Approximating Ground States by Neural Network Quantum States

The many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Motivated by the Giuseppe Carleo's work titled solving the quantum many-body problem with artificial neural networks [Science, 2017, 355: 602], we focus on finding the NNQS approximation of the unknown ground state of a given Hamiltonian $H$ in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

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Approximating Ground States by Neural Network Quantum States

Entropy ◽

10.3390/e21010082 ◽

2019 ◽

Vol 21 (1) ◽

pp. 82 ◽

Cited By ~ 1

Author(s):

Ying Yang ◽

Chengyang Zhang ◽

Huaixin Cao

Keyword(s):

Neural Network ◽

Tensor Product ◽

Relative Error ◽

Ground State ◽

Ground States ◽

Quantum States ◽

The Neural Network

Motivated by the Carleo’s work (Science, 2017, 355: 602), we focus on finding the neural network quantum statesapproximation of the unknown ground state of a given Hamiltonian H in terms of the best relative error and explore the influences of sum, tensor product, local unitary of Hamiltonians on the best relative error. Besides, we illustrate our method with some examples.

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Digraph states and their neural network representations

Chinese Physics B ◽

10.1088/1674-1056/ac401d ◽

2021 ◽

Author(s):

Ying Yang ◽

Huaixin Cao

Keyword(s):

Neural Network ◽

Machine Learning ◽

Body Problem ◽

Theoretical Foundation ◽

Rapid Development ◽

Quantum States ◽

Machine Learning Method ◽

Learning Method ◽

Many Body ◽

Graph State

Abstract With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. In this paper, we aim to introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly the NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.

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Wave equation for dissipative systems derived from a quantized many-body problem

Canadian Journal of Physics ◽

10.1139/p80-140 ◽

1980 ◽

Vol 58 (7) ◽

pp. 1019-1025 ◽

Cited By ~ 4

Author(s):

M. Razavy

Keyword(s):

Wave Function ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Body Problem ◽

Body Wave ◽

Time Dependent ◽

Dissipative Systems ◽

Many Body ◽

Dependent Part ◽

The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

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THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

International Journal of Modern Physics B ◽

10.1142/s0217979207043592 ◽

2007 ◽

Vol 21 (13n14) ◽

pp. 2204-2214 ◽

Cited By ~ 7

Author(s):

BEATE PAULUS

Keyword(s):

Experimental Data ◽

Ab Initio ◽

Ground State ◽

Infinite System ◽

Correlation Energy ◽

Correlation Method ◽

Many Body ◽

Hartree Fock ◽

The Many ◽

Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

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