Quantum Hamiltonian complexity in thermal equilibrium

The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Here we study the computational complexity of approximating these quantities for n -qubit local Hamiltonians. First, we report a classical algorithm with poly( n ) r...

Full description

Saved in:

Bibliographic Details
Published in:	Nature physics Vol. 18; no. 11; pp. 1367 - 1370
Main Authors:	Bravyi, Sergey, Chowdhury, Anirban, Gosset, David, Wocjan, Pawel
Format:	Journal Article
Language:	English
Published:	London Nature Publishing Group UK 01.11.2022 Nature Publishing Group
Subjects:	639/766/483/481 639/766/530/2804 639/766/530/951 Algorithms Approximation Atomic Circuits Classical and Continuum Physics Complex Systems Complexity Condensed Matter Physics Energy Equilibrium Free energy Hamiltonian functions Ising model Mathematical analysis Mathematical and Computational Physics Molecular Optical and Plasma Physics Optimization Partitions (mathematics) Physical properties Physics Physics and Astronomy Polynomials Quantum computing Qubits (quantum computing) Run time (computers) Theoretical
ISSN:	1745-2473, 1745-2481
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Here we study the computational complexity of approximating these quantities for n -qubit local Hamiltonians. First, we report a classical algorithm with poly( n ) runtime, which approximates the free energy of a given 2-local Hamiltonian provided that it satisfies a certain denseness condition. Our algorithm contributes to a body of work investigating the hardness of approximation for difficult optimization problems. Specifically, this extends existing efficient approximation algorithms for dense instances of the ground energy of 2-local quantum Hamiltonians and the free energy of classical Ising models. Second, we establish polynomial-time equivalence between the problem of approximating the free energy of local Hamiltonians and several other natural tasks ubiquitous in condensed-matter physics and quantum computing, such as the problem of approximating the number of input states accepted by a polynomial-size quantum circuit. These results suggest that the simulation of quantum many-body systems in thermal equilibrium may precisely capture the complexity of a broad family of computational problems that have yet to be defined or characterized in terms of known complexity classes. Finally, we summarize state-of-the-art classical and quantum algorithms for approximating the free energy and show how to improve their runtime and memory footprint. A quantum many-body system’s equilibrium behaviour is described by its partition function, which is hard to compute. Now it has been shown that the easier task of finding an approximation could define a distinct class of computational problems.
AbstractList	The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Here we study the computational complexity of approximating these quantities for n-qubit local Hamiltonians. First, we report a classical algorithm with poly(n) runtime, which approximates the free energy of a given 2-local Hamiltonian provided that it satisfies a certain denseness condition. Our algorithm contributes to a body of work investigating the hardness of approximation for difficult optimization problems. Specifically, this extends existing efficient approximation algorithms for dense instances of the ground energy of 2-local quantum Hamiltonians and the free energy of classical Ising models. Second, we establish polynomial-time equivalence between the problem of approximating the free energy of local Hamiltonians and several other natural tasks ubiquitous in condensed-matter physics and quantum computing, such as the problem of approximating the number of input states accepted by a polynomial-size quantum circuit. These results suggest that the simulation of quantum many-body systems in thermal equilibrium may precisely capture the complexity of a broad family of computational problems that have yet to be defined or characterized in terms of known complexity classes. Finally, we summarize state-of-the-art classical and quantum algorithms for approximating the free energy and show how to improve their runtime and memory footprint.A quantum many-body system’s equilibrium behaviour is described by its partition function, which is hard to compute. Now it has been shown that the easier task of finding an approximation could define a distinct class of computational problems. The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Here we study the computational complexity of approximating these quantities for n -qubit local Hamiltonians. First, we report a classical algorithm with poly( n ) runtime, which approximates the free energy of a given 2-local Hamiltonian provided that it satisfies a certain denseness condition. Our algorithm contributes to a body of work investigating the hardness of approximation for difficult optimization problems. Specifically, this extends existing efficient approximation algorithms for dense instances of the ground energy of 2-local quantum Hamiltonians and the free energy of classical Ising models. Second, we establish polynomial-time equivalence between the problem of approximating the free energy of local Hamiltonians and several other natural tasks ubiquitous in condensed-matter physics and quantum computing, such as the problem of approximating the number of input states accepted by a polynomial-size quantum circuit. These results suggest that the simulation of quantum many-body systems in thermal equilibrium may precisely capture the complexity of a broad family of computational problems that have yet to be defined or characterized in terms of known complexity classes. Finally, we summarize state-of-the-art classical and quantum algorithms for approximating the free energy and show how to improve their runtime and memory footprint. A quantum many-body system’s equilibrium behaviour is described by its partition function, which is hard to compute. Now it has been shown that the easier task of finding an approximation could define a distinct class of computational problems.
