From Architectures to Applications: A Review of Neural Quantum States

TL;DR

This review discusses neural quantum states (NQS), a promising variational approach that compresses quantum many-body states using neural networks to overcome exponential complexity in simulations.

Contribution

It provides a comprehensive overview of NQS architectures, applications, and their potential in simulating various quantum states and dynamics, highlighting recent advancements.

Findings

NQS effectively simulate ground and excited states.

NQS can model finite temperature and open system states.

NQS approaches facilitate quantum state tomography.

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.