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arXiv:2305.07240 · Physical review. B./Physical review. B

Message-passing neural quantum states for the homogeneous electron gas

Gabriel Pescia, Jannes Nys, Jane Kim, Alessandro Lovato, Giuseppe Carleo

Published Jul 2, 2024• 52 citations
arXivHTMLPDF

Abstract

The immense parameter complexity of current neural-network quantum states (NQS) in continuous space renders their application to realistic physical systems impossible. Here, the authors rigorously motivate a many-body coordinate transformation as basis for a variational neural-network Ansatz, implement it via message-passing neural networks, and show a resulting reduction of two orders of magnitude in parameter complexity and convergence speed. With this, the authors open the door for future NQS studies of extended systems in the thermodynamic limit.

DOI
10.1103/physrevb.110.035108

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The immense parameter complexity of current neural-network quantum states (NQS) in continuous space renders their application to realistic physical systems impossible. Here, the authors rigorously motivate a many-body coordinate transformation as basis for a variational neural-network Ansatz, implement it via message-passing neural networks, and show a resulting reduction of two orders of magnitude in parameter complexity and convergence speed. With this, the authors open the door for future NQS studies of extended systems in the thermodynamic limit.
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Abstract Neural-network quantum states (NQS) are powerful neural-network ansätzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be systematically improvable by increasing the number of parameters. Here we demonstrate an Adaptive scheme to optimize NQSs, through the example of recurrent neural networks (RNNs), using a fraction of the computation cost while reducing training fluctuations and improving the quality of variational calculations targeting ground states of prototypical models in one- and two-spatial dimensions. This Adaptive framework reduces the computational cost through training small RNNs and reusing them to initialize larger RNNs. This work opens up the possibility for optimizing graphical processing unit resources deployed in large-scale NQS simulations.
Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.
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Abstract Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.