Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks

Liu, Jin-Guo; Gao, Xun; Cain, Madelyn; Lukin, Mikhail D.; Wang, Sheng-Tao

doi:10.1137/22m1501787

Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks

Journal Article · 13 June 2023 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/22m1501787· OSTI ID:2421692

^[1]; Gao, Xun ^[2]; Cain, Madelyn ^[3]; Lukin, Mikhail D. ^[3]; Wang, Sheng-Tao ^[4]

Department of Physics, Harvard University, Cambridge, MA 02138 USA, and QuEra Computing, Boston, MA 02135 USA.; OSTI
Department of Physics, Harvard University, Cambridge, MA 02138 USA.
Department of Physics, Harvard University, Cambridge, MA 02138 USA, and QuEra Computing, Boston, MA 02135 USA.
QuEra Computing, Boston, MA 02135 USA.

Not provided.

Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: SC0021013

OSTI ID:: 2421692

Journal Information:: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 45; ISSN 1064-8275

Publisher:: Society for Industrial and Applied Mathematics (SIAM)

Country of Publication:: United States

Language:: English

References (32)

Array programming with NumPy Harris, Charles R.; Millman, K. Jarrod; van der Walt, Stéfan J. Nature, Vol. 585, Issue 7825 https://doi.org/10.1038/s41586-020-2649-2	journal	September 2020
Quantum optimization of maximum independent set using Rydberg atom arrays Ebadi, S.; Keesling, A.; Cain, M. Science, Vol. 376, Issue 6598 https://doi.org/10.1126/science.abo6587	journal	June 2022
Fast counting with tensor networks Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo SciPost Physics, Vol. 7, Issue 5 https://doi.org/10.21468/SciPostPhys.7.5.060	journal	November 2019
Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example Xu, Yi-Zhi; Yeung, Chi Ho; Zhou, Hai-Jun Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.210602	journal	November 2018
A practical introduction to tensor networks: Matrix product states and projected entangled pair states Orús, Román Annals of Physics, Vol. 349 https://doi.org/10.1016/j.aop.2014.06.013	journal	October 2014
A review on algorithms for maximum clique problems Wu, Qinghua; Hao, Jin-Kao European Journal of Operational Research, Vol. 242, Issue 3 https://doi.org/10.1016/j.ejor.2014.09.064	journal	May 2015
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems Cirac, J. Ignacio; Pérez-García, David; Schuch, Norbert Reviews of Modern Physics, Vol. 93, Issue 4 https://doi.org/10.1103/RevModPhys.93.045003	journal	December 2021
Hyper-optimized tensor network contraction Gray, Johnnie; Kourtis, Stefanos Quantum, Vol. 5 https://doi.org/10.22331/q-2021-03-15-410	journal	March 2021
Simulating Quantum Computation by Contracting Tensor Networks Markov, Igor L.; Shi, Yaoyun SIAM Journal on Computing, Vol. 38, Issue 3 https://doi.org/10.1137/050644756	journal	January 2008
Monte Carlo simulations of two-dimensional hard core lattice gases Fernandes, Heitor C. Marques; Arenzon, Jeferson J.; Levin, Yan The Journal of Chemical Physics, Vol. 126, Issue 11 https://doi.org/10.1063/1.2539141	journal	March 2007
Exact exponential algorithms Fomin, Fedor V.; Kaski, Petteri Communications of the ACM, Vol. 56, Issue 3 https://doi.org/10.1145/2428556.2428575	journal	March 2013
Local algorithms for independent sets are half-optimal Rahman, Mustazee; Virág, Bálint The Annals of Probability, Vol. 45, Issue 3 https://doi.org/10.1214/16-AOP1094	journal	May 2017
Anderson localization makes adiabatic quantum optimization fail Altshuler, Boris; Krovi, Hari; Roland, Jérémie Proceedings of the National Academy of Sciences, Vol. 107, Issue 28 https://doi.org/10.1073/pnas.1002116107	journal	June 2010
On the independence complex of square grids Bousquet-Mélou, Mireille; Linusson, Svante; Nevo, Eran Journal of Algebraic Combinatorics, Vol. 27, Issue 4 https://doi.org/10.1007/s10801-007-0096-x	journal	October 2007
Hard-square lattice gas Baxter, R. J.; Enting, I. G.; Tsang, S. K. Journal of Statistical Physics, Vol. 22, Issue 4 https://doi.org/10.1007/BF01012867	journal	April 1980
A classical theory of hard squares Pearce, Paul A.; Seaton, Katherine A. Journal of Statistical Physics, Vol. 53, Issue 5-6 https://doi.org/10.1007/BF01023857	journal	December 1988
Matrix Computations Golub, Gene H.; Van Loan, Charles F. https://doi.org/10.56021/9781421407944	book	February 2013
Tensor Network Contractions for #SAT Biamonte, Jacob D.; Morton, Jason; Turner, Jacob Journal of Statistical Physics, Vol. 160, Issue 5 https://doi.org/10.1007/s10955-015-1276-z	journal	June 2015
Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model Lee, T. D.; Yang, C. N. Physical Review, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRev.87.410	journal	August 1952
Schnelle Multiplikation großer Zahlen Schönhage, A.; Strassen, V. Computing, Vol. 7, Issue 3-4 https://doi.org/10.1007/BF02242355	journal	September 1971
The monadic second-order logic of graphs. I. Recognizable sets of finite graphs Courcelle, Bruno Information and Computation, Vol. 85, Issue 1 https://doi.org/10.1016/0890-5401(90)90043-H	journal	March 1990
Tropical Tensor Network for Ground States of Spin Glasses Liu, Jin-Guo; Wang, Lei; Zhang, Pan Physical Review Letters, Vol. 126, Issue 9 https://doi.org/10.1103/PhysRevLett.126.090506	journal	March 2021
Algorithm 457: finding all cliques of an undirected graph Bron, Coen; Kerbosch, Joep Communications of the ACM, Vol. 16, Issue 9 https://doi.org/10.1145/362342.362367	journal	September 1973
On generating all maximal independent sets Johnson, David S.; Yannakakis, Mihalis; Papadimitriou, Christos H. Information Processing Letters, Vol. 27, Issue 3 https://doi.org/10.1016/0020-0190(88)90065-8	journal	March 1988
The overlap gap property: A topological barrier to optimizing over random structures Gamarnik, David Proceedings of the National Academy of Sciences, Vol. 118, Issue 41 https://doi.org/10.1073/pnas.2108492118	journal	October 2021
Simple liquids’ quasiuniversality and the hard-sphere paradigm Dyre, Jeppe C. Journal of Physics: Condensed Matter, Vol. 28, Issue 32 https://doi.org/10.1088/0953-8984/28/32/323001	journal	June 2016
Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation Yang, C. N.; Lee, T. D. Physical Review, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRev.87.404	journal	August 1952
On Independent Sets and Bicliques in Graphs Gaspers, Serge; Kratsch, Dieter; Liedloff, Mathieu Algorithmica, Vol. 62, Issue 3-4 https://doi.org/10.1007/s00453-010-9474-1	journal	November 2010
Tensor-Train Decomposition Oseledets, I. V. SIAM Journal on Scientific Computing, Vol. 33, Issue 5 https://doi.org/10.1137/090752286	journal	January 2011
Effective Extensible Programming: Unleashing Julia on GPUs Besard, Tim; Foket, Christophe; De Sutter, Bjorn IEEE Transactions on Parallel and Distributed Systems, Vol. 30, Issue 4 https://doi.org/10.1109/TPDS.2018.2872064	journal	April 2019
The complexity of tropical matrix factorization Shitov, Yaroslav Advances in Mathematics, Vol. 254 https://doi.org/10.1016/j.aim.2013.12.013	journal	March 2014
The Rectilinear Steiner Tree Problem is $NP$-Complete Garey, M. R.; Johnson, D. S. SIAM Journal on Applied Mathematics, Vol. 32, Issue 4 https://doi.org/10.1137/0132071	journal	June 1977

Similar Records

A Quantum-Inspired Tensor Network Algorithm for Constrained Combinatorial Optimization Problems

Journal Article · 2022 · Frontiers in Physics · OSTI ID:1872978

Computing the Feasible Spaces of Optimal Power Flow Problems

Journal Article · 2017 · IEEE Transactions on Power Systems · OSTI ID:1401986

A Parallel Computing Framework for Finding the Supported Solutions to a Biobjective Network Optimization Problem

Journal Article · 2015 · Journal of Multi-Criteria Decision Analysis · OSTI ID:1401385

Related Subjects

Mathematics

Computing Solution Space Properties of Combinatorial Optimization Problems Via Generic Tensor Networks

Citation Formats

References (32)

Similar Records

Related Subjects