Neural-network states for the classical simulation of quantum computing

TL;DR

This paper introduces a neural-network based classical simulation method for quantum circuits, capable of handling highly-entangled states and surpassing current brute-force techniques in system size and depth.

Contribution

It develops a novel neural-network approach for simulating general quantum circuits, including rules for applying certain gates and a learning scheme for others, advancing classical simulation capabilities.

Findings

Successfully simulated large entangled states and deep circuits

Achieved accuracy comparable to noisy quantum hardware

Outperformed existing brute-force simulation methods

Abstract

Simulating quantum algorithms with classical resources generally requires exponential resources. However, heuristic classical approaches are often very efficient in approximately simulating special circuit structures, for example with limited entanglement, or based on one-dimensional geometries. Here we introduce a classