Classical and quantum algorithms for many-body problems

Thomas Ayral

doi:10.5802/crphys.229

Article de recherche

Classical and quantum algorithms for many-body problems
[Algorithmes classiques et quantiques pour le problème à N corps]

Thomas Ayral ¹

¹ Eviden Quantum Laboratory, Les Clayes-sous-Bois, France

Comptes Rendus. Physique, Volume 26 (2025), pp. 25-89.

Résumé
Abstract

Le problème à N corps est un problème central pour nombre de domaines comme la physique de la matière condensée ou la chimie, mais aussi celui de l’optimisation combinatoire, qui n’est autre qu’un problème à N corps classique. Ce manuscrit, rédigé dans le cadre d’une Habilitation à Diriger des Recherches, présente les différentes approches algorithmiques, qu’elles soient classiques ou quantiques, pour résoudre ce problème. Nous commenàçons par y passer en revue les principales méthodes classiques et quantiques existantes, avec un accent mis sur leurs succès ainsi que leurs limitations actuelles. En particulier, nousc présentons un état de l’art des méthodes quantiques, en distinguant processeurs parfaits et processeurs bruités. Ensuite, nous présentons des travaux récents permettant de combiner algorithmes classiques et quantiques pour surmonter les limitations inhérentes aux deux paradigmes. En particulier, nous commenàçons par montrer comment les réseaux de tenseurs, souvent utilisés comme outils de référence pour jauger de l’intérêt des méthodes quantiques, peuvent aussi être utilisés pour initialiser un calcul quantique, en plus de le simuler de faàçon réaliste. Nous passons ensuite au cas particulier des problèmes fermioniques. Après avoir décrit une méthode à base d’orbitales naturelles permettant de raccourcir, et donc de fiabiliser, des circuits quantiques pour préparer des états fermioniques, nous exposons une méthode à base de spins esclaves permettant d’utiliser une plateforme d’atomes de Rydberg pour simuler des modèles de fermions sur réseau. Nous montrons enfin comment ces mêmes plateformes de Rydberg peuvent être utilisées pour résoudre des problèmes combinatoires, et comment la décoherence influence la qualité des résultats obtenus. Ceci nous amène à la définition d’une nouvelle métrique d’utilité des processeurs quantiques, le Q-score.

The many-body problem is central to many fields, such as condensed-matter physics and chemistry, but also to combinatorial optimization, which is nothing but a classical many-body problem. This manuscript, written as part of an Habilitation à Diriger des Recherches, presents the various algorithmic approaches, both classical and quantum, to solving this problem. We begin by reviewing the main existing classical and quantum methods, focusing on their successes as well as their current limitations. In particular, we present the state-of-the-art in quantum methods, distinguishing between perfect and noisy processors. We then present recent work on combining classical and quantum algorithms to overcome the limitations inherent to both paradigms. In particular, we begin by showing how tensor networks, often used as reference tools to gauge the interest of quantum methods, can also be used to initialize a quantum computation, in addition to simulating it realistically. We then turn to the special case of fermionic problems. After describing a method based on natural orbitals for shortening, and thus making more reliable, quantum circuits to prepare fermionic states, we present a method based on slave spins for using a platform of Rydberg atoms to simulate lattice models of fermions. Finally, we show how these same Rydberg platforms can be used to solve combinatorial problems, and how decoherence influences the quality of the results obtained. This leads to the definition of a new utility metric for quantum processors, the Q-score.

Reçu le : 2024-12-19
Accepté le : 2024-12-20
Publié le : 2025-01-27

DOI : 10.5802/crphys.229

Keywords: Many-body physics, Quantum computing, Algorithms, Condensed-matter physics, Numerical methods
Mots-clés : Problème à N corps, Informatique quantique, Algorithmes, Physique de la matière condensée, Méthodes numériques

Affiliations des auteurs :

Thomas Ayral ¹

¹ Eviden Quantum Laboratory, Les Clayes-sous-Bois, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRPHYS_2025__26_G1_25_0,
     author = {Thomas Ayral},
     title = {Classical and quantum algorithms for many-body problems},
     journal = {Comptes Rendus. Physique},
     pages = {25--89},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {26},
     year = {2025},
     doi = {10.5802/crphys.229},
     language = {en},
}

TY  - JOUR
AU  - Thomas Ayral
TI  - Classical and quantum algorithms for many-body problems
JO  - Comptes Rendus. Physique
PY  - 2025
SP  - 25
EP  - 89
VL  - 26
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.229
LA  - en
ID  - CRPHYS_2025__26_G1_25_0
ER  -

%0 Journal Article
%A Thomas Ayral
%T Classical and quantum algorithms for many-body problems
%J Comptes Rendus. Physique
%D 2025
%P 25-89
%V 26
%I Académie des sciences, Paris
%R 10.5802/crphys.229
%G en
%F CRPHYS_2025__26_G1_25_0

Thomas Ayral. Classical and quantum algorithms for many-body problems. Comptes Rendus. Physique, Volume 26 (2025), pp. 25-89. doi : 10.5802/crphys.229. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.229/

Bibliographie
Cité par

[1] J. Hubbard Electron correlations in narrow energy bands, Proc. R. Soc. A: Math. Phys. Eng. Sci., Volume 276 (1963) no. 1365, pp. 238-257 | DOI

[2] F. Aryasetiawan; M. Imada; A. Georges; G. Kotliar; S. Biermann; A. Lichtenstein Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B, Volume 70 (2004) no. 19, 195104 | DOI

[3] S. Jiang; D. J. Scalapino; S. R. White Density matrix renormalization group based downfolding of the three-band Hubbard model: Importance of density-assisted hopping, Phys. Rev. B, Volume 108 (2023) no. 16, L161111 | DOI

[4] J. G. Bednorz; K. A. Muller Possible high Tc superconductivity in the Ba–La–Cu–O system, Z. Phys. B: Condens. Matter, Volume 64 (1986), pp. 189-193 | DOI

[5] N. F. Mott; R. Peierls Discussion of the paper by de Boer and Verwey, Proc. Phys. Soc., Volume 49 (1937) no. 4S, pp. 72-73 | DOI

[6] W. Kohn Nobel lecture: electronic structure of matter-wave functions and density functionals, Rev. Mod. Phys., Volume 71 (1999) no. 5, pp. 1253-1266 | DOI

[7] W. Kohn; L. J. Sham Self-consistent equations including exchange and correlation effects, Phys. Rev., Volume 385 (1965) no. 1951, pp. 1133-1138 | DOI

[8] F. A. Evangelista Perspective: multireference coupled cluster theories of dynamical electron correlation, J. Chem. Phys., Volume 149 (2018) no. 3, 030901 | DOI

[9] E. Koch The Lanczos method, The LDA+DMFT Approach to Strongly Correlated Materials (E. Pavarini; E. Koch; D. Vollhardt; A. Lichtenstein, eds.), Volume 1, Verlag des Forschungszentrum Jülich, Jülich, 2011 https://www.cond-mat.de/events/correl11/manuscripts/koch.pdf

[10] A. Wietek; A. M. Läuchli Sublattice coding algorithm and distributed memory parallelization for large-scale exact diagonalizations of quantum many-body systems, Phys. Rev. E, Volume 98 (2018) no. 3, 033309 | DOI

[11] W. Krauth Introduction to Monte Carlo algorithms, Advances in Computer Simulation (J. Kertesz; I. Kondor, eds.) (Lecture Notes in Physics), Springer Verlag, 1998 | DOI

[12] M. Troyer; U. J. Wiese Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations, Phys. Rev. Lett., Volume 94 (2005) no. 17, pp. 1-4 | DOI

[13] N. Prokof’ev Diagrammatic Monte Carlo, Many-Body Methods for Real Materials Modeling and Simulation (E. Pavarini; E. Koch; S. Zhang, eds.), Volume 9, Forschungszentrum Jülich, Jülich, 2019

[14] R. Rossi Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit, Phys. Rev. Lett., Volume 119 (2017) no. 4, 045701 | DOI

[15] R. Rossi; N. Prokof’ev; B. Svistunov; K. Van Houcke; F. Werner Polynomial complexity despite the fermionic sign, Europhys. Lett., Volume 118 (2017) no. 1, 10004 | DOI

[16] E. Pavarini; E. Koch; U. Schollwöck Emergent Phenomena in Correlated Matter, Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich, Jülich, 2013, 562 pages http://hdl.handle.net/2128/5389

[17] R. C. Grimm; R. G. Storer Monte-Carlo solution of Schrödinger’s equation, J. Comput. Phys., Volume 7 (1971) no. 1, pp. 134-156 | DOI

[18] S. Zhang; J. Carlson; J. E. Gubernatis Constrained path Monte Carlo method for fermion ground states, Phys. Rev. B, Volume 55 (1997) no. 12, pp. 7464-7477 | DOI

[19] G. H. Booth; A. J. W. Thom; A. Alavi Fermion Monte Carlo without fixed nodes: a game of life, death, and annihilation in Slater determinant space, J. Chem. Phys., Volume 131 (2009) no. 5, 054106 | DOI

[20] G. Carleo; M. Troyer Solving the quantum many-body problem with artificial neural networks, Science, Volume 355 (2017) no. 6325, pp. 602-606 | DOI

[21] G. Mazzola Quantum computing for chemistry and physics applications from a Monte Carlo perspective, J. Chem. Phys., Volume 160 (2024), 010901 | DOI

[22] T. Jiang; J. Zhang; M. K. A. Baumgarten et al. Walking through Hilbert space with quantum computers, preprint, 2024 | arXiv

[23] U. Schollwöck The density-matrix renormalization group in the age of matrix product states, Ann. Phys., Volume 326 (2011) no. 1, pp. 96-192 | DOI

[24] M. B. Hastings An area law for one-dimensional quantum systems, J. Stat. Mech.: Theory Exp., Volume 2007 (2007) no. 08, p. P08024-P08024 | DOI

[25] F. Verstraete; J. I. Cirac Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, preprint, 2004 (p. 1–5) | arXiv

[26] I. L. Markov; Y. Shi Simulating quantum computation by contracting tensor networks, SIAM J. Comput., Volume 38 (2008) no. 3, pp. 963-981 | DOI

[27] M. P. Zaletel; F. Pollmann Isometric tensor network states in two dimensions, Phys. Rev. Lett., Volume 124 (2020) no. 3, 037201 | DOI

[28] R. Alkabetz; I. Arad Tensor networks contraction and the belief propagation algorithm, Phys. Rev. Res., Volume 3 (2021) no. 2, 023073 | DOI

[29] S. Sahu; B. Swingle Efficient tensor network simulation of quantum many-body physics on sparse graphs, preprint, 2022 | arXiv

[30] P. Calabrese; J. Cardy Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech.: Theory Exp., Volume 2005 (2005) no. 04, p. P04010 | DOI

[31] J. P. F. LeBlanc; A. E. Antipov; F. Becca et al. Solutions of the two-dimensional Hubbard model: benchmarks and results from a wide range of numerical algorithms, Phys. Rev. X, Volume 5 (2015) no. 4, 041041 | DOI

[32] H. Xu; C.-M. Chung; M. Qin; U. Schollwöck; S. R. White; S. Zhang Coexistence of superconductivity with partially filled stripes in the Hubbard model, preprint, 2023 | arXiv

[33] P. O. Löwdin Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals, and convergence problems in the method of configurational interaction, Phys. Rev., Volume 97 (1955) no. 6, pp. 1474-1489 | DOI

[34] F. Coester; H. Kümmel Short-range correlations in nuclear wave functions, Nucl. Phys., Volume 17 (1960) no. C, pp. 477-485 | DOI

[35] J. B. Robinson; P. J. Knowles Approximate variational coupled cluster theory, J. Chem. Phys., Volume 135 (2011) no. 4, 044113 | DOI

[36] G. Harsha; T. Shiozaki; G. E. Scuseria On the difference between variational and unitary coupled cluster theories, J. Chem. Phys., Volume 148 (2018) no. 4, 044107 | DOI

[37] W. Kutzelnigg Pair correlation theories, Methods of Electronic Structure Theory (H. F. Schaefer, ed.), Springer US, 1977, pp. 129-182 | DOI

[38] W. Kutzelnigg Error analysis and improvements of coupled-cluster theory, Theoret. Chim. Acta, Volume 80 (1991) no. 4–5, pp. 349-386 | DOI

[39] P. G. Szalay; M. Nooijen; R. J. Bartlett Alternative ansätze in single reference coupled-cluster theory. III. A critical analysis of different methods, J. Chem. Phys., Volume 103 (1995) no. 1, pp. 281-298 | DOI

[40] R. F. Bishop The coupled cluster method, Microscopic Quantum Many-Body Theories and Their Applications, Springer, Berlin, Heidelberg, 2008, pp. 1-70 | DOI

[41] B. O. Roos; P. R. Taylor; P. E. M. Sigbahn A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach, Chem. Phys., Volume 48 (1980) no. 2, pp. 157-173 | DOI

[42] B. O. Roos The complete active space self-consistent field method and its applications in electronic structure calculations, Adv. Chem. Phys., Volume 69 (1987), pp. 399-445 | DOI

[43] B. Huron; J. P. Malrieu; P. Rancurel Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions, J. Chem. Phys., Volume 58 (1973) no. 12, pp. 5745-5759 | DOI

[44] G. K.-L. Chan Quantum chemistry, classical heuristics, and quantum advantage, Faraday Discuss., Volume 254 (2024), pp. 11-52 | DOI

[45] A. Georges; G. Kotliar; W. Krauth; M. J. Rozenberg Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys., Volume 68 (1996) no. 1, pp. 13-125 | DOI

[46] T. Ayral; P. Besserve; D. Lacroix; E. A. Ruiz Guzman Quantum computing with and for many-body physics, Eur. Phys. J. A, Volume 59 (2023) no. 10, 227 | DOI

[47] A. Georges Strongly correlated electron materials: dynamical mean-field theory and electronic structure, AIP Conf. Proc., Volume 715 (2004) no. 1, pp. 3-74 | DOI

[48] E. Gull; A. J. Millis; A. I. Lichtenstein; A. N. Rubtsov; M. Troyer; P. Werner Continuous-time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys., Volume 83 (2011) no. 2, pp. 349-404 | DOI

[49] H. Aoki; N. Tsuji; M. Eckstein; M. Kollar; T. Oka; P. Werner Nonequilibrium dynamical mean-field theory and its applications, Rev. Mod. Phys., Volume 86 (2014) no. 2, pp. 779-837 | DOI

[50] F. Lechermann; A. Georges; G. Kotliar; O. Parcollet Rotationally invariant slave-boson formalism and momentum dependence of the quasiparticle weight, Phys. Rev. B, Volume 76 (2007) no. 15, 155102 | DOI

[51] J. Bünemann; F. Gebhard Equivalence of Gutzwiller and slave-boson mean-field theories for multiband Hubbard models, Phys. Rev. B, Volume 76 (2007) no. 19, 193104 | DOI

[52] N. Lanatà; Y. Yao; C.-Z. Wang; K.-M. Ho; G. Kotliar Phase diagram and electronic structure of praseodymium and plutonium, Phys. Rev. X, Volume 5 (2015) no. 1, 011008 | DOI

