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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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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4
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Sun Q, Zhang X, Banerjee S, Bao P, Barbry M, Blunt NS, Bogdanov NA, Booth GH, Chen J, Cui ZH, Eriksen JJ, Gao Y, Guo S, Hermann J, Hermes MR, Koh K, Koval P, Lehtola S, Li Z, Liu J, Mardirossian N, McClain JD, Motta M, Mussard B, Pham HQ, Pulkin A, Purwanto W, Robinson PJ, Ronca E, Sayfutyarova ER, Scheurer M, Schurkus HF, Smith JET, Sun C, Sun SN, Upadhyay S, Wagner LK, Wang X, White A, Whitfield JD, Williamson MJ, Wouters S, Yang J, Yu JM, Zhu T, Berkelbach TC, Sharma S, Sokolov AY, Chan GKL. Recent developments in the PySCF program package. J Chem Phys 2020; 153:024109. [DOI: 10.1063/5.0006074] [Citation(s) in RCA: 151] [Impact Index Per Article: 37.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- Qiming Sun
- AxiomQuant Investment Management LLC, Shanghai 200120, China
| | - Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Samragni Banerjee
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Peng Bao
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Marc Barbry
- Simbeyond B.V., P.O. Box 513, NL-5600 MB, Eindhoven, The Netherlands
| | - Nick S. Blunt
- Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Nikolay A. Bogdanov
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - George H. Booth
- Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom
| | - Jia Chen
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Zhi-Hao Cui
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Janus J. Eriksen
- School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
| | - Yang Gao
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Sheng Guo
- Google Inc., Mountain View, California 94043, USA
| | - Jan Hermann
- FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany
- TU Berlin, Machine Learning Group, Marchstr. 23, 10587 Berlin, Germany
| | - Matthew R. Hermes
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Kevin Koh
- Department of Chemistry and Biochemistry, The University of Notre Dame du Lac, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, USA
| | - Peter Koval
- Simune Atomistics S.L., Avenida Tolosa 76, Donostia-San Sebastian, Spain
| | - Susi Lehtola
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FI-00014 Helsinki, Finland
| | - Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Junzi Liu
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Narbe Mardirossian
- AMGEN Research, One Amgen Center Drive, Thousand Oaks, California 91320, USA
| | | | - Mario Motta
- IBM Almaden Research Center, San Jose, California 95120, USA
| | - Bastien Mussard
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Hung Q. Pham
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, USA
| | - Artem Pulkin
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, The Netherlands
| | - Wirawan Purwanto
- Information Technology Services, Old Dominion University, Norfolk, Virginia 23529, USA
| | - Paul J. Robinson
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Enrico Ronca
- Istituto per i Processi Chimico Fisici del CNR (IPCF-CNR), Via G. Moruzzi, 1, 56124 Pisa, Italy
| | - Elvira R. Sayfutyarova
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Maximilian Scheurer
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University of Heidelberg, 205 Im Neuenheimer Feld, 69120 Heidelberg, Germany
| | - Henry F. Schurkus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James E. T. Smith
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Chong Sun
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Shi-Ning Sun
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA
| | - Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Lucas K. Wagner
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA
| | - Xiao Wang
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Alec White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - James Daniel Whitfield
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Mark J. Williamson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Jason M. Yu
- Department of Chemistry, University of California, Irvine, 1102 Natural Sciences II, Irvine, California 92697-2025, USA
| | - Tianyu Zhu
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Colorado 80302, USA
| | - Alexander Yu. Sokolov
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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5
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Schurkus HF, Chan GKL, Chen DT, Cheng HP, Stanton JF. Theoretical prediction of magnetic exchange coupling constants from broken-symmetry coupled cluster calculations. J Chem Phys 2020; 152:234115. [PMID: 32571049 DOI: 10.1063/1.5144696] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [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
Exchange coupling constants (J) are fundamental to the understanding of spin spectra of magnetic systems. Here, we investigate the broken-symmetry (BS) approaches of Noodleman and Yamaguchi in conjunction with coupled cluster (CC) methods to obtain exchange couplings. J values calculated from CC in this fashion converge smoothly toward the full configuration interaction result with increasing level of CC excitation. We compare this BS-CC scheme to the complementary equation-of-motion CC approach on a selection of bridged molecular cases and give results from a few other methodologies for context.