Author	Gosset, David Chowdhury, Anirban Wocjan, Pawel Bravyi, Sergey
Author_xml	– sequence: 1 givenname: Sergey surname: Bravyi fullname: Bravyi, Sergey organization: IBM Quantum, IBM T.J. Watson Research Center – sequence: 2 givenname: Anirban orcidid: 0000-0001-9743-7978 surname: Chowdhury fullname: Chowdhury, Anirban email: anirban.n.chowdhury@gmail.com organization: Institute for Quantum Computing, University of Waterloo, Department of Combinatorics and Optimization, University of Waterloo, Perimeter Institute for Theoretical Physics – sequence: 3 givenname: David surname: Gosset fullname: Gosset, David organization: Institute for Quantum Computing, University of Waterloo, Department of Combinatorics and Optimization, University of Waterloo, Perimeter Institute for Theoretical Physics – sequence: 4 givenname: Pawel surname: Wocjan fullname: Wocjan, Pawel organization: IBM Quantum, IBM T.J. Watson Research Center
BookMark	eNp9kE1Lw0AQhhepYFv9A54CnqP7lWxylKJWKIig52W6meiWZNPubsD-e9NGFDz0NO_hfWaGZ0YmrnNIyDWjt4yK4i5IluUqpZynlCnJ0-yMTIeQpVwWbPKblbggsxA2lEqeMzEl2WsPLvZtsoTWNrFzFlxiunbb4JeN-8S6JH6ib6FJcNfbxq697dtLcl5DE_DqZ87J--PD22KZrl6enhf3q9QIVsYUJVWsBMGEoUUJqgJkuQJWQ6V4VUNBpSgqRbHGGows8gw5X4uSlmhyg6WYk5tx79Z3ux5D1Juu9244qbkSvGQyF4dWMbaM70LwWGtjI0TbuejBNppRfZCkR0l6kKSPknQ2oPwfuvW2Bb8_DYkRCkPZfaD_--oE9Q3px3vj
CitedBy_id	crossref_primary_10_1103_k5tx_xtr3 crossref_primary_10_1137_24M1654749 crossref_primary_10_1038_s41534_024_00883_0 crossref_primary_10_1063_5_0218349 crossref_primary_10_22331_q_2025_08_29_1843 crossref_primary_10_1038_s41598_024_64854_3 crossref_primary_10_1038_s42005_024_01763_x crossref_primary_10_1103_PRXQuantum_5_010329 crossref_primary_10_1038_s41467_024_54118_z crossref_primary_10_1103_PRXQuantum_5_010305 crossref_primary_10_1103_PhysRevX_14_011013 crossref_primary_10_1103_PRXQuantum_4_040201 crossref_primary_10_1038_s41467_024_51592_3 crossref_primary_10_1186_s13321_025_01026_z crossref_primary_10_1038_s41467_024_51439_x
Cites_doi	10.1145/3313276.3316366 10.1090/conm/305/05215 10.1137/S0097539704445226 10.1145/2554797.2554836 10.1103/PhysRevA.103.032422 10.1103/PhysRevLett.124.220601 10.1103/PhysRevA.80.012304 10.1145/800061.808740 10.1145/1236457.1236459 10.1137/110842272 10.1137/1.9781611976014.5 10.1142/2262 10.1145/3357713.3384322 10.1007/s00023-021-01111-7 10.22331/q-2020-02-14-230 10.1090/gsm/047 10.1145/2488608.2488719 10.26421/QIC16.9-10-1 10.26421/QIC8.5-1 10.1073/pnas.1804949115 10.1109/TIT.2021.3081415 10.1080/03610918908812806 10.1145/1008731.1008733 10.1007/978-3-319-51829-9_2 10.1103/PhysRevLett.103.220502 10.1103/PRXQuantum.3.010308 10.1103/PhysRevLett.119.100503 10.1103/PhysRevLett.81.5672 10.22331/q-2021-02-11-395 10.1109/FOCS.2011.95 10.1007/s00037-017-0162-2 10.1038/s41567-020-0932-7 10.1007/s00037-005-0194-x 10.1007/3-540-62592-5_80 10.22331/q-2022-03-17-668 10.1137/1.9781611976496.16
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer Nature Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer Nature Limited 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
DBID	AAYXX CITATION 3V. 7U5 7XB 88I 8FD 8FE 8FG 8FK ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR CCPQU DWQXO GNUQQ HCIFZ L7M M2P P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI Q9U
DOI	10.1038/s41567-022-01742-5
DatabaseName	CrossRef ProQuest Central (Corporate) Solid State and Superconductivity Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology Collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection Advanced Technologies Database with Aerospace Science Database (ProQuest) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central Basic
DatabaseTitle	CrossRef ProQuest Central Student Technology Collection Technology Research Database ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central Earth, Atmospheric & Aquatic Science Collection ProQuest One Applied & Life Sciences ProQuest One Sustainability Natural Science Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Advanced Technologies & Aerospace Collection ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Solid State and Superconductivity Abstracts ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New)
DatabaseTitleList	ProQuest Central Student
Database_xml	– sequence: 1 dbid: BENPR name: Proquest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Physics
EISSN	1745-2481
EndPage	1370
ExternalDocumentID	10_1038_s41567_022_01742_5
GrantInformation_xml	– fundername: Canadian Institute for Advanced Research (L'Institut Canadien de Recherches Avancées) funderid: https://doi.org/10.13039/100007631 – fundername: IBM Research – fundername: IBM Research Frontiers – fundername: United States Department of Defense \| United States Army \| U.S. Army Research, Development and Engineering Command \| Army Research Office (ARO) grantid: W911NF-20-1-001; W911NF-20-1-001; W911NF-20-1-001 funderid: https://doi.org/10.13039/100000183
GroupedDBID	0R~ 123 29M 39C 3V. 4.4 5BI 5M7 6OB 70F 88I 8FE 8FG 8FH 8R4 8R5 AAEEF AARCD AAYZH AAZLF ABAWZ ABDBF ABJNI ABLJU ABUWG ABZEH ACBWK ACGFO ACGFS ACGOD ACMJI ACUHS ADBBV ADFRT AENEX AEUYN AFBBN AFKRA AFSHS AFWHJ AGAYW AGHTU AHBCP AHOSX AHSBF AIBTJ ALFFA ALMA_UNASSIGNED_HOLDINGS AMTXH ARAPS ARMCB ASPBG AVWKF AXYYD AZFZN AZQEC BENPR BGLVJ BHPHI BKKNO BKSAR BPHCQ CCPQU DB5 DU5 DWQXO EBS EE. EJD ESX EXGXG F5P FEDTE FQGFK FSGXE GNUQQ HCIFZ HVGLF HZ~ I-F LGEZI LK5 LOTEE M2P M7R N9A NADUK NNMJJ NXXTH O9- ODYON P2P P62 PCBAR PQQKQ PROAC Q2X RNS RNT RNTTT SHXYY SIXXV SJN SNYQT SOJ TAOOD TBHMF TDRGL TSG TUS ~8M AAYXX ABFSG ACSTC AEZWR AFANA AFFHD AFHIU AGSTI AHWEU AIXLP ALPWD ATHPR CITATION PHGZM PHGZT PQGLB 7U5 7XB 8FD 8FK L7M PKEHL PQEST PQUKI Q9U
ID	FETCH-LOGICAL-c319t-e40719a313c089a7dae167a1fad72dfa80438d70efefac4865e22b3909ec6ce93
IEDL.DBID	M2P
ISICitedReferencesCount	20
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000864597400002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1745-2473
IngestDate	Sat Aug 16 18:51:26 EDT 2025 Tue Nov 18 21:04:29 EST 2025 Sat Nov 29 01:38:11 EST 2025 Fri Feb 21 02:38:01 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	11
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c319t-e40719a313c089a7dae167a1fad72dfa80438d70efefac4865e22b3909ec6ce93
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0001-9743-7978
PQID	2732914639
PQPubID	27545
PageCount	4
ParticipantIDs	proquest_journals_2732914639 crossref_citationtrail_10_1038_s41567_022_01742_5 crossref_primary_10_1038_s41567_022_01742_5 springer_journals_10_1038_s41567_022_01742_5
PublicationCentury	2000
PublicationDate	2022-11-01
PublicationDateYYYYMMDD	2022-11-01
PublicationDate_xml	– month: 11 year: 2022 text: 2022-11-01 day: 01
PublicationDecade	2020
PublicationPlace	London
PublicationPlace_xml	– name: London
PublicationTitle	Nature physics
PublicationTitleAbbrev	Nat. Phys
PublicationYear	2022
Publisher	Nature Publishing Group UK Nature Publishing Group
Publisher_xml	– name: Nature Publishing Group UK – name: Nature Publishing Group
References	Barak, B., Raghavendra, P. & Steurer, D. Rounding semidefinite programming hierarchies via global correlation. IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 472-481 (2011). Risteski, A. How to calculate partition functions using convex programming hierarchies: provable bounds for variational methods. In 29th Annual Conference on Learning Theory (eds. Feldman, V., Rakhlin, A. & Shamir, O.) vol. 49 of Proceedings of Machine Learning Research 1402–1416 (PMLR, 2016). DinurIThe PCP theorem by gap amplificationJ. ACM20075412es231425410.1145/1236457.12364591292.68074 van ApeldoornJGilyénAGriblingSde WolfRQuantum SDP-solvers: better upper and lower boundsQuantum2020423010.22331/q-2020-02-14-230 Cade, C. & Montanaro, A. The quantum complexity of computing Schatten p-norms. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) (Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik 2018). Brandão, F. G. S. L. Entanglement Theory and the Quantum Simulation of Many-Body Physics. PhD thesis, Imperial College of Science, Technology and Medicine (2008). DankertCCleveREmersonJLivineEExact and approximate unitary 2-designs and their application to fidelity estimationPhys. Rev. A2009800123042009PhRvA..80a2304D10.1103/PhysRevA.80.012304 Brassard, G., Høyer, P., Mosca, M. and Tapp, A. Quantum amplitude amplification and estimation. In Quantum Computation and Information Vol. 305 of Contemporary Mathematics 53–74 (AMS, 2002). KitaevAYShenAHVyalyiMNClassical and