Toward Neural Network Simulation of Variational Quantum Algorithms

TL;DR

This paper explores whether classical neural network-based algorithms can simulate variational quantum algorithms, specifically the variational quantum linear solver, potentially extending to other similar quantum algorithms.

Contribution

It demonstrates that classical stochastic optimization algorithms can be constructed to parallel VQAs like VQLS, offering a new simulation paradigm.

Findings

Classical neural networks can emulate VQLS behavior.

The proposed approach could extend to other VQAs.

Potential for classical simulation of quantum algorithms.

Abstract

Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term quantum resources to accelerate this task, the computational advantage of VQAs over wholly classical algorithms has not been firmly established. For instance, while the variational quantum eigensolver (VQE) has been developed to approximate low-lying eigenmodes of high-dimensional sparse linear operators, analogous classical optimization algorithms exist in the variational Monte Carlo (VMC) literature, utilizing neural networks in place of quantum circuits to represent quantum states. In this paper we ask if classical stochastic optimization algorithms can be constructed paralleling other VQAs, focusing on the example of the variational quantum linear solver (VQLS). We find that such a construction can be applied to the VQLS, yielding a paradigm that could theoretically extend to other VQAs of similar form.