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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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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Abstract
OBJECTIVES Understanding the pattern of middle-ear cholesteatoma becomes pertinent with the rise of endoscopic surgery as surgeons decide on the optimal approach to visualise and extirpate disease. With modifications to the Telmesani attic-tympanum-mastoid staging system, this study aimed to evaluate the commonest patterns of middle-ear cholesteatoma and their implications for surgical approach. METHODS A retrospective study was conducted in a single tertiary institution in Singapore. All patients undergoing cholesteatoma surgery between January 2012 and June 2015 were included. Staging of cholesteatoma was based on clinical assessment corroborated by radiological findings. RESULTS Out of the 55 ears included, 98.2 per cent had cholesteatoma involving the attic. The disease extended into the mastoid antrum and beyond in 43 cases (78.2 per cent). The facial recess and/or sinus tympanum was affected in 26 cases (47.3 per cent). CONCLUSION The majority of cholesteatoma cases present with extensive attic disease and significant mastoid involvement. In these cases, endoscopes may be best suited to adjunctive rather than exclusive use in surgery.
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Affiliation(s)
- Y Yu
- Department of Otolaryngology, Changi General Hospital, Singapore
| | - J See
- Department of Otolaryngology, Changi General Hospital, Singapore
| | - J H Ng
- Department of Otolaryngology, Changi General Hospital, Singapore
| | - D Low
- Department of Otolaryngology, Changi General Hospital, Singapore
| | - T Y Tan
- Department of Diagnostic Radiology, Changi General Hospital, Singapore
| | - H W Yuen
- Department of Otolaryngology, Changi General Hospital, Singapore
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Mandelblatt JS, Bierman AS, Gold K, Zhang Y, Ng JH, Maserejian N, Maserejan N, Hwang YT, Meropol NJ, Hadley J, Silliman RA. Constructs of burden of illness in older patients with breast cancer: a comparison of measurement methods. Health Serv Res 2001; 36:1085-107. [PMID: 11775669 PMCID: PMC1089280] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023] Open
Abstract
OBJECTIVE The burden of illness can influence treatment decisions, but there are limited data comparing the performance of different illness burden measures. We assessed the correlations between five previously validated measures of illness burden and global health and physical function and evaluated how each measure correlates with breast cancer treatment patterns in older women. DATA SOURCE A cohort of 718 women > 67 years with early-stage breast cancer formed the study group. STUDY DESIGN/DATA COLLECTION METHODS: The study made a cross-sectional comparison of illness burden measures (Charlson index, Index of Co-existent Diseases, cardiopulmonary burden of illness, patient-specific life expectancy, and disease counts) and physical function and self-rated global health status. Data were collected from records and patient interviews. PRINCIPAL FINDINGS All of the measures were significantly correlated with each other and with physical function and self-rated health (p < .001). After controlling for age and stage, life expectancy had the largest effect on surgical treatment, followed by self-rated physical function and health; life expectancy was also independent of physical function. For instance, women with higher life expectancy and better self-rated physical function and health were more likely to receive breast conservation and radiation than sicker women. Women with higher physical functioning were more likely to receive adjuvant chemotherapy than women with lower functioning. CONCLUSIONS Several measures of illness burden were associated with breast cancer therapy, but each measure accounted for only a small amount of variance in treatment patterns. Future work is needed to develop and validate measures of burden of illness that are feasible, comprehensive, and relevant for diverse clinical and health services objectives.
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Affiliation(s)
- J S Mandelblatt
- Department of Oncology, Lombardi Cancer Center, Georgetown University Medical Center, Washington, DC 20007, USA
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Ng JH, Nesaretnam K, Reimann K, Lai LC. Effect of retinoic acid and palm oil carotenoids on oestrone sulphatase and oestradiol-17beta hydroxysteroid dehydrogenase activities in MCF-7 and MDA-MB-231 breast cancer cell lines. Int J Cancer 2000; 88:135-8. [PMID: 10962451 DOI: 10.1002/1097-0215(20001001)88:1<135::aid-ijc21>3.0.co;2-s] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Oestrogen is important in the development of breast cancer. Oestrogen receptor positive breast cancers are associated with a better prognosis than oestrogen-receptor negative breast cancers since they are more responsive to hormonal treatment. Oestrone sulphate acts as a huge reservoir for oestrogens in the breast. It is converted to the potent oestrogen, oestradiol (E(2)) by the enzymes oestrone sulphatase and oestradiol-17beta hydroxysteroid dehydrogenase (E(2)DH). Retinoic acid and carotenoids have been shown to have chemopreventive activity against some cancers. The aim of our study was to determine and compare the effects of retinoic acid and palm oil carotenoids on growth of and oestrone sulphatase and E(2)DH activities in the oestrogen receptor positive, MCF-7 and oestrogen receptor negative, MDA-MB-231 breast cancer cell lines. Retinoic acid and carotenoids inhibited MCF-7 cell growth but had no effect on MDA-MB-231 cell growth. Both retinoic acid and carotenoids stimulated oestrone sulphatase activity in the MCF-7 cell line. E(1) to E(2) conversion was inhibited by 10(-7) M carotenoids but was stimulated at 10(-6) M in the MCF-7 cell line. Retinoic acid had no effect on E(1) to E(2) conversion at 10(-7) M but stimulated E(1) to E(2) conversion at 10(-6) M. Retinoic acid and carotenoids had no effect on E(2) to E(1) conversion in the MCF-7 cell line. Retinoic acid stimulated E(1) to E(2) conversion in the MDA-MB-231 cell line but had no effect on oestrone sulphatase activity or E(2) to E(1) conversion in this cell line. Both oestrone sulphatase and E(2)DH activity were not affected by carotenoids in the MDA-MB-231 cell line. In conclusion, retinoic acid and carotenoids may prevent the development of hormone-dependent breast cancers since they inhibit the growth of the MCF-7 cell line.