Quantum Computation2002American Mathematical Society10.1090/gsm/0471022.68001 Kohler, T., Piddock, S., Bausch, J. & Cubitt, T. General conditions for universality of quantum Hamiltonians. PRX Quantum 3, 010308 (2022). BravyiSGossetDPolynomial-time classical simulation of quantum ferromagnetsPhys. Rev. Lett.20171191005032017PhRvL.119j0503B10.1103/PhysRevLett.119.100503 HuangH-YKuengRPreskillJPredicting many properties of a quantum system from very few measurementsNat. Phys.2020161050105710.1038/s41567-020-0932-7 CrossonEHarrowAWRapid mixing of path integral Monte Carlo for 1D stoquastic HamiltoniansQuantum2021539510.22331/q-2021-02-11-395 CubittTSMontanaroAPiddockSUniversal quantum HamiltoniansProc. Natl Acad. Sci. USA2018115949795022018PNAS..115.9497C385903710.1073/pnas.18049491151416.82008 HutchinsonMFA stochastic estimator of the trace of the influence matrix for Laplacian smoothing splinesCommun. Stat. Simul. Comput.19891810591076103184010.1080/036109189088128060695.62113 Harrow, A. W., Mehraban, S. & Soleimanifar, M. Classical algorithms, correlation decay, and complex zeros of partition functions of quantum many-body systems. In Proc. 52nd Annual ACM SIGACT Symposium on Theory of Computing 378–386 (ACM, 2020). KempeJKitaevARegevOThe complexity of the local Hamiltonian problemSIAM J. Comput.20063510701097221713810.1137/S00975397044452261102.81032 Brandao, F. G. & Harrow, A. W. Product-state approximations to quantum ground states. In Proc. Forty-Fifth Annual ACM Symposium on Theory of Computing STOC ’13 871–880 (ACM, 2013). Aaronson, S. and Rall, P. Quantum approximate counting, simplified. In Symposium on Simplicity in Algorithms 24–32 (SIAM, 2020). Zhou, L. & Aharonov, D. Strongly universal Hamiltonian simulators. Preprint at https://arxiv.org/abs/2102.02991 (2021). KuwaharaTKatoKBrandãoFGSLClustering of conditional mutual information for quantum Gibbs states above a threshold temperaturePhys. Rev. Lett.20201242206012020PhRvL.124v0601K411120410.1103/PhysRevLett.124.220601 Grötschel, M., Lovász, L. & Schrijver, A. Geometric Algorithms and Combinatorial Optimization Vol. 2 (Springer Science & Business Media, 2012). Stockmeyer, L. The complexity of approximate counting. In Proc. Fifteenth Annual ACM Symposium on Theory of Computing STOC ’83 118–126 (ACM, 1983). BravyiSMaslovDHadamard-free circuits expose the structure of the Clifford groupIEEE Trans. Inf. Theory20216745464563430628410.1109/TIT.2021.30814151475.68132 BertsimasDVempalaSSolving convex programs by random walksJ. ACM200451540556214784710.1145/1008731.10087331204.90074 Gosset, D. & Smolin, J. A compressed classical description of quantum states. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019) (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2019). PoulinDWocjanPSampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computerPhys. Rev. Lett.20091032205022009PhRvL.103v0502P257021810.1103/PhysRevLett.103.220502 GoldbergLAGuoHThe complexity of approximating complex-valued Ising and Tutte partition functionscomput. complex.201726765833372334910.1007/s00037-017-0162-21382.68090 Yoshida, Y. & Zhou, Y. Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems. In Proc. 5th Conference on Innovations in Theoretical Computer Science ITCS ’14 423–438 (ACM, 2014). KnillELaflammeRPower of one bit of quantum informationPhys. Rev. Lett.19988156721998PhRvL..81.5672K10.1103/PhysRevLett.81.5672 Bravyi, S., Divincenzo, D. P., Oliveira, R. I. & Terhal, B. M. The complexity of stoquastic local Hamiltonian problems. Quant. Inf. Comp. vol. 8, no. 5, pp. 0361-0385 (2008). ChowdhuryANSommaRDSubasiYComputing partition functions in the one-clean-qubit modelPhys. Rev. A20211030324222021PhRvA.103c2422C424393610.1103/PhysRevA.103.032422 Aharonov, D., Ben-Or, M., Brandao, F. G. & Sattath, O. The pursuit for uniqueness: extending Valiant-Vazirani theorem to the probabilistic and quantum settings. Quantum 6, 668 (2022). GharibianSKempeJApproximation algorithms for QMA-complete problemsSIAM J. Comput.20124110281050297476110.1137/1108422721286.68496 Marriott, C. & Watrous, J. Quantum Arthur–Merlin games. Comput. Complex.14, 122–152 (2005). ChowdhuryANSommaRDQuantum algorithms for Gibbs sampling and hitting-time estimationQuant. Inf. Comp.20171741643676655 Suzuki, M. Quantum Monte Carlo Methods in Condensed Matter Physics (World Scientific, 1993). Barvinok, A. Combinatorics and Complexity of Partition Functions Vol. 9 (Springer, 2016). Gilyén, A., Su, Y., Low, G. H. & Wiebe, N. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proc. 51st Annual ACM SIGACT Symposium on Theory of Computing 193–204 (ACM, 2019). Kohler, T., Piddock, S., Bausch, J. & Cubitt, T. Translationally-invariant universal quantum Hamiltonians in 1D. Annales Henri Poincaré Vol. 23, pp. 223–254 (2022). Meyer, R. A., Musco, C., Musco, C. & Woodruff, D. P. Hutch++: optimal stochastic trace estimation. In Symposium on Simplicity in Algorithms (SOSA) 142–155 (SIAM, 2021). Alimonti, P. & Kann, V. Hardness of approximating problems on cubic graphs. In Italian Conference on Algorithms and Complexity 288–298 (Springer, 1997). Cleve, R., Leung, D., Liu, L. & Wang, C. Near-linear constructions of exact unitary 2-designs. Quant. Info. Comp. vol. 16, no. 9–10 pp. 721–756 (2016). 1742_CR22 AN Chowdhury (1742_CR36) 2017; 17 1742_CR42 1742_CR26 1742_CR27 1742_CR24 I Dinur (1742_CR2) 2007; 54 T Kuwahara (1742_CR10) 2020; 124 J van Apeldoorn (1742_CR38) 2020; 4 1742_CR41 TS Cubitt (1742_CR25) 2018; 115 J Kempe (1742_CR40) 2006; 35 S Bravyi (1742_CR43) 2021; 67 E Crosson (1742_CR8) 2021; 5 1742_CR28 1742_CR29 AY Kitaev (1742_CR1) 2002 1742_CR11 1742_CR12 1742_CR34 1742_CR31 1742_CR15 1742_CR37 1742_CR16 S Gharibian (1742_CR17) 2012; 41 1742_CR14 LA Goldberg (1742_CR23) 2017; 26 C Dankert (1742_CR32) 2009; 80 1742_CR3 H-Y Huang (1742_CR30) 2020; 16 MF Hutchinson (1742_CR33) 1989; 18 1742_CR5 1742_CR4 1742_CR7 E Knill (1742_CR21) 1998; 81 1742_CR6 D Bertsimas (1742_CR13) 2004; 51 1742_CR19 1742_CR39 1742_CR18 AN Chowdhury (1742_CR20) 2021; 103 D Poulin (1742_CR35) 2009; 103 S Bravyi (1742_CR9) 2017; 119
References_xml	– reference: ChowdhuryANSommaRDQuantum algorithms for Gibbs sampling and hitting-time estimationQuant. Inf. Comp.20171741643676655 – reference: ChowdhuryANSommaRDSubasiYComputing partition functions in the one-clean-qubit modelPhys. Rev. A20211030324222021PhRvA.103c2422C424393610.1103/PhysRevA.103.032422 – reference: Brandão, F. G. S. L. Entanglement Theory and the Quantum Simulation of Many-Body Physics. PhD thesis, Imperial College of Science, Technology and Medicine (2008). – reference: BertsimasDVempalaSSolving convex programs by random walksJ. ACM200451540556214784710.1145/1008731.10087331204.90074 – reference: CubittTSMontanaroAPiddockSUniversal quantum HamiltoniansProc. Natl Acad. Sci. USA2018115949795022018PNAS..115.9497C385903710.1073/pnas.18049491151416.82008 – reference: Kohler, T., Piddock, S., Bausch, J. & Cubitt, T. Translationally-invariant universal quantum Hamiltonians in 1D. Annales Henri Poincaré Vol. 23, pp. 223–254 (2022). – reference: Meyer, R. A., Musco, C., Musco, C. & Woodruff, D. P. Hutch++: optimal stochastic trace estimation. In Symposium on Simplicity in Algorithms (SOSA) 142–155 (SIAM, 2021). – reference: van ApeldoornJGilyénAGriblingSde WolfRQuantum SDP-solvers: better upper and lower boundsQuantum2020423010.22331/q-2020-02-14-230 – reference: Stockmeyer, L. The complexity of approximate counting. In Proc. Fifteenth Annual ACM Symposium on Theory of Computing STOC ’83 118–126 (ACM, 1983). – reference: Zhou, L. & Aharonov, D. Strongly universal Hamiltonian simulators. Preprint at https://arxiv.org/abs/2102.02991 (2021). – reference: Kohler, T., Piddock, S., Bausch, J. & Cubitt, T. General conditions for universality of quantum Hamiltonians. PRX Quantum 3, 010308 (2022). – reference: DinurIThe PCP theorem by gap amplificationJ. ACM20075412es231425410.1145/1236457.12364591292.68074 – reference: DankertCCleveREmersonJLivineEExact and approximate unitary 2-designs and their application to fidelity estimationPhys. Rev. A2009800123042009PhRvA..80a2304D10.1103/PhysRevA.80.012304 – reference: BravyiSGossetDPolynomial-time classical simulation of quantum ferromagnetsPhys. Rev. Lett.20171191005032017PhRvL.119j0503B10.1103/PhysRevLett.119.100503 – reference: KnillELaflammeRPower of one bit of quantum informationPhys. Rev. Lett.19988156721998PhRvL..81.5672K10.1103/PhysRevLett.81.5672 – reference: Cleve, R., Leung, D., Liu, L. & Wang, C. Near-linear constructions of exact unitary 2-designs. Quant. Info. Comp. vol. 16, no. 9–10 pp. 721–756 (2016). – reference: Marriott, C. & Watrous, J. Quantum Arthur–Merlin games. Comput. Complex.14, 122–152 (2005). – reference: HuangH-YKuengRPreskillJPredicting many properties of a quantum system from very few measurementsNat. Phys.2020161050105710.1038/s41567-020-0932-7 – reference: Gilyén, A., Su, Y., Low, G. H. & Wiebe, N. Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In Proc. 51st Annual ACM SIGACT Symposium on Theory of Computing 193–204 (ACM, 2019). – reference: Alimonti, P. & Kann, V. Hardness of approximating problems on cubic graphs. In Italian Conference on Algorithms and Complexity 288–298 (Springer, 1997). – reference: Cade, C. & Montanaro, A. The quantum complexity of computing Schatten p-norms. In 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) (Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik 2018). – reference: KitaevAYShenAHVyalyiMNClassical and Quantum Computation2002American Mathematical Society10.1090/gsm/0471022.68001 – reference: Barvinok, A. Combinatorics and Complexity of Partition Functions Vol. 9 (Springer, 2016). – reference: Grötschel, M., Lovász, L. & Schrijver, A. Geometric Algorithms and Combinatorial Optimization Vol. 2 (Springer Science & Business Media, 2012). – reference: BravyiSMaslovDHadamard-free circuits expose the structure of the Clifford groupIEEE Trans. Inf. Theory20216745464563430628410.1109/TIT.2021.30814151475.68132 – reference: GoldbergLAGuoHThe complexity of approximating complex-valued Ising and Tutte partition functionscomput. complex.201726765833372334910.1007/s00037-017-0162-21382.68090 – reference: KuwaharaTKatoKBrandãoFGSLClustering of conditional mutual information for quantum Gibbs states above a threshold temperaturePhys. Rev. Lett.20201242206012020PhRvL.124v0601K411120410.1103/PhysRevLett.124.220601 – reference: Aaronson, S. and Rall, P. Quantum approximate counting, simplified. In Symposium on Simplicity in Algorithms 24–32 (SIAM, 2020). – reference: Barak, B., Raghavendra, P. & Steurer, D. Rounding semidefinite programming hierarchies via global correlation. IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 472-481 (2011). – reference: KempeJKitaevARegevOThe complexity of the local Hamiltonian problemSIAM J. Comput.20063510701097221713810.1137/S00975397044452261102.81032 – reference: Brandao, F. G. & Harrow, A. W. Product-state approximations to quantum ground states. In Proc. Forty-Fifth Annual ACM Symposium on Theory of Computing STOC ’13 871–880 (ACM, 2013). – reference: Bravyi, S., Divincenzo, D. P., Oliveira, R. I. & Terhal, B. M. The complexity of stoquastic local Hamiltonian problems. Quant. Inf. Comp. vol. 8, no. 5, pp. 0361-0385 (2008). – reference: Gosset, D. & Smolin, J. A compressed classical description of quantum states. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019) (Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2019). – reference: Brassard, G., Høyer, P., Mosca, M. and Tapp, A. Quantum amplitude amplification and estimation. In Quantum Computation and Information Vol. 305 of Contemporary Mathematics 53–74 (AMS, 2002). – reference: Suzuki, M. Quantum Monte Carlo Methods in Condensed Matter Physics (World Scientific, 1993). – reference: Harrow, A. W., Mehraban, S. & Soleimanifar, M. Classical algorithms, correlation decay, and complex zeros of partition functions of quantum many-body systems. In Proc. 52nd Annual ACM SIGACT Symposium on Theory of Computing 378–386 (ACM, 2020). – reference: PoulinDWocjanPSampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computerPhys. Rev. Lett.20091032205022009PhRvL.103v0502P257021810.1103/PhysRevLett.103.220502 – reference: GharibianSKempeJApproximation algorithms for QMA-complete problemsSIAM J. Comput.20124110281050297476110.1137/1108422721286.68496 – reference: Aharonov, D., Ben-Or, M., Brandao, F. G. & Sattath, O. The pursuit for uniqueness: extending Valiant-Vazirani theorem to the probabilistic and quantum settings. Quantum 6, 668 (2022). – reference: CrossonEHarrowAWRapid mixing of path integral Monte Carlo for 1D stoquastic HamiltoniansQuantum2021539510.22331/q-2021-02-11-395 – reference: Risteski, A. How to calculate partition functions using convex programming hierarchies: provable bounds for variational methods. In 29th Annual Conference on Learning Theory (eds. Feldman, V., Rakhlin, A. & Shamir, O.) vol. 49 of Proceedings of Machine Learning Research 1402–1416 (PMLR, 2016). – reference: Yoshida, Y. & Zhou, Y. Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems. In Proc. 5th Conference on Innovations in Theoretical Computer Science ITCS ’14 423–438 (ACM, 2014). – reference: HutchinsonMFA stochastic estimator of the trace of the influence matrix for Laplacian smoothing splinesCommun. Stat. Simul. Comput.19891810591076103184010.1080/036109189088128060695.62113 – ident: 1742_CR37 doi: 10.1145/3313276.3316366 – ident: 1742_CR41 doi: 10.1090/conm/305/05215 – volume: 35 start-page: 1070 year: 2006 ident: 1742_CR40 publication-title: SIAM J. Comput. doi: 10.1137/S0097539704445226 – ident: 1742_CR12 doi: 10.1145/2554797.2554836 – volume: 103 start-page: 032422 year: 2021 ident: 1742_CR20 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.103.032422 – volume: 124 start-page: 220601 year: 2020 ident: 1742_CR10 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.124.220601 – volume: 80 start-page: 012304 year: 2009 ident: 1742_CR32 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.80.012304 – ident: 1742_CR22 doi: 10.1145/800061.808740 – volume: 17 start-page: 41 year: 2017 ident: 1742_CR36 publication-title: Quant. Inf. Comp. – volume: 54 start-page: 12 year: 2007 ident: 1742_CR2 publication-title: J. ACM doi: 10.1145/1236457.1236459 – volume: 41 start-page: 1028 year: 2012 ident: 1742_CR17 publication-title: SIAM J. Comput. doi: 10.1137/110842272 – ident: 1742_CR42 doi: 10.1137/1.9781611976014.5 – ident: 1742_CR26 – ident: 1742_CR4 doi: 10.1142/2262 – ident: 1742_CR6 doi: 10.1145/3357713.3384322 – ident: 1742_CR27 doi: 10.1007/s00023-021-01111-7 – volume: 4 start-page: 230 year: 2020 ident: 1742_CR38 publication-title: Quantum doi: 10.22331/q-2020-02-14-230 – volume-title: Classical and Quantum Computation year: 2002 ident: 1742_CR1 doi: 10.1090/gsm/047 – ident: 1742_CR16 doi: 10.1145/2488608.2488719 – ident: 1742_CR11 – ident: 1742_CR31 doi: 10.26421/QIC16.9-10-1 – ident: 1742_CR7 doi: 10.26421/QIC8.5-1 – volume: 115 start-page: 9497 year: 2018 ident: 1742_CR25 publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.1804949115 – volume: 67 start-page: 4546 year: 2021 ident: 1742_CR43 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2021.3081415 – volume: 18 start-page: 1059 year: 1989 ident: 1742_CR33 publication-title: Commun. Stat. Simul. Comput. doi: 10.1080/03610918908812806 – volume: 51 start-page: 540 year: 2004 ident: 1742_CR13 publication-title: J. ACM doi: 10.1145/1008731.1008733 – ident: 1742_CR5 doi: 10.1007/978-3-319-51829-9_2 – ident: 1742_CR19 – volume: 103 start-page: 220502 year: 2009 ident: 1742_CR35 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.103.220502 – ident: 1742_CR28 doi: 10.1103/PRXQuantum.3.010308 – volume: 119 start-page: 100503 year: 2017 ident: 1742_CR9 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.119.100503 – volume: 81 start-page: 5672 year: 1998 ident: 1742_CR21 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.81.5672 – volume: 5 start-page: 395 year: 2021 ident: 1742_CR8 publication-title: Quantum doi: 10.22331/q-2021-02-11-395 – ident: 1742_CR29 – ident: 1742_CR15 doi: 10.1109/FOCS.2011.95 – ident: 1742_CR14 – volume: 26 start-page: 765 year: 2017 ident: 1742_CR23 publication-title: comput. complex. doi: 10.1007/s00037-017-0162-2 – volume: 16 start-page: 1050 year: 2020 ident: 1742_CR30 publication-title: Nat. Phys. doi: 10.1038/s41567-020-0932-7 – ident: 1742_CR39 doi: 10.1007/s00037-005-0194-x – ident: 1742_CR3 doi: 10.1007/3-540-62592-5_80 – ident: 1742_CR24 doi: 10.22331/q-2022-03-17-668 – ident: 1742_CR34 doi: 10.1137/1.9781611976496.16 – ident: 1742_CR18
SSID	ssj0042613
Score	2.5094795
Snippet	The physical properties of a quantum many-body system in thermal equilibrium are determined by its partition function and free energy. Here we study the...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1367