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Affiliation(s)
- Henry F Schurkus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Dian-Teng Chen
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
| | - Hai-Ping Cheng
- Department of Physics, University of Florida, Gainesville, Florida 32611, USA
| | - John F Stanton
- Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA
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6
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Abstract
The giant {Mn70} and {Mn84} wheels are the largest nuclearity single-molecule magnets synthesized to date, and understanding their magnetic properties poses a challenge to theory. Starting from first-principles calculations, we explore the magnetic properties and excitations in these wheels using effective spin Hamiltonians. We find that the unusual geometry of the superexchange pathways leads to weakly coupled {Mn7} subunits carrying an effective S = 2 spin. The spectrum exhibits a hierarchy of energy scales and massive degeneracies, with the lowest-energy excitations arising from Heisenberg-ring-like excitations of the {Mn7} subunits around the wheel. We further describe how weak longer-range couplings can select the precise spin ground-state of the Mn wheels out of the nearly degenerate ground-state band.
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Affiliation(s)
- Henry F Schurkus
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Dianteng Chen
- Department of Physics, University of Florida, Gainesville, Florida 32611, United States
| | - Matthew J O'Rourke
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Hai-Ping Cheng
- Department of Physics, University of Florida, Gainesville, Florida 32611, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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7
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Beuerle M, Graf D, Schurkus HF, Ochsenfeld C. Efficient calculation of beyond RPA correlation energies in the dielectric matrix formalism. J Chem Phys 2018; 148:204104. [DOI: 10.1063/1.5025938] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthias Beuerle
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Daniel Graf
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Henry F. Schurkus
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany and Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU), Butenandtstr. 5–13, D-81377 München, Germany
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8
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Graf D, Beuerle M, Schurkus HF, Luenser A, Savasci G, Ochsenfeld C. Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method. J Chem Theory Comput 2018; 14:2505-2515. [PMID: 29658715 DOI: 10.1021/acs.jctc.8b00177] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.
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Affiliation(s)
- Daniel Graf
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Matthias Beuerle
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Henry F Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Arne Luenser
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany
| | - Gökcen Savasci
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany.,Max Planck Institute for Solid State Research , Heisenbergstraße 1 , 70569 Stuttgart , Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry , University of Munich (LMU) , D-81377 Munich , Germany.,Max Planck Institute for Solid State Research , Heisenbergstraße 1 , 70569 Stuttgart , Germany
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9
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Schurkus HF, Luenser A, Ochsenfeld C. Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions. J Chem Phys 2017; 146:211106. [PMID: 28595410 PMCID: PMC5462614 DOI: 10.1063/1.4985085] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Accepted: 05/24/2017] [Indexed: 11/14/2022] Open
Abstract
We present a method to improve upon the resolution-of-the-identity (RI) for correlation methods. While RI is known to allow for drastic speedups, it relies on a cancellation of errors. Our method eliminates the errors introduced by RI which are known to be problematic for absolute energies. In this way, independence of the error compensation assumption for relative energies is also achieved. The proposed method is based on the idea of starting with an oversized RI basis and projecting out all of its unphysical parts. The approach can be easily implemented into existing RI codes and results in an overhead of about 30%, while effectively removing the RI error. In passing, this process alleviates the problem that for many frequently employed basis sets no optimized RI basis sets have been constructed. In this paper, the theory is presented and results are discussed exemplarily for the random phase approximation and Møller-Plesset perturbation theory.
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Affiliation(s)
- Henry F Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Arne Luenser
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
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10
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Luenser A, Schurkus HF, Ochsenfeld C. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric. J Chem Theory Comput 2017; 13:1647-1655. [DOI: 10.1021/acs.jctc.6b01235] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arne Luenser
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Henry F. Schurkus
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
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11
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Schurkus HF, Ochsenfeld C. Communication: An effective linear-scaling atomic-orbital reformulation of the random-phase approximation using a contracted double-Laplace transformation. J Chem Phys 2016; 144:031101. [DOI: 10.1063/1.4939841] [Citation(s) in RCA: 58] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Henry F. Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), D-81377 Munich, Germany
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