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Affiliation(s)
- J H Ng
- Faculty of Medicine and Health Sciences, Universiti Putra Malaysia, Selangor, Malaysia
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Abstract
OBJECTIVE To examine the survival, developmental status, quality of life, and direct medical costs of children with hypoplastic left heart syndrome who have undergone stage I, II, and III reconstructive surgery. METHODS A total of 106 children underwent staged repair for classic hypoplastic left heart syndrome between February 1990 and March 1999 (stage I: 106; stage II: 49; stage III: 25; 4 converted to heart transplantation). Survival was analyzed by the Kaplan-Meier method. In a cross-sectional study, parents assessed quality of life by completing the Infant/Toddler Child Health Questionnaire or Child Health Questionnaire Parent Format-28; they assessed developmental progress by completing the Ages and Stages Questionnaire. The ratio-of-costs-to-charges method was used to derive hospital costs, and payments were used to capture physician time and wholesale pricing for outpatient medications. RESULTS Institutional 1-year and 5-year actuarial survivals were 58% and 54%. Birth weight, the need for preoperative inotropic drugs, and surgical experience were predictors of survival. Norwood I patients achieved fewer developmental benchmarks than those who survived to subsequent stages. Child Health Questionnaire Parent Format-28 mean summary scores for physical and psychosocial health were 48.5 +/- 6.3 and 42.8 +/- 9.9. The median inpatient costs for stage I, II, and III repairs were $51,000, $33,892, and $52,183, respectively. Monthly outpatient and readmission costs were less than 10% of total costs. CONCLUSION A prospective, large-scale study of the comprehensive outcomes of staged repair and transplantation is needed. This study will need to address the longer-term developmental and quality-of-life outcomes, as well as the long-term cost effectiveness of these procedures.
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Affiliation(s)
- D L Williams
- International Center for Health Outcomes and Innovation Research, Department of Surgery, Columbia University, College of Physicians and Surgeons, New York Presbyterian Hospital, New York, NY, USA
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Colman-Saizarbitoria T, Zambrano J, Ferrigni NR, Gu ZM, Ng JH, Smith DL, McLaughlin JL. Bioactive annonaceous acetogenins from the bark of Xylopia aromatica. J Nat Prod 1994; 57:486-493. [PMID: 8021648 DOI: 10.1021/np50106a007] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Bioactive Annonaceous acetogenins have been isolated from the EtOH extract of the bark of Xylopia aromatica by bioactivity-directed fractionation using lethality to brine shrimp. These acetogenins include xylopianin [1 , xylopiacin [2], and xylomaticin [3], which are three new mono-tetrahydrofuran ring type acetogenins, in addition to the known compounds, annomontacin, gigantetronenin, gigantetrocin A, and annonacin. Compounds 1 and 2 are unusual in having hydroxylation at C-8; 3 has the same functionalities as annonacin but with 37 carbons instead of 35 carbons. The structures were elucidated by spectral analysis of the parent compounds and/or simple chemical derivatives. These acetogenins showed cytotoxicities, comparable to adriamycin, against three human solid tumor cell lines.
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Abstract
Palm oil carotenoids are analyzed by nonaqueous reversed-phase high-performance liquid chromatography (NARP-HPLC) with UV/vis diode-array detection. Isocratic elution with 60% acetonitrile/35% methanol/5% methylene chloride at 2 mL/min on a 25-cm C18 column results in an analysis time of 30 min. Identification is made through absorption spectra and chromatographic elution behaviors, for example, polyenic pi conjugation, dipole moment of end-groups, and oxygen function on the chromophores. At least 12 carotenoids are identified with alpha- and beta-carotene as the dominant carotenoids (1:2 ratio). Several mono- and di-epoxides of alpha- and beta-isomers and hydrocarbon carotenes are found, including the UV-absorbing phytoene identified by spectral substraction. cis-Isomerization is found and discussed in the light of spectral evidence. The effect of saponification time on the amount of extracted carotenes is investigated. Quantitation results in a combined alpha- and beta-carotene concentration of at least 506 ppm. The detection limit for beta-carotene is 31 ng.
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Affiliation(s)
- J H Ng
- Department of Chemistry, University of Massachusetts, Amherst 01003
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