SubjectTerms	639/766/483/481 639/766/530/2804 639/766/530/951 Algorithms Approximation Atomic Circuits Classical and Continuum Physics Complex Systems Complexity Condensed Matter Physics Energy Equilibrium Free energy Hamiltonian functions Ising model Mathematical analysis Mathematical and Computational Physics Molecular Optical and Plasma Physics Optimization Partitions (mathematics) Physical properties Physics Physics and Astronomy Polynomials Quantum computing Qubits (quantum computing) Run time (computers) Theoretical
Title	Quantum Hamiltonian complexity in thermal equilibrium
URI	https://link.springer.com/article/10.1038/s41567-022-01742-5 https://www.proquest.com/docview/2732914639
Volume	18
WOSCitedRecordID	wos000864597400002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1745-2481 dateEnd: 20221231 omitProxy: false ssIdentifier: ssj0042613 issn: 1745-2473 databaseCode: P5Z dateStart: 20220101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Earth, Atmospheric & Aquatic Science Database customDbUrl: eissn: 1745-2481 dateEnd: 20221231 omitProxy: false ssIdentifier: ssj0042613 issn: 1745-2473 databaseCode: PCBAR dateStart: 20220101 isFulltext: true titleUrlDefault: https://search.proquest.com/eaasdb providerName: ProQuest – providerCode: PRVPQU databaseName: Proquest Central customDbUrl: eissn: 1745-2481 dateEnd: 20221231 omitProxy: false ssIdentifier: ssj0042613 issn: 1745-2473 databaseCode: BENPR dateStart: 20220101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1745-2481 dateEnd: 20221231 omitProxy: false ssIdentifier: ssj0042613 issn: 1745-2473 databaseCode: M2P dateStart: 20220101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58ghff4vqiB29abJLtJjmJiuJBl1UUxEtJ0wksuOujW_HnO8m2Lgp68dJL2yF8mcx7MgD7PGdc2sJH7lMbt40TsRFWxYnhVjokFVGEK_OvZLerHh50rw64lXVZZSMTg6Aunq2PkR-RmuWajrXQxy-vsZ8a5bOr9QiNaZgly4b5kq5r3msksfcOxLghMqW1SFE3zSRCHZXecZGxr2UnnmyTQ_ZdMU2szR8J0qB3Lpb-u-JlWKwtzuhkzCIrMIXDVZgPlZ-2XIP0piJwq0F06UMdZAkSv0Sh0Bw_yEKP-sPI24gDIoGvVT-0CFSDdbi_OL87u4zrWQqxpUM2itE7btoIJmyitJGFQdaRhjlTSF44o3xGsJAJOnTGtlUnRc5zoRONtmNRiw2YGT4PcRMikzuWG63z1LE2IlOOHGyFknSdUchtC1gDZGbri8b9vIunLCS8hcrG4GcEfhbAz9IWHHz98zK-ZuPPr3caxLP6yJXZBO4WHDZ7Nnn9O7Wtv6ltwwL3bBL6D3dgZvRW4S7M2fdRv3zbg9nT827vdi8wHj176eMnr5ndKA
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB5VBQSX8qzYUiAHOEHUxE7W9gEhBFRbdVkVqUi9GccZSyux20c2PP4Uv5EZJ2EFEr31wDnJKMk3T88L4JmocqF8zSf3pU8LF2TqpNdp5oRXAclE1HFk_lTNZvrkxBxtwM-hF4bLKgedGBV1fer5jHyPzKwwJNbSvD47T3lrFGdXhxUaHVsc4o9vFLI1rw7eEb7Phdh_f_x2kvZbBVJP7LZKkUMY42QufaaNU7XDfKxcHlytRB2c5txYrTIMGJwv9LhEISppMoN-7JGHL5HKv1bwZDEuFRRHg-bnaER2DZglfbuSfZNOJvVew4GSSrl2nmSgoADwT0O49m7_SshGO7d_-3_7Q3dgq_eokzedCNyFDVzegxuxstU396H82BLztItkwkc55OmSPCSxkB6_UwSSzJcJ-8ALIoHn7Ty2QLSLB_DpSt55GzaXp0t8CImrQl45Y6oy5AViroMhPwoV2XKnUfgR5ANw1veD1HmfxxcbE_pS2w5sS2DbCLYtR_Di9zNn3RiRS-_eHRC2vUpp7BreEbwceGR9-d_Udi6n9hRuTo4_TO30YHb4CG4JZtHYa7kLm6uLFh_Ddf91NW8unkRmT-DzVfPOL_mQOPY
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9NAEB5VhSIuFFoqAgV8KCdqxd6Ns7uHqkKEqFWjKEggRb1s1-tZKRJJH455_DV-XWfXdiOQyK0HzrZH1s43r50XwAHLUyZs4W_uMxv3jOOx4VbGiWFWOCQTUYSR-SMxHsvpVE024HfbC-PLKludGBR1cWn9HXmXzCxTJNZcdV1TFjEZDI-vrmO_QcpnWtt1GjVEzvDXDwrfyqPTAfH6HWPDT18-nsTNhoHYEvSWMfpwRhmecptIZURhMO0LkzpTCFY4I32erBAJOnTG9mQ_Q8ZyrhKFtm_RD2Ii9f9AUIzpywkn2XlrBXxkwutmzIzOQfCmYSfhslv6oEnEvo6e5KFHweCfRnHl6f6VnA02b7j9P5_WU3jSeNrRh1o0nsEGLnZgK1S82nIXss8VgaqaRyf-ioc8YJKTKBTY40-KTKLZIvK-8ZxI4HU1C60R1fw5fL2Xf96DzcXlAl9AZHKX5kapPHNpDzGVTpF_hYJsvJHIbAfSlonaNgPW_Z6Pbzok-rnUNeM1MV4HxuusA-_vvrmqx4usfXu_5bZuVE2pV6zuwGGLl9Xjf1N7uZ7aW3hEkNGj0_HZK3jMPFpDC-Y-bC5vKnwND-335ay8eRNwH8HFfUPnFgHmQeI
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Quantum+Hamiltonian+complexity+in+thermal+equilibrium&rft.jtitle=Nature+physics&rft.au=Bravyi%2C+Sergey&rft.au=Chowdhury%2C+Anirban&rft.au=Gosset%2C+David&rft.au=Wocjan%2C+Pawel&rft.date=2022-11-01&rft.pub=Nature+Publishing+Group&rft.issn=1745-2473&rft.eissn=1745-2481&rft.volume=18&rft.issue=11&rft.spage=1367&rft.epage=1370&rft_id=info:doi/10.1038%2Fs41567-022-01742-5&rft.externalDBID=HAS_PDF_LINK
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1745-2473&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1745-2473&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1745-2473&client=summon