Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Martyn, John M.; Najafi, Khadijeh; Luo, Di

doi:10.1103/physrevlett.131.081601

Title: Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Journal Article · 23 August 2023 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.131.081601 · OSTI ID:2425552

^[1]; Najafi, Khadijeh ^[2];

^[3]

Massachusetts Institute of Technology, Cambridge, MA (United States); The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA (United States)
IBM Quantum, Yorktown Heights, NY (United States); MIT-IBM Watson AI Lab, Cambridge, MA (United States)
Massachusetts Institute of Technology, Cambridge, MA (United States); The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, MA (United States); Harvard University, Cambridge, MA (United States)

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state’s Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States); National Quantum Information Science (QIS) Research Centers (United States). Co-design Center for Quantum Advantage (C2QA)

Sponsoring Organization:: National Science Foundation Graduate Research Fellowship; USDOE Office of Science (SC)

Grant/Contract Number:: SC0012704

OSTI ID:: 2425552

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 8 Vol. 131; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (72)

On the eigenfunctions of many-particle systems in quantum mechanics Kato, Tosio Communications on Pure and Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1002/cpa.3160100201	journal	January 1957
Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions Gnech, Alex; Adams, Corey; Brawand, Nicholas Few-Body Systems, Vol. 63, Issue 1 https://doi.org/10.1007/s00601-021-01706-0	journal	December 2021
Why Does Deep and Cheap Learning Work So Well? Lin, Henry W.; Tegmark, Max; Rolnick, David Journal of Statistical Physics, Vol. 168, Issue 6 https://doi.org/10.1007/s10955-017-1836-5	journal	July 2017
Compression effects in helium-like atoms constrained by hard spherical walls Flores-Riveros, A.; Rodríguez-Contreras, A. Physics Letters A, Vol. 372, Issue 40 https://doi.org/10.1016/j.physleta.2008.08.027	journal	September 2008
Condensed Matter Field Theory Altland, Alexander; Simons, Ben D. https://doi.org/10.1017/CBO9780511789984	book	August 2010
Variational Monte Carlo Method with Dirichlet Boundary Conditions: Application to the Study of Confined Systems by Impenetrable Surfaces with Different Symmetries Sarsa, Antonio; Le Sech, Claude Journal of Chemical Theory and Computation, Vol. 7, Issue 9 https://doi.org/10.1021/ct200284q	journal	August 2011
Tonks–Girardeau gas of ultracold atoms in an optical lattice Paredes, Belén; Widera, Artur; Murg, Valentin Nature, Vol. 429, Issue 6989 https://doi.org/10.1038/nature02530	journal	May 2004
In situ click chemistry generation of cyclooxygenase-2 inhibitors Bhardwaj, Atul; Kaur, Jatinder; Wuest, Melinda Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-016-0009-6	journal	February 2017
Deep-neural-network solution of the electronic Schrödinger equation Hermann, Jan; Schätzle, Zeno; Noé, Frank Nature Chemistry, Vol. 12, Issue 10 https://doi.org/10.1038/s41557-020-0544-y	journal	September 2020
Neural-network quantum state tomography Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan Nature Physics, Vol. 14, Issue 5 https://doi.org/10.1038/s41567-018-0048-5	journal	February 2018
Restricted Boltzmann machines in quantum physics Melko, Roger G.; Carleo, Giuseppe; Carrasquilla, Juan Nature Physics, Vol. 15, Issue 9 https://doi.org/10.1038/s41567-019-0545-1	journal	June 2019
Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension Girardeau, M. Journal of Mathematical Physics, Vol. 1, Issue 6 https://doi.org/10.1063/1.1703687	journal	November 1960
Primitive model electrolytes. I. Grand canonical Monte Carlo computations Valleau, John P.; Cohen, L. Kenneth The Journal of Chemical Physics, Vol. 72, Issue 11 https://doi.org/10.1063/1.439092	journal	June 1980
