | | | | | | | - Z. Jiang
- Google Research, Mountain View, CA, USA
| | - C. Jones
- Google Research, Mountain View, CA, USA
| | - D. Kafri
- Google Research, Mountain View, CA, USA
| | | | | | - S. Kim
- Google Research, Mountain View, CA, USA
| | - A. Y. Kitaev
- Google Research, Mountain View, CA, USA
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, 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
| | - J. Lee
- Google Research, Mountain View, CA, USA
| | - L. Laws
- Google Research, Mountain View, CA, USA
| | - W. Liu
- Google Research, Mountain View, CA, USA
| | | | - O. Martin
- Google Research, Mountain View, CA, USA
| | | | - M. McEwen
- Google Research, Mountain View, CA, USA
- Department of Physics, University of California, Santa Barbara, CA, USA
| | | | | | | | | | - A. Morvan
- Google Research, Mountain View, CA, USA
| | - E. Mount
- Google Research, Mountain View, CA, USA
| | | | - O. Naaman
- Google Research, Mountain View, CA, USA
| | - M. Neeley
- Google Research, Mountain View, CA, USA
| | - C. Neill
- Google Research, Mountain View, CA, USA
| | - M. Newman
- Google Research, Mountain View, CA, USA
| | | | | | | | - R. Potter
- Google Research, Mountain View, CA, USA
| | | | | | - N. Saei
- Google Research, Mountain View, CA, USA
| | - D. Sank
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - D. Strain
- Google Research, Mountain View, CA, USA
| | - Y. Su
- Google Research, Mountain View, CA, USA
| | - M. Szalay
- Google Research, Mountain View, CA, USA
| | - G. Vidal
- Google Research, Mountain View, CA, USA
| | | | | | - T. White
- Google Research, Mountain View, CA, USA
| | - Z. Yao
- Google Research, Mountain View, CA, USA
| | - P. Yeh
- Google Research, Mountain View, CA, USA
| | - J. Yoo
- Google Research, Mountain View, CA, USA
| | | | - Y. Zhang
- Google Research, Mountain View, CA, USA
| | - N. Zhu
- Google Research, Mountain View, CA, USA
| | - H. Neven
- Google Research, Mountain View, CA, USA
| | - D. Bacon
- Google Research, Mountain View, CA, USA
| | - J. Hilton
- Google Research, Mountain View, CA, USA
| | - E. Lucero
- Google Research, Mountain View, CA, USA
| | | | - S. Boixo
- Google Research, Mountain View, CA, USA
| | | | - Y. Chen
- Google Research, Mountain View, CA, USA
| | - J. Kelly
- Google Research, Mountain View, CA, USA
| | | | - D. A. Abanin
- Google Research, Mountain View, CA, USA
- Department of Theoretical Physics, University of Geneva, Geneva, Switzerland
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7
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Farhi E, Roudenko O, Picca F, Bellachehab A, Bac S, Ounsy M. Data treatment at Synchrotron SOLEIL: automation, IA, on-demand computing, packaging. Acta Cryst Sect A 2022. [DOI: 10.1107/s2053273322090155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
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8
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Farhi E. DARTS on-demand computing. Acta Cryst Sect A 2022. [DOI: 10.1107/s2053273322090143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/19/2023]
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9
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Ebadi S, Keesling A, Cain M, Wang TT, Levine H, Bluvstein D, Semeghini G, Omran A, Liu JG, Samajdar R, Luo XZ, Nash B, Gao X, Barak B, Farhi E, Sachdev S, Gemelke N, Zhou L, Choi S, Pichler H, Wang ST, Greiner M, Vuletic V, Lukin MD. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 2022; 376:1209-1215. [PMID: 35511943 DOI: 10.1126/science.abo6587] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [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
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
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Affiliation(s)
- S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - M Cain
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - J-G Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - X-Z Luo
- QuEra Computing Inc., Boston, MA 02135, USA.,Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - B Nash
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - X Gao
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B Barak
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - E Farhi
- Google Quantum AI, Venice, CA 90291, USA.,Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - N Gemelke
- QuEra Computing Inc., Boston, MA 02135, USA
| | - L Zhou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - S Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - S-T Wang
