Neural-Network Quantum States: from Condensed Matter to Quantum Computing

Matija Medvidović, Javier Robledo Moreno

Álvaro Díaz Fernández, Chao Fang, Volker Knecht

This chapter describes the usage of ML to study condensed matter. ML is shown to accelerate the sampling of spin glass configurations in computer simulations by up to five orders of magnitude. On the analysis side, ML is very efficient for evaluating the output of simulations of topological order transitions. The latter are characterized by the temperature-driven unbinding of vortex/antivortex pairs. Such transitions may be detected by analyzing configurations using neural networks implemented with the aim of learning vortices. Incorporated in the heart of computer simulations, ML is used to study quantum many-body systems. Here, the mathematical object describing the quantum-mechanical state of a system – the many-body wave function – is implemented in a neural-network representation. Away from pure theory, ML allows the quantum state of a system to be reconstructed based on experimental measurements. Here, the experimental data are used to train a neural network via unsupervised learning to output the state as a neural-network quantum state. As a more technological application, ML is efficient in predicting new materials with desired properties. Neural networks or other ML techniques enable the prediction of thermodynamically stable compounds with a desired structure by searching over the entire compound space.

Subhash C. Kak

Ivan Glasser, Nicola Pancotti, Moritz August +2 more

Two tools show great promise in approximating low-temperature, condensed-matter systems: Tensor-network states and artificial neural networks. A new analysis builds a bridge between these techniques, opening the way to a host of powerful approaches to understanding complex quantum systems.

Pavlo V. Bilous, Louis Thirion, Henri Menke +3 more

A neural-network approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground state wave function. We benchmark our results against established methods and investigate the efficiency of our approach compared to another basis truncation scheme without a neural network. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural-network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.

Alessandro Lovato, Giuseppe Carleo, Bryce Fore +4 more

A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.