The 1D interacting Bose gas in a hard wall box Batchelor, M. T.; Guan, X. W.; Oelkers, N. Journal of Physics A: Mathematical and General, Vol. 38, Issue 36 https://doi.org/10.1088/0305-4470/38/36/001	journal	August 2005
Study of confined many electron atoms by means of the POEP method Sarsa, A.; Buendía, E.; Gálvez, F. J. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 47, Issue 18 https://doi.org/10.1088/0953-4075/47/18/185002	journal	August 2014
Continuum tensor network field states, path integral representations and spatial symmetries Jennings, David; Brockt, Christoph; Haegeman, Jutho New Journal of Physics, Vol. 17, Issue 6 https://doi.org/10.1088/1367-2630/17/6/063039	journal	June 2015
A highly accurate study of a helium atom under pressure Laughlin, Cecil; Chu, Shih-I Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 26 https://doi.org/10.1088/1751-8113/42/26/265004	journal	June 2009
Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State Lieb, Elliott H.; Liniger, Werner Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1605	journal	May 1963
Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum Lieb, Elliott H. Physical Review, Vol. 130, Issue 4 https://doi.org/10.1103/PhysRev.130.1616	journal	May 1963
Probabilistic simulation of quantum circuits using a deep-learning architecture Carrasquilla, Juan; Luo, Di; Pérez, Felipe Physical Review A, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevA.104.032610	journal	September 2021
Exact Results for a Quantum Many-Body Problem in One Dimension Sutherland, Bill Physical Review A, Vol. 4, Issue 5 https://doi.org/10.1103/PhysRevA.4.2019	journal	November 1971
Boundary Energy of a Bose Gas in One Dimension Gaudin, M. Physical Review A, Vol. 4, Issue 1 https://doi.org/10.1103/PhysRevA.4.386	journal	July 1971
Exact Results for a Quantum Many-Body Problem in One Dimension. II Sutherland, Bill Physical Review A, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevA.5.1372	journal	March 1972
Continuous matrix-product states in inhomogeneous systems with long-range interactions Lukin, I. V.; Sotnikov, A. G. Physical Review B, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevB.106.144206	journal	October 2022
Neural tensor contractions and the expressive power of deep neural quantum states Sharir, Or; Shashua, Amnon; Carleo, Giuseppe Physical Review B, Vol. 106, Issue 20 https://doi.org/10.1103/PhysRevB.106.205136	journal	November 2022
Neural network ansatz for periodic wave functions and the homogeneous electron gas Wilson, Max; Moroni, Saverio; Holzmann, Markus Physical Review B, Vol. 107, Issue 23 https://doi.org/10.1103/PhysRevB.107.235139	journal	June 2023
Generalized Lanczos algorithm for variational quantum Monte Carlo Sorella, Sandro Physical Review B, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevB.64.024512	journal	June 2001
Calculus of continuous matrix product states Haegeman, Jutho; Cirac, J. Ignacio; Osborne, Tobias J. Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085118	journal	August 2013
Conformal data from finite entanglement scaling Stojevic, Vid; Haegeman, Jutho; McCulloch, I. P. Physical Review B, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevB.91.035120	journal	January 2015
Lieb-Liniger model with exponentially decaying interactions: A continuous matrix product state study Rincón, Julián; Ganahl, Martin; Vidal, Guifre Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115107	journal	September 2015
Equivalence of restricted Boltzmann machines and tensor network states Chen, Jing; Cheng, Song; Xie, Haidong Physical Review B, Vol. 97, Issue 8 https://doi.org/10.1103/PhysRevB.97.085104	journal	February 2018
Continuous matrix product states for nonrelativistic quantum fields: A lattice algorithm for inhomogeneous systems Ganahl, Martin; Vidal, Guifre Physical Review B, Vol. 98, Issue 19 https://doi.org/10.1103/PhysRevB.98.195105	journal	November 2018
Constructing neural stationary states for open quantum many-body systems Yoshioka, Nobuyuki; Hamazaki, Ryusuke Physical Review B, Vol. 99, Issue 21 https://doi.org/10.1103/PhysRevB.99.214306	journal	June 2019
Flow-based generative models for Markov chain Monte Carlo in lattice field theory Albergo, M. S.; Kanwar, G.; Shanahan, P. E. Physical Review D, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevD.100.034515	journal	August 2019
Flow-based sampling for fermionic lattice field theories Albergo, Michael S.; Kanwar, Gurtej; Racanière, Sébastien Physical Review D, Vol. 104, Issue 11 https://doi.org/10.1103/PhysRevD.104.114507	journal	December 2021
Approximating relativistic quantum field theories with continuous tensor networks Shachar, Tom; Zohar, Erez Physical Review D, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevD.105.045016	journal	February 2022
Off-diagonal correlations of the Calogero-Sutherland model Astrakharchik, G. E.; Gangardt, D. M.; Lozovik, Yu. E. Physical Review E, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevE.74.021105	journal	August 2006
Continuous Matrix Product States for Quantum Fields Verstraete, F.; Cirac, J. I. Physical Review Letters, Vol. 104, Issue 19 https://doi.org/10.1103/PhysRevLett.104.190405	journal	May 2010
Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm Ganahl, Martin; Rincón, Julián; Vidal, Guifre Physical Review Letters, Vol. 118, Issue 22 https://doi.org/10.1103/PhysRevLett.118.220402	journal	June 2017
Symmetries and Many-Body Excitations with Neural-Network Quantum States Choo, Kenny; Carleo, Giuseppe; Regnault, Nicolas Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.167204	journal	October 2018
Quantum Entanglement in Deep Learning Architectures Levine, Yoav; Sharir, Or; Cohen, Nadav Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/PhysRevLett.122.065301	journal	February 2019
Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems Nagy, Alexandra; Savona, Vincenzo Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250501	journal	June 2019
Neural-Network Approach to Dissipative Quantum Many-Body Dynamics Hartmann, Michael J.; Carleo, Giuseppe Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250502	journal	June 2019
Variational Neural-Network Ansatz for Steady States in Open Quantum Systems Vicentini, Filippo; Biella, Alberto; Regnault, Nicolas Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.250503	journal	June 2019
Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems Sharir, Or; Levine, Yoav; Wies, Noam Physical Review Letters, Vol. 124, Issue 2 https://doi.org/10.1103/PhysRevLett.124.020503	journal	January 2020
Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks Schmitt, Markus; Heyl, Markus Physical Review Letters, Vol. 125, Issue 10 https://doi.org/10.1103/PhysRevLett.125.100503	journal	September 2020
Equivariant Flow-Based Sampling for Lattice Gauge Theory Kanwar, Gurtej; Albergo, Michael S.; Boyda, Denis Physical Review Letters, Vol. 125, Issue 12 https://doi.org/10.1103/PhysRevLett.125.121601	journal	September 2020
Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models Nicoli, Kim A.; Anders, Christopher J.; Funcke, Lena Physical Review Letters, Vol. 126, Issue 3 https://doi.org/10.1103/PhysRevLett.126.032001	journal	January 2021
Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz Adams, Corey; Carleo, Giuseppe; Lovato, Alessandro Physical Review Letters, Vol. 127, Issue 2 https://doi.org/10.1103/PhysRevLett.127.022502	journal	July 2021
Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks Reh, Moritz; Schmitt, Markus; Gärttner, Martin Physical Review Letters, Vol. 127, Issue 23 https://doi.org/10.1103/PhysRevLett.127.230501	journal	December 2021
Gauge Equivariant Neural Networks for Quantum Lattice Gauge Theories Luo, Di; Carleo, Giuseppe; Clark, Bryan K. Physical Review Letters, Vol. 127, Issue 27 https://doi.org/10.1103/PhysRevLett.127.276402	journal	December 2021
Variational Optimization of Continuous Matrix Product States Tuybens, Benoît; De Nardis, Jacopo; Haegeman, Jutho Physical Review Letters, Vol. 128, Issue 2 https://doi.org/10.1103/PhysRevLett.128.020501	journal	January 2022
Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation Luo, Di; Chen, Zhuo; Carrasquilla, Juan Physical Review Letters, Vol. 128, Issue 9 https://doi.org/10.1103/PhysRevLett.128.090501	journal	February 2022
One-Dimensional Bosons in Three-Dimensional Traps Lieb, Elliott H.; Seiringer, Robert; Yngvason, Jakob Physical Review Letters, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevLett.91.150401	journal	October 2003
Recurrent neural network wave functions Hibat-Allah, Mohamed; Ganahl, Martin; Hayward, Lauren E. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevResearch.2.023358	journal	June 2020
Ab initio solution of the many-electron Schrödinger equation with deep neural networks Pfau, David; Spencer, James S.; Matthews, Alexander G. D. G. Physical Review Research, Vol. 2, Issue 3 https://doi.org/10.1103/PhysRevResearch.2.033429	journal	September 2020
Gaussian continuous tensor network states for simple bosonic field theories Karanikolaou, Teresa D.; Emonts, Patrick; Tilloy, Antoine Physical Review Research, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevResearch.3.023059	journal	April 2021
Neural-network quantum states for periodic systems in continuous space Pescia, Gabriel; Han, Jiequn; Lovato, Alessandro Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023138	journal	May 2022
Hidden-nucleons neural-network quantum states for the nuclear many-body problem Lovato, Alessandro; Adams, Corey; Carleo, Giuseppe Physical Review Research, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevResearch.4.043178	journal	December 2022
Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models Luo, Di; Chen, Zhuo; Hu, Kaiwen Physical Review Research, Vol. 5, Issue 1 https://doi.org/10.1103/PhysRevResearch.5.013216	journal	March 2023
Quantum Entanglement in Neural Network States Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S. Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevX.7.021021	journal	May 2017
Neural-Network Quantum States, String-Bond States, and Chiral Topological States Glasser, Ivan; Pancotti, Nicola; August, Moritz Physical Review X, Vol. 8, Issue 1 https://doi.org/10.1103/PhysRevX.8.011006	journal	January 2018
Continuous Tensor Network States for Quantum Fields Tilloy, Antoine; Cirac, J. Ignacio Physical Review X, Vol. 9, Issue 2 https://doi.org/10.1103/PhysRevX.9.021040	journal	May 2019
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
Observation of a One-Dimensional Tonks-Girardeau Gas Kinoshita, T. Science, Vol. 305, Issue 5687 https://doi.org/10.1126/science.1100700	journal	August 2004
Solving the quantum many-body problem with artificial neural networks Carleo, Giuseppe; Troyer, Matthias Science, Vol. 355, Issue 6325 https://doi.org/10.1126/science.aag2302	journal	February 2017
Lattice Gauge Theories: An Introduction Rothe, Heinz J. World Scientific Lecture Notes in Physics https://doi.org/10.1142/8229	book	March 2012
Path-Integral Renormalization Group Method for Numerical Study on Ground States of Strongly Correlated Electronic Systems Kashima, Tsuyoshi; Imada, Masatoshi Journal of the Physical Society of Japan, Vol. 70, Issue 8 https://doi.org/10.1143/JPSJ.70.2287	journal	August 2001
Quantum Gross-Pitaevskii Equation Haegeman, Jutho; Draxler, Damian; Stojevic, Vid SciPost Physics, Vol. 3, Issue 1 https://doi.org/10.21468/SciPostPhys.3.1.006	journal	July 2017
NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems Vicentini, Filippo; Hofmann, Damian; Szabó, Attila SciPost Physics Codebases https://doi.org/10.21468/scipostphyscodeb.7	journal	August 2022
Real time evolution with neural-network quantum states Gutiérrez, Irene López; Mendl, Christian B. Quantum, Vol. 6 https://doi.org/10.22331/q-2022-01-20-627	journal	January 2022
Machine Learning Technique to Find Quantum Many-Body Ground States of Bosons on a Lattice Saito, Hiroki; Kato, Masaya Journal of the Physical Society of Japan, Vol. 87, Issue 1 https://doi.org/10.7566/JPSJ.87.014001	journal	January 2018

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Title: Variational Neural-Network Ansatz for Continuum Quantum Field Theory

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