- QuEra Computing Inc., Boston, MA 02135, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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10
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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: 38] [Impact Index Per Article: 12.7] [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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11
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Noguere G, Scotta JP, Xu S, Farhi E, Ollivier J, Calzavarra Y, Rols S, Koza M, Marquez Damian JI. Temperature-dependent dynamic structure factors for liquid water inferred from inelastic neutron scattering measurements. J Chem Phys 2021; 155:024502. [PMID: 34266266 DOI: 10.1063/5.0055779] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Temperature-dependent dynamic structure factors S(Q, ω) for liquid water have been calculated using a composite model, which is based on the decoupling approximation of the mean square displacement of the water molecules into diffusion and solid-like vibrational parts. The solid-like vibrational part Svib(Q, ω) is calculated with the phonon expansion method established in the framework of the incoherent Gaussian approximation. The diffusion part Sdiff(Q, ω) relies on the Egelstaff-Schofield translational diffusion model corrected for jump diffusions and rotational diffusions with the Singwi-Sjölander random model and Sears expansion, respectively. Systematics of the model parameters as a function of temperature were deduced from quasi-elastic neutron scattering data analysis reported in the literature and from molecular dynamics (MD) simulations relying on the TIP4P/2005f model. The resulting S(Q, ω) values are confronted by means of Monte Carlo simulations to inelastic neutron scattering data measured with IN4, IN5, and IN6 time-of-flight spectrometers of the Institut Laue-Langevin (ILL) (Grenoble, France). A modest range of temperatures (283-494 K) has been investigated with neutron wavelengths corresponding to incident neutron energies ranging from 0.57 to 67.6 meV. The neutron-weighted multiphonon spectra deduced from the ILL data indicate a slight overestimation by the MD simulations of the frequency shift and broadening of the librational band. The descriptive power of the composite model was suited for improving the comparison to experiments via Bayesian updating of prior model parameters inferred from MD simulations. The reported posterior temperature-dependent densities of state of hydrogen in H2O would represent valuable insights for studying the collective coupling interactions in the water molecule between the inter- and intramolecular degrees of freedom.
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Affiliation(s)
- G Noguere
- CEA, DES, IRESNE, Cadarache, F-13108 Saint Paul Les Durance, France
| | - J P Scotta
- CEA, DES, IRESNE, Cadarache, F-13108 Saint Paul Les Durance, France
| | - S Xu
- CEA, DES, IRESNE, Cadarache, F-13108 Saint Paul Les Durance, France
| | - E Farhi
- Institut Laue-Langevin, F-38042 Grenoble, France
| | - J Ollivier
- Institut Laue-Langevin, F-38042 Grenoble, France
| | - Y Calzavarra
- Institut Laue-Langevin, F-38042 Grenoble, France
| | - S Rols
- Institut Laue-Langevin, F-38042 Grenoble, France
| | - M Koza
- Institut Laue-Langevin, F-38042 Grenoble, France
| | - J I Marquez Damian
- Neutron Physics Departement and Instituto Balseiro, Centro Atomico Bariloche, CNEA, Bariloche, Argentina
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12
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Foxen B, Neill C, Dunsworth A, Roushan P, Chiaro B, Megrant A, Kelly J, Chen Z, Satzinger K, Barends R, Arute F, Arya K, Babbush R, Bacon D, Bardin JC, Boixo S, Buell D, Burkett B, Chen Y, Collins R, Farhi E, Fowler A, Gidney C, Giustina M, Graff R, Harrigan M, Huang T, Isakov SV, Jeffrey E, Jiang Z, Kafri D, Kechedzhi K, Klimov P, Korotkov A, Kostritsa F, Landhuis D, Lucero E, McClean J, McEwen M, Mi X, Mohseni M, Mutus JY, Naaman O, Neeley M, Niu M, Petukhov A, Quintana C, Rubin N, Sank D, Smelyanskiy V, Vainsencher A, White TC, Yao Z, Yeh P, Zalcman A, Neven H, Martinis JM. Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms. Phys Rev Lett 2020; 125:120504. [PMID: 33016760 DOI: 10.1103/physrevlett.125.120504] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Revised: 06/27/2020] [Accepted: 07/22/2020] [Indexed: 06/11/2023]
Abstract
Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.
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Affiliation(s)
- B Foxen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
- Google Research, Santa Barbara, California 93117, USA
| | - C Neill
- Google Research, Santa Barbara, California 93117, USA
| | - A Dunsworth
- Google Research, Santa Barbara, California 93117, USA
| | - P Roushan
- Google Research, Santa Barbara, California 93117, USA
| | - B Chiaro
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - A Megrant
- Google Research, Santa Barbara, California 93117, USA
| | - J Kelly
- Google Research, Santa Barbara, California 93117, USA
| | - Zijun Chen
- Google Research, Santa Barbara, California 93117, USA
| | - K Satzinger
- Google Research, Santa Barbara, California 93117, USA
| | - R Barends
- Google Research, Santa Barbara, California 93117, USA
| | - F Arute
- Google Research, Santa Barbara, California 93117, USA
| | - K Arya
- Google Research, Santa Barbara, California 93117, USA
| | - R Babbush
- Google Research, Santa Barbara, California 93117, USA
| | - D Bacon
- Google Research, Santa Barbara, California 93117, USA
| | - J C Bardin
- Google Research, Santa Barbara, California 93117, USA
- Department of Electrical and Computer Engineering, University of Massachusetts-Amherst, Amherst, Massachusetts 01003, USA
| | - S Boixo
- Google Research, Santa Barbara, California 93117, USA
| | - D Buell
- Google Research, Santa Barbara, California 93117, USA
| | - B Burkett
- Google Research, Santa Barbara, California 93117, USA
| | - Yu Chen
- Google Research, Santa Barbara, California 93117, USA
| | - R Collins
- Google Research, Santa Barbara, California 93117, USA
| | - E Farhi
- Google Research, Santa Barbara, California 93117, USA
| | - A Fowler
- Google Research, Santa Barbara, California 93117, USA
| | - C Gidney
- Google Research, Santa Barbara, California 93117, USA
| | - M Giustina
- Google Research, Santa Barbara, California 93117, USA
| | - R Graff
- Google Research, Santa Barbara, California 93117, USA
| | - M Harrigan
- Google Research, Santa Barbara, California 93117, USA
| | - T Huang
- Google Research, Santa Barbara, California 93117, USA
| | - S V Isakov
- Google Research, Santa Barbara, California 93117, USA
| | - E Jeffrey
- Google Research, Santa Barbara, California 93117, USA
| | - Z Jiang
- Google Research, Santa Barbara, California 93117, USA
| | - D Kafri
- Google Research, Santa Barbara, California 93117, USA
| | - K Kechedzhi
- Google Research, Santa Barbara, California 93117, USA
| | - P Klimov
- Google Research, Santa Barbara, California 93117, USA
| | - A Korotkov
- Google Research, Santa Barbara, California 93117, USA
| | - F Kostritsa
- Google Research, Santa Barbara, California 93117, USA
| | - D Landhuis
- Google Research, Santa Barbara, California 93117, USA
| | - E Lucero
- Google Research, Santa Barbara, California 93117, USA
| | - J McClean
- Google Research, Santa Barbara, California 93117, USA
| | - M McEwen
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - X Mi
- Google Research, Santa Barbara, California 93117, USA
| | - M Mohseni
- Google Research, Santa Barbara, California 93117, USA
| | - J Y Mutus
- Google Research, Santa Barbara, California 93117, USA
| | - O Naaman
- Google Research, Santa Barbara, California 93117, USA
| | - M Neeley
- Google Research, Santa Barbara, California 93117, USA
| | - M Niu
- Google Research, Santa Barbara, California 93117, USA
| | - A Petukhov
- Google Research, Santa Barbara, California 93117, USA
| | - C Quintana
- Google Research, Santa Barbara, California 93117, USA
| | - N Rubin
- Google Research, Santa Barbara, California 93117, USA
| | - D Sank
- Google Research, Santa Barbara, California 93117, USA
| | - V Smelyanskiy
- Google Research, Santa Barbara, California 93117, USA
| | - A Vainsencher
- Google Research, Santa Barbara, California 93117, USA
| | - T C White
- Google Research, Santa Barbara, California 93117, USA
| | - Z Yao
- Google Research, Santa Barbara, California 93117, USA