[53] T. Ayral; T.-H. Lee; G. Kotliar Dynamical mean-field theory, density-matrix embedding theory, and rotationally invariant slave bosons: A unified perspective, Phys. Rev. B, Volume 96 (2017) no. 23, 235139 | DOI

[54] M. Ferrero; P. Cornaglia; L. De Leo; O. Parcollet; G. Kotliar; A. Georges Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space, Phys. Rev. B, Volume 80 (2009) no. 6, 064501 | DOI

[55] G. Knizia; G. K.-L. Chan Density matrix embedding: a simple alternative to dynamical mean-field theory, Phys. Rev. Lett., Volume 109 (2012) no. 18, 186404 | DOI

[56] T. Ayral; P. Besserve; D. Lacroix; E. A. R. Guzman Quantum Computing with and for Many-Body Physics, 123, Springer, Berlin, Heidelberg, 2023, pp. 1-46 | arXiv

[57] S. Bravyi Monte Carlo simulation of stoquastic Hamiltonians, Quantum Inf. Comput., Volume 15 (2015) no. 13–14, pp. 1122-1140 | DOI

[58] B. Heim; T. F. Rønnow; S. V. Isakov; M. Troyer Quantum versus classical annealing of Ising spin glasses, Science, Volume 348 (2015) no. 6231, pp. 215-217 | DOI

[59] V. S. Denchev; S. Boixo; S. V. Isakov; N. Ding; R. Babbush; V. Smelyanskiy; J. Martinis; H. Neven What is the computational value of finite-range tunneling?, Phys. Rev. X, Volume 6 (2016), 031015 | DOI

[60] R. P. Feynman Simulating physics with computers, Int. J. Theor. Phys., Volume 21 (1982) no. 6–7, pp. 467-488 | DOI

[61] I. Bloch; J. Dalibard; W. Zwerger Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. September, 885 | DOI

[62] A. Browaeys; T. Lahaye Many-body physics with individually controlled Rydberg atoms, Nat. Phys., Volume 16 (2020) no. 2, pp. 132-142 | DOI

[63] R. Jördens; N. Strohmaier; K. Günter; M. Henning; T. Esslinger A Mott insulator of fermionic atoms in an optical lattice, Nature, Volume 455 (2008), pp. 204-207 | DOI

[64] P. Scholl; M. Schuler; H. J. Williams et al. Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms, Nature, Volume 595 (2021) no. 7866, pp. 233-238 | DOI

[65] M. Xu; L. H. Kendrick; A. Kale; Y. Gang; G. Ji; R. T. Scalettar; M. Lebrat; M. Greiner Frustration- and doping-induced magnetism in a Fermi–Hubbard simulator, Nature, Volume 620 (2023) no. 7976, pp. 971-976 | DOI

[66] P. W. Shor Algorithms for quantum computation: discrete logarithms and factoring, Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, 1995, pp. 124-134 http://ieeexplore.ieee.org/document/365700 | DOI

[67] L. K. Grover A fast quantum mechanical algorithm for database search, Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing - STOC ’96, ACM Press, 1996, pp. 212-219 | DOI

[68] P. W. Shor Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A, Volume 52 (1995) no. 4, pp. 2493-2496 | DOI

[69] P. W. Shor Fault-tolerant quantum computation, Proceedings of 37th Conference on Foundations of Computer Science, IEEE Computer Society Press, 1996, pp. 56-65 | DOI

[70] Z. Chen; K. J. Satzinger; J. Atalaya et al. Exponential suppression of bit or phase errors with cyclic error correction, Nature, Volume 595 (2021) no. 7867, pp. 383-387 | DOI

[71] S. Krinner; N. Lacroix; A. Remm et al. Realizing repeated quantum error correction in a distance-three surface code, Nature, Volume 605 (2022) no. 7911, pp. 669-674 | DOI

[72] D. Bluvstein; S. J. Evered; A. A. Geim et al. Logical quantum processor based on reconfigurable atom arrays, Nature, Volume 626 (2024) no. 7997, pp. 58-65 | DOI

[73] M. P. da Silva; C. Ryan-Anderson; J. M. Bello-Rivas et al. Demonstration of logical qubits and repeated error correction with better-than-physical error rates, preprint, 2024 (p. 1–13) | arXiv

[74] T. Albash; D. A. Lidar Adiabatic quantum computation, Rev. Mod. Phys., Volume 90 (2018) no. 1, 015002 | DOI

[75] V. Lienhard; S. de Léséleuc; D. Barredo; T. Lahaye; A. Browaeys; M. Schuler; L.-P. Henry; A. M. Läuchli Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic ising models with antiferromagnetic interactions, Phys. Rev. X, Volume 8 (2018) no. 2, 021070 | DOI

[76] S. Lloyd Universal quantum simulators, Science, Volume 273 (1996) no. 5278, pp. 1073-1078 | DOI

[77] A. M. Childs; Y. Su; M. C. Tran; N. Wiebe; S. Zhu Theory of trotter error with commutator scaling, Phys. Rev. X, Volume 11 (2021) no. 1, 011020 | DOI

[78] L. Lin; Y. Tong Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers, Phys. Rev. X Quantum, Volume 3 (2022), 010318 | DOI

[79] A. M. Childs; N. Wiebe Hamiltonian simulation using linear combinations of unitary operations, Quantum Inform. Comput., Volume 12 (2012), pp. 901-924

[80] G. H. Low; I. L. Chuang Optimal Hamiltonian simulation by quantum signal processing, Phys. Rev. Lett., Volume 118 (2017) no. 1, 010501 | DOI

[81] G. H. Low; I. L. Chuang Hamiltonian simulation by qubitization, Quantum, Volume 3 (2019), p. 163 | DOI

[82] J. Haah; M. B. Hastings; R. Kothari; G. H. Low Quantum algorithm for simulating real time evolution of lattice Hamiltonians, SIAM J. Comput., Volume 52 (2023) no. 6, pp. 250-284 | DOI

[83] A. Y. Kitaev Quantum measurements and the Abelian Stabilizer Problem, preprint, 1995 (p. 1–22) | arXiv

[84] R. Cleve; A. Ekert; C. Macchiavello; M. Mosca Quantum algorithms revisited, Proc. R. Soc. A: Math. Phys. Eng. Sci., Volume 454 (1998) no. 1969, pp. 339-354 | DOI

[85] A. Aspuru-Guzik; A. D. Dutoi; P. J. Love; M. Head-Gordon Chemistry: simulated quantum computation of molecular energies, Science, Volume 309 (2005) no. 5741, pp. 1704-1707 | DOI

[86] N. M. Tubman; C. Mejuto-Zaera; J. M. Epstein et al. Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices, preprint, 2018 (p. 1–13) | arXiv

[87] S. Lee; J. Lee; H. Zhai et al. Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry, Nat. Commun., Volume 14 (2023) no. 1, 1952 | DOI

[88] B. Bauer; D. Wecker; A. J. Millis; M. B. Hastings; M. Troyer Hybrid quantum-classical approach to correlated materials, Phys. Rev. X, Volume 6 (2016) no. 3, 031045 | DOI

[89] J. M. Kreula; S. R. Clark; D. Jaksch Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics, Sci. Rep., Volume 6 (2016) no. 1, 32940 | DOI

[90] J. M. Kreula; L. García-Álvarez; L. Lamata; S. R. Clark; E. Solano; D. Jaksch Few-qubit quantum-classical simulation of strongly correlated lattice fermions, EPJ Quantum Technol., Volume 3 (2016) no. 1, 11 | DOI

[91] I. D. Kivlichan; C. Gidney; D. W. Berry et al. Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization, Quantum, Volume 4 (2020), 296 | DOI

[92] A. G. Fowler; M. Mariantoni; J. M. Martinis; A. N. Cleland Surface codes: towards practical large-scale quantum computation, Phys. Rev. A, Volume 86 (2012) no. 3, 032324 | DOI

[93] A. Morvan; B. Villalonga; X. Mi et al. Phase transition in random circuit sampling, Nature, Volume 634 (2024), pp. 328-333 | DOI

[94] F. Arute; K. Arya; R. Babbush et al. Quantum supremacy using a programmable superconducting processor, Nature, Volume 574 (2019) no. 7779, pp. 505-510 | DOI

[95] A. Peruzzo; J. McClean; P. Shadbolt; M.-H. Yung; X.-Q. Zhou; P. J. Love; A. Aspuru-Guzik; J. L. O’Brien A variational eigenvalue solver on a quantum processor, Nat. Commun., Volume 5 (2013) no. 1, 4213 | DOI

[96] J. Tilly; H. Chen; S. Cao et al. The variational quantum eigensolver: a review of methods and best practices, Phys. Rep., Volume 986 (2022), pp. 1-128 | DOI

[97] C. Kokail; C. Maier; R. van Bijnen et al. Self-verifying variational quantum simulation of lattice models, Nature, Volume 569 (2019) no. 7756, pp. 355-360 | DOI

[98] J. R. McClean; S. Boixo; V. N. Smelyanskiy; R. Babbush; H. Neven Barren plateaus in quantum neural network training landscapes, Nat. Commun., Volume 9 (2018), 4812 | DOI

[99] M. Larocca; S. Thanasilp; S. Wang et al. A review of barren plateaus in variational quantum computing, preprint, 2024 (p. 1–21) | arXiv

[100] R. Mao; G. Tian; X. Sun Barren plateaus of alternated disentangled UCC ansatzs, preprint, 2023 (p. 18–21) | arXiv

[101] M. Ragone; B. N. Bakalov; F. Sauvage; A. F. Kemper; C. O. Marrero; M. Larocca; M. Cerezo A unified theory of barren plateaus for deep parametrized quantum circuits, Nat. Commun., Volume 15 (2024), 7172 | DOI

[102] A. Arrasmith; Z. Holmes; M. Cerezo; P. J. Coles Equivalence of quantum barren plateaus to cost concentration and narrow gorges, Quantum Sci. Technol., Volume 7 (2022) no. 4, 045015 | DOI

[103] H. R. Grimsley; S. E. Economou; E. Barnes; N. J. Mayhall An adaptive variational algorithm for exact molecular simulations on a quantum computer, Nat. Commun., Volume 10 (2019) no. 1, 3007 | DOI

[104] H. L. Tang; V. O. Shkolnikov; G. S. Barron; H. R. Grimsley; N. J. Mayhall; E. Barnes; S. E. Economou qubit-ADAPT-VQE: an adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor, Phys. Rev. X Quantum, Volume 2 (2021), 020310 | DOI

[105] A. Kandala; A. Mezzacapo; K. Temme; M. Takita; M. Brink; J. M. Chow; J. M. Gambetta Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature, Volume 549 (2017) no. 7671, pp. 242-246 | DOI

[106] D. Wecker; M. B. Hastings; M. Troyer Progress towards practical quantum variational algorithms, Phys. Rev. A, Volume 92 (2015) no. 4, 042303 | DOI

[107] P. J. J. O’Malley; R. Babbush; I. D. Kivlichan et al. Scalable quantum simulation of molecular energies, Phys. Rev. X, Volume 6 (2015) no. 3, 031007 | DOI

[108] N. C. Rubin; R. Babbush; J. McClean Application of fermionic marginal constraints to hybrid quantum algorithms, J. Phys., Volume 20 (2018) no. 5, 053020 | DOI

[109] A. Arrasmith; L. Cincio; R. D. Somma; P. J. Coles Operator sampling for shot-frugal optimization in variational algorithms, preprint, 2020 (p. 1–11) | arXiv

[110] M. Potthoff Two-site dynamical mean-field theory, Phys. Rev. B, Volume 64 (2001) no. 16, 165114 | DOI

[111] I. Rungger; N. Fitzpatrick; H. Chen et al. Dynamical mean field theory algorithm and experiment on quantum computers, preprint, 2019 (p. 1-10) | arXiv

[112] B. Jaderberg; A. Agarwal; K. Leonhardt; M. Kiffner; D. Jaksch Minimum hardware requirements for hybrid quantum–classical DMFT, Quantum Sci. Technol., Volume 5 (2020) no. 3, 034015 | DOI

[113] Y. Yao; F. Zhang; C.-Z. Wang; K.-M. Ho; P. P. Orth Gutzwiller hybrid quantum-classical computing approach for correlated materials, Phys. Rev. Res., Volume 3 (2021) no. 1, 013184 | DOI

[114] J. Selisko; M. Amsler; C. Wever et al. Dynamical mean field theory for real materials on a quantum computer, preprint, 2024 (p. 1–25) | arXiv

[115] S. Boixo; S. V. Isakov; V. N. Smelyanskiy et al. Characterizing quantum supremacy in near-term devices, Nat. Phys., Volume 14 (2016) no. 6, pp. 595-600 | DOI

[116] B. Rudiak-Gould The sum-over-histories formulation of quantum computing, preprint, 2006 | arXiv

[117] F. Pan; P. Zhang Simulating the Sycamore quantum supremacy circuits, preprint, 2021 (p. 1–9) | arXiv

[118] F. Pan; K. Chen; P. Zhang Solving the sampling problem of the Sycamore quantum supremacy circuits, Phys. Rev. Lett., Volume 129 (2022), 090502 | DOI

[119] J. Gray; S. Kourtis Hyper-optimized tensor network contraction, Quantum, Volume 5 (2021), pp. 1-22 | DOI

[120] C. Huang; F. Zhang; M. Newman et al. Efficient parallelization of tensor network contraction for simulating quantum computation, Nat. Comput. Sci., Volume 1 (2021) no. 9, pp. 578-587 | DOI

[121] Y. Zhou; E. M. Stoudenmire; X. Waintal What limits the simulation of quantum computers?, Phys. Rev. X, Volume 10 (2020) no. 4, 041038 | DOI

[122] G. Vidal Efficient classical simulation of slightly entangled quantum computations, Phys. Rev. Lett., Volume 91 (2003) no. 14, 147902 | DOI

[123] T. Ayral; T. Louvet; Y. Zhou; C. Lambert; E. M. Stoudenmire; X. Waintal Density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity, PRX Quantum, Volume 4 (2023) no. 2, 020304 | DOI

[124] E. Farhi; J. Goldstone; S. Gutmann A quantum approximate optimization algorithm, preprint, 2014 | arXiv

[125] K. Noh; L. Jiang; B. Fefferman Efficient classical simulation of noisy random quantum circuits in one dimension, Quantum, Volume 4 (2020), p. 318 | DOI

[126] A. Müller; T. Ayral; C. Bertrand Enabling large-depth simulation of noisy quantum circuits with positive tensor networks, preprint, 2024 (p. 1–17) | arXiv

[127] S. Cheng; C. Cao; C. Zhang; Y. Liu; S.-Y. Hou; P. Xu; B. Zeng Simulating noisy quantum circuits with matrix product density operators, Phys. Rev. Res., Volume 3 (2021) no. 2, 023005 | DOI

[128] T. Ayral; F. M. Le Regent; Z. Saleem; Y. Alexeev; M. Suchara Quantum divide and compute: Hardware demonstrations and noisy simulations, Proceedings of IEEE Computer Society Annual Symposium on VLSI, ISVLSI, 2020, pp. 138-140 | DOI

[129] T. Ayral; F.-marie L. Régent; Z. Saleem; Y. Alexeev; M. Suchara Quantum divide and compute: exploring the effect of different noise sources, SN Comput. Sci., Volume 2 (2021) no. 3, 132 | DOI

[130] M. Mohseni; A. Scherer; K. G. Johnson et al. How to build a quantum supercomputer: scaling challenges and opportunities, preprint, 2024 | arXiv

[131] B. Anselme Martin; T. Ayral; F. Jamet; M. J. Ranvcić; P. Simon Combining matrix product states and noisy quantum computers for quantum simulation, Phys. Rev. A, Volume 109 (2024) no. 6, 062437 | DOI

[132] S.-H. Lin; R. Dilip; A. G. Green; A. Smith; F. Pollmann Real- and imaginary-time evolution with compressed quantum circuits, PRX Quantum, Volume 2 (2021) no. 1, 010342 | DOI

[133] M. Schwarz; K. Temme; F. Verstraete Preparing projected entangled pair states on a quantum computer, Phys. Rev. Lett., Volume 108 (2012) no. 11, 110502 | DOI

[134] M. Schwarz; K. Temme; F. Verstraete; D. Perez-Garcia; T. S. Cubitt Preparing topological projected entangled pair states on a quantum computer, Phys. Rev. A, Volume 88 (2013) no. 3, 032321 | DOI

[135] Y. Wu; W.-S. Bao; S. Cao et al. Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett., Volume 127 (2021) no. 18, 180501 | DOI

[136] Y. Kim; A. Eddins; S. Anand et al. Evidence for the utility of quantum computing before fault tolerance, Nature, Volume 618 (2023) no. 7965, pp. 500-505 | DOI

[137] J. Tindall; M. Fishman; E. M. Stoudenmire; D. Sels Efficient tensor network simulation of IBM’s eagle kicked ising experiment, PRX Quantum, Volume 5 (2024) no. 1, 010308 | DOI

[138] T. Begušić; J. Gray; G. K.-L. Chan Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance, Sci. Adv., Volume 10 (2024) no. 3, pp. 1-4 | DOI

[139] K. Kechedzhi; S. V. Isakov; S. Mandrà; B. Villalonga; X. Mi; S. Boixo; V. Smelyanskiy Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments, Future Gener. Comput. Syst., Volume 153 (2024), pp. 431-441 | DOI

[140] E. G. D. Torre; M. M. Roses Dissipative mean-field theory of IBM utility experiment, Volume 1 (2023), pp. 1-4 | arXiv

[141] P. Besserve; T. Ayral Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach, Phys. Rev. B, Volume 105 (2022) no. 11, 115108 | DOI

[142] P. Besserve; M. Ferrero; T. Ayral Compact fermionic quantum state preparation with a natural-orbitalizing variational quantum eigensolving scheme, preprint, 2024 (p. 1–15) | arXiv

[143] I. D. Kivlichan; J. McClean; N. Wiebe; C. Gidney; A. Aspuru-Guzik; G. K.-L. Chan; R. Babbush Quantum simulation of electronic structure with linear depth and connectivity, Phys. Rev. Lett., Volume 120 (2018) no. 11, 110501 | DOI

[144] Y. Lu; M. Höppner; O. Gunnarsson; M. W. Haverkort Efficient real-frequency solver for dynamical mean-field theory, Phys. Rev. B, Volume 90 (2014) no. 8, 085102 | DOI

[145] Y. Lu; X. Cao; P. Hansmann; M. W. Haverkort Natural-orbital impurity solver and projection approach for Green’s functions, Phys. Rev. B, Volume 100 (2019) no. 11, 115134 | DOI

[146] F. Jamet; C. Lenihan; L. P. Lindoy; A. Agarwal; E. Fontana; B. A. Martin; I. Rungger Anderson impurity solver integrating tensor network methods with quantum computing, preprint, 2023 (p. 1–8) | arXiv

[147] V. Havlívcek; M. Troyer; J. D. Whitfield Operator locality in the quantum simulation of fermionic models, Phys. Rev. A, Volume 95 (2017) no. 3, 032332 | DOI

[148] F. Verstraete; J. I. Cirac Mapping local Hamiltonians of fermions to local Hamiltonians of spins, J. Stat. Mech.: Theory Exp., Volume 2005 (2005) no. 09, p. P09012-P09012 | DOI

[149] A. Michel; Lïc Henriet; C. Domain; A. Browaeys; T. Ayral Hubbard physics with Rydberg atoms: Using a quantum spin simulator to simulate strong fermionic correlations, Phys. Rev. B, Volume 109 (2024) no. 17, 174409 | DOI

[150] L. De’Medici; A. Georges; S. Biermann Orbital-selective Mott transition in multiband systems: Slave-spin representation and dynamical mean-field theory, Phys. Rev. B, Volume 72 (2005) no. 20, 205124 | DOI

[151] A. Rüegg; S. D. Huber; M. Sigrist Z2-slave-spin theory for strongly correlated fermions, Phys. Rev. B, Volume 81 (2010) no. 15, 155118 | DOI

[152] L. de’ Medici; M. Capone Modeling many-body physics with Slave-Spin mean-field: Mott and Hund’s physics in Fe-superconductors, The Iron Pnictide Superconductors (Springer Series in Solid-State Sciences), Springer, 2017, pp. 115-185 | DOI

[153] M. Schiró; M. Fabrizio Quantum quenches in the Hubbard model: time-dependent mean-field theory and the role of quantum fluctuations, Phys. Rev. B, Volume 83 (2011) no. 16, pp. 1-19 | DOI

[154] M. Sandri; M. Schiro; M. Fabrizio Linear ramps of interaction in the fermionic hubbard model, Phys. Rev. B, Volume 86 (2012), 075122 | DOI

[155] S. R. Hassan; L. de’ Medici Slave spins away from half filling: cluster mean-field theory of the Hubbard and extended Hubbard models, Phys. Rev. B, Volume 81 (2010) no. 3, 035106 | DOI

[156] M. F. Serret; B. Marchand; T. Ayral Solving optimization problems with Rydberg analog quantum computers: realistic requirements for quantum advantage using noisy simulation and classical benchmarks, Phys. Rev. A, Volume 102 (2020) no. 5, 052617 | DOI

[157] M. Rader; A. M. Läuchli Finite correlation length scaling in lorentz-invariant gapless iPEPS wave functions, Phys. Rev. X, Volume 8 (2018) no. 3, 31030 | DOI

[158] T. Louvet; T. Ayral; X. Waintal On the feasibility of performing quantum chemistry calculations on quantum computers, preprint, 2023 | arXiv

[159] C. Mora; X. Waintal Variational wave functions and their overlap with the ground state, Phys. Rev. Lett., Volume 99 (2007) no. 3, 030403 | DOI

[160] D. Wu; R. Rossi; F. Vicentini et al. Variational benchmarks for quantum many-body problems, Science, Volume 386 (2024), pp. 296-301 | DOI

[161] A. Abbas; A. Ambainis; B. Augustino et al. Quantum optimization: potential, challenges, and the path forward, Nat. Rev. Phys., Volume 6 (2024), 718 | DOI

[162] F. Barahona On the computational complexity of ising spin glass models, J. Phys. A: Math. General, Volume 15 (1982) no. 10, pp. 3241-3253 | DOI

[163] A. Y. Kitaev; A. H. Shen; M. N. Vyalyi Classical and Quantum Computation, American Mathematical Society, Providence, RI, 2002

[164] D. Aharonov; A. Ta-Shma Adiabatic quantum state generation and statistical zero knowledge, Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, ACM, 2003, pp. 20-29 | DOI

[165] H. Pichler; S.-T. Wang; L. Zhou; S. Choi; M. D. Lukin Quantum optimization for maximum independent set using Rydberg atom arrays, preprint, 2018 | arXiv

[166] M. T. Nguyen; J. G. Liu; J. Wurtz; M. D. Lukin; S. T. Wang; H. Pichler Quantum optimization with arbitrary connectivity using Rydberg atom arrays, PRX Quantum, Volume 4 (2023) no. 1, pp. 1-19 | DOI

[167] C. Dalyac; L.-P. Henry; M. Kim; J. Ahn; Lïc Henriet Exploring the impact of graph locality for the resolution of the maximum-independent-set problem with neutral atom devices, Phys. Rev. A, Volume 108 (2023) no. 5, 052423 | DOI

[168] S. Martiel; T. Ayral; C. Allouche Benchmarking quantum coprocessors in an application-centric, hardware-agnostic, and scalable way, IEEE Trans. Quantum Eng., Volume 2 (2021), pp. 1-11 | DOI

[169] E. Magesan; J. M. Gambetta; J. Emerson Characterizing quantum gates via randomized benchmarking, Phys. Rev. A, Volume 85 (2012) no. 4, 042311 | DOI

[170] E. Magesan; J. M. Gambetta; J. Emerson Scalable and robust randomized benchmarking of quantum processes, Phys. Rev. Lett., Volume 106 (2011) no. 18, 180504 | DOI

[171] W. van der Schoot; D. Leermakers; R. Wezeman; N. Neumann; F. Phillipson Evaluating the Q-score of quantum annealers, 2022 IEEE International Conference on Quantum Software (QSW), IEEE, 2022, pp. 9-16 | DOI

[172] W. da S. Coelho; M. D’Arcangelo; L.-P. Henry Efficient protocol for solving combinatorial graph problems on neutral-atom quantum processors, preprint, 2022 | arXiv

[173] N. H. Stair; F. A. Evangelista Simulating many-body systems with a projective quantum eigensolver, PRX Quantum, Volume 2 (2021) no. 3, 030301 | DOI

[174] J. Robledo-Moreno; M. Motta; H. Haas et al. Chemistry beyond exact solutions on a quantum-centric supercomputer, preprint, 2024 | arXiv

[175] W. J. Huggins; B. A. O’Gorman; N. C. Rubin; D. R. Reichman; R. Babbush; J. Lee Unbiasing fermionic quantum Monte Carlo with a quantum computer, Nature, Volume 603 (2022) no. 7901, pp. 416-420 | DOI

[176] Y. Zhang; Y. Huang; J. Sun; D. Lv; X. Yuan Quantum computing quantum Monte Carlo, preprint, 2022 (p. 1–7) | arXiv

Cité par Sources :

Commentaires - Politique