Symmetries and Many-Body Excitations with Neural-Network Quantum States

Choo, Kenny; Carleo, Giuseppe; Regnault, Nicolas; Neupert, Titus

doi:10.1103/physrevlett.121.167204

Cited by 221 publications

(213 citation statements)

References 40 publications

(55 reference statements)

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“…Method in Ref. 29. For a spin configuration, we can generate shifted configurations by applying the translation operators.…”

Section: Quantum Number Projectionmentioning

confidence: 99%

“…In Ref. 29, the canonical configuration σ canonical is chosen to be the lexicographically smallest one. By introducing an operator T shifting spin configurations by one site, the amplitude of the wave function for a configuration T n σ canonical (0 ≤ n < N site ) is given by…”

Section: Quantum Number Projectionmentioning

confidence: 99%

“…In Ref. 29, Ψ(σ canonical ) is prepared by the RBM or three-layer feedforward neural networks (FFNN). Present Scheme.…”

Section: Quantum Number Projectionmentioning

confidence: 99%

“…2, the computational cost of the scheme in Ref. 29 scales as O(αN 2 site ). On the other hand, the present scheme scales as O(αN 3 site ) because we need to compute the summation over n in Eq.…”

Section: Quantum Number Projectionmentioning

confidence: 99%

“…As for the calculations of excited states, we propose a different approach than that employed in Ref. 29.…”

Section: Introductionmentioning

confidence: 99%

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Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations

Nomura

2020

J. Phys. Soc. Jpn.

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To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that make it possible to apply machine learning techniques to analyze fermion-boson coupled Hamiltonians and to calculate excited states. As for the extension to fermion-boson coupled systems, we study the Holstein model as a representative of the fermion-boson coupled Hamiltonians. We show that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method. As for the calculations of excited states, we propose a different approach than that proposed in K. Choo et al., Phys. Rev. Lett. 121 (2018) 167204. We discuss the difference in detail and compare the accuracy of two methods using the one-dimensional S = 1/2 Heisenberg chain. We also show the benchmark for the frustrated two-dimensional S = 1/2 J 1 -J 2 Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.

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“…Method in Ref. 29. For a spin configuration, we can generate shifted configurations by applying the translation operators.…”

Section: Quantum Number Projectionmentioning

confidence: 99%

Section: Quantum Number Projectionmentioning

confidence: 99%

“…In Ref. 29, Ψ(σ canonical ) is prepared by the RBM or three-layer feedforward neural networks (FFNN). Present Scheme.…”

Section: Quantum Number Projectionmentioning

confidence: 99%

Section: Quantum Number Projectionmentioning

confidence: 99%

“…As for the calculations of excited states, we propose a different approach than that employed in Ref. 29.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations

Nomura

2020

J. Phys. Soc. Jpn.

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In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Aldossary,

Campos‐Gonzalez‐Angulo,

Pablo‐García

et al. 2024

Advanced Materials

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Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

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Finding the Dynamics of an Integrable Quantum Many‐Body System via Machine Learning

Wei,

Orfi,

Fehse

et al. 2023

Advanced Physics Research

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The dynamics of the Gaudin magnet (“central‐spin model”) is studied using machine‐learning methods. This model is of practical importance, for example, for studying non‐Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities. Machine‐learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, a neural‐network representation (restricted Boltzmann machine) is used for each variational eigenstate of the model Hamiltonian. Accurate representations of the ground state and of the low‐lying excited states of the Gaudin‐magnet Hamiltonian are then obtained through a variational Monte Carlo calculation. From the low‐lying eigenstates, the non‐perturbative dynamic transverse spin susceptibility is found, describing the linear response of a central spin to a time‐varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two‐level systems.

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Symmetries and Many-Body Excitations with Neural-Network Quantum States

Cited by 221 publications

References 40 publications

Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations

Machine Learning Quantum States — Extensions to Fermion–Boson Coupled Systems and Excited-State Calculations

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Finding the Dynamics of an Integrable Quantum Many‐Body System via Machine Learning

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