| | - P Yeh
- Google Research, Santa Barbara, California 93117, USA
| | - A Zalcman
- Google Research, Santa Barbara, California 93117, USA
| | - H Neven
- Google Research, Santa Barbara, California 93117, USA
| | - J M Martinis
- Department of Physics, University of California, Santa Barbara, California 93106, USA
- Google Research, Santa Barbara, California 93117, USA
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13
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Zanatta M, Barocchi F, De Francesco A, Farhi E, Formisano F, Guarini E, Laloni A, Orecchini A, Paciaroni A, Petrillo C, Pilgrim WC, Suck JB, Sacchetti F. A high-flux upgrade for the BRISP spectrometer at ILL. Rev Sci Instrum 2017; 88:053905. [PMID: 28571465 DOI: 10.1063/1.4983572] [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] [Indexed: 06/07/2023]
Abstract
To date, the BRISP spectrometer represents the state-of-the-art for every instrument aiming to perform Brillouin neutron scattering. Exploiting accurate ray-tracing McStas simulations, we investigate an improved configuration of the BRISP primary spectrometer to provide a higher flux at the sample position, while preserving all the present capabilities of the instrument. This configuration is based on a neutron guide system and is designed to fit the instrument platform with no modifications of the secondary spectrometer. These evaluations show that this setup can achieve a flux gain factor ranging from 3 to 6, depending on the wavelength. This can expand the experimental possibilities of BRISP towards smaller samples, possibly using also complex sample environments.
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Affiliation(s)
- M Zanatta
- Dipartimento di Informatica, Università di Verona, I-37134 Verona, Italy
| | - F Barocchi
- Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019 Sesto Fiorentino, Italy
| | - A De Francesco
- IOM-CNR, Operative Group in Grenoble (OGG), c/o Institut Laue Langevin, F-38042 Grenoble, France
| | - E Farhi
- Institut Laue Langevin, F-38042 Grenoble, France
| | - F Formisano
- IOM-CNR, Operative Group in Grenoble (OGG), c/o Institut Laue Langevin, F-38042 Grenoble, France
| | - E Guarini
- Dipartimento di Fisica e Astronomia, Università di Firenze, I-50019 Sesto Fiorentino, Italy
| | - A Laloni
- IOM-CNR, Operative Group in Grenoble (OGG), c/o Institut Laue Langevin, F-38042 Grenoble, France
| | - A Orecchini
- Dipartimento di Fisica e Geologia, Università di Perugia, I-06123 Perugia, Italy
| | - A Paciaroni
- IOM-CNR, c/o Dipartimento di Fisica e Geologia, Università di Perugia, I-06123 Perugia, Italy
| | - C Petrillo
- Dipartimento di Fisica e Geologia, Università di Perugia, I-06123 Perugia, Italy
| | - W-C Pilgrim
- Physikalische Chemie, Philipps Universität Marburg, D-35032 Marburg, Germany
| | - J-B Suck
- Institute of Physics, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
| | - F Sacchetti
- Dipartimento di Fisica e Geologia, Università di Perugia, I-06123 Perugia, Italy
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Guarini E, Bellissima S, Bafile U, Farhi E, De Francesco A, Formisano F, Barocchi F. Density of states from mode expansion of the self-dynamic structure factor of a liquid metal. Phys Rev E 2017; 95:012141. [PMID: 28208346 DOI: 10.1103/physreve.95.012141] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2016] [Indexed: 11/07/2022]
Abstract
We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q→0 extrapolation required to determine the spectrum Z(ω) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q=0 a simple procedure from which Z(ω) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z(ω). In the specific case considered in this work, i.e., liquid Au, analysis of Z(ω) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z(ω), and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we provide our estimate of the self-diffusion coefficient of liquid gold just above melting.
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Affiliation(s)
- E Guarini
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
| | - S Bellissima
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.,Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - U Bafile
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - E Farhi
- Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, F-38042 Grenoble Cedex 9, France
| | - A De Francesco
- Consiglio Nazionale delle Ricerche, Istituto Officina dei Materiali c/o Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, F-38042 Grenoble Cedex 9, France
| | - F Formisano
- Consiglio Nazionale delle Ricerche, Istituto Officina dei Materiali c/o Institut Laue-Langevin, 71 avenue des Martyrs, CS 20156, F-38042 Grenoble Cedex 9, France
| | - F Barocchi
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
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Leonardo T, Farhi E, Boisson AM, Vial J, Cloetens P, Bohic S, Rivasseau C. Determination of elemental distribution in green micro-algae using synchrotron radiation nano X-ray fluorescence (SR-nXRF) and electron microscopy techniques--subcellular localization and quantitative imaging of silver and cobalt uptake by Coccomyxa actinabiotis. Metallomics 2014; 6:316-29. [PMID: 24394991 DOI: 10.1039/c3mt00281k] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The newly discovered unicellular micro-alga Coccomyxa actinabiotis proves to be highly radio-tolerant and strongly concentrates radionuclides, as well as large amounts of toxic metals. This study helps in the understanding of the mechanisms involved in the accumulation and detoxification of silver and cobalt. Elemental distribution inside Coccomyxa actinabiotis cells was determined using synchrotron nano X-ray fluorescence spectroscopy at the ID22 nano fluorescence imaging beamline of the European Synchrotron Radiation Facility. The high resolution and high sensitivity of this technique enabled the assessment of elemental associations and exclusions in subcellular micro-algae compartments. A quantitative treatment of the scans was implemented to yield absolute concentrations of each endogenous and exogenous element with a spatial resolution of 100 nm and compared to the macroscopic content in cobalt and silver determined using inductively coupled plasma-mass spectrometry. The nano X-ray fluorescence imaging was complemented by transmission electron microscopy coupled to X-ray microanalysis (TEM-EDS), yielding differential silver distribution in the cell wall, cytosol, nucleus, chloroplast and mitochondria with unique resolution. The analysis of endogenous elements in control cells revealed that iron had a unique distribution; zinc, potassium, manganese, molybdenum, and phosphate had their maxima co-localized in the same area; and sulfur, copper and chlorine were almost homogeneously distributed among the whole cell. The subcellular distribution and quantification of cobalt and silver in micro-alga, assessed after controlled exposure to various concentrations, revealed that exogenous metals were mainly sequestered inside the cell rather than on mucilage or the cell wall, with preferential compartmentalization. Cobalt was homogeneously distributed outside of the chloroplast. Silver was localized in the cytosol at low concentration and in the whole cell excluding the nucleus at high concentration. Exposure to low concentrations of cobalt or silver did not alter the localization nor the concentration of endogenous elements within the cells. To our knowledge, this is the first report on element co-localization and segregation at the sub-cellular level in micro-algae by means of synchrotron nano X-ray fluorescence spectroscopy.
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Affiliation(s)
- T Leonardo
- CEA, IRTSV, Laboratoire de Physiologie Cellulaire Végétale, F-38054 Grenoble, France
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Affiliation(s)
- P. Willendrup
- DTU Physics, Kongens Lyngby, Denmark
- ESS Collaboration, DTU, Physics, Kongens Lyngby, Denmark
| | | | - E. Knudsen
- DTU Physics, Kongens Lyngby, Denmark
- ESS Collaboration, DTU, Physics, Kongens Lyngby, Denmark
| | | | - K. Lefmann
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
- ESS Collaboration, NBI, Copenhagen, Denmark
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Farhi E, Monzat C, Arnerin R, van Vuure T, Castán-Guerrero C, Hennane C, Harraud P, Campioni G, Fuard S, Ollivier J, Willendrup P. Advanced sources and optical components for the McStas neutron scattering instrument simulation package. Journal of Neutron Research 2014. [DOI: 10.3233/jnr-130007] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- E. Farhi
- Institut Laue Langevin, Grenoble, France
| | - C. Monzat
- Institut Laue Langevin, Grenoble, France
| | - R. Arnerin
- Institut Laue Langevin, Grenoble, France
| | | | | | - C. Hennane
- Institut Laue Langevin, Grenoble, France
| | | | - G. Campioni
- CEA Saclay SERMA/LCA, Gif-sur-Yvette cedex, France
| | - S. Fuard
- Institut Laue Langevin, Grenoble, France
| | | | - P. Willendrup
- Technical University of Denmark, Kongens Lyngby, Denmark
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Farhi E, Debab Y, Willendrup P. iFit: A new data analysis framework. Applications for data reduction and optimization of neutron scattering instrument simulations with McStas. Journal of Neutron Research 2014. [DOI: 10.3233/jnr-130001] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
| | | | - P. Willendrup
- Technical University of Denmark, Kongens Lyngby, Denmark
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Francesca N, Peters J, Russo D, Barbieri S, Chiapponi C, Cupane A, Deriu A, Di Bari MT, Farhi E, Gerelli Y, Mariani P, Paciaroni A, Rivasseau C, Schirò G, Sonvico F. IN13 Backscattering Spectrometer at ILL: Looking for Motions in Biological Macromolecules and Organisms. ACTA ACUST UNITED AC 2008. [DOI: 10.1080/10448630802474083] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Lefmann K, Willendrup PK, Udby L, Lebech B, Mortensen K, Birk JO, KlenØ K, Knudsen E, Christiansen P, Saroun J, Kulda J, Filges U, Konnecke M, Tregenna-Piggott P, Peters J, Lieutenant K, Zsigmond G, Bentley P, Farhi E. Virtual experiments: the ultimate aim of neutron ray-tracing simulations. J of Neutron Res 2008. [DOI: 10.1080/10238160902819684] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Filhol A, Willendrup P, Farhi E, Knudsen E, Lefmann K. Anniversary – 10 years of MCSTASfor instrument design and science. Acta Crystallogr A 2008. [DOI: 10.1107/s0108767308093914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
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Markovich T, Polturak E, Bossy J, Farhi E. Observation of a new excitation in bcc 4He by inelastic neutron scattering. Phys Rev Lett 2002; 88:195301. [PMID: 12005643 DOI: 10.1103/physrevlett.88.195301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2002] [Indexed: 05/23/2023]
Abstract
We report neutron-scattering measurements of the phonons in bcc solid 4He. In general, only three acoustic phonon branches should exist in a monatomic cubic crystal. In addition to these phonon branches, we found a new "opticlike" mode along the [110] direction. One possible interpretation of this new mode is in terms of localized excitations unique to a quantum solid.
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Affiliation(s)
- T Markovich
- Physics Department, Technion-IIT, Haifa, Israel 3200
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Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, Preda D. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 2001; 292:472-5. [PMID: 11313487 DOI: 10.1126/science.1057726] [Citation(s) in RCA: 303] [Impact Index Per Article: 13.2] [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
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We tested one such algorithm by applying it to randomly generated hard instances of an NP-complete problem. For the small examples that we could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
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Affiliation(s)
- E Farhi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
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Farhi E, Goldstone J, Lue A, Rajagopal K. Collision-induced decays of electroweak solitons: Fermion number violation with two and few initial particles. Phys Rev D Part Fields 1996; 54:5336-5360. [PMID: 10021222 DOI: 10.1103/physrevd.54.5336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Farhi E, Rajagopal K, Singleton R. Gauge-invariant variables for spontaneously broken SU(2) gauge theory in the spherical ansatz. Int J Clin Exp Med 1995; 52:2394-2401. [PMID: 10019454 DOI: 10.1103/physrevd.52.2394] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Farhi E, Goldstone J, Gutmann S, Rajagopal K, Singleton R. Fermion production in the background of Minkowski space classical solutions in spontaneously broken gauge theory. Phys Rev D Part Fields 1995; 51:4561-4572. [PMID: 10018930 DOI: 10.1103/physrevd.51.4561] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Farhi E, Khoze VV, Rajagopal K, Singleton R. Spherical shells of a classical gauge field and their topological charge as a perturbative expansion. Int J Clin Exp Med 1994; 50:4162-4174. [PMID: 10018055 DOI: 10.1103/physrevd.50.4162] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Farhi E, Gutmann S. Correlation functions of the one-dimensional random-field Ising model at zero temperature. Phys Rev B Condens Matter 1993; 48:9508-9514. [PMID: 10007192 DOI: 10.1103/physrevb.48.9508] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Farhi E, Khoze VV, Singleton R. Minkowski space non-Abelian classical solutions with noninteger winding number change. Int J Clin Exp Med 1993; 47:5551-5564. [PMID: 10015582 DOI: 10.1103/physrevd.47.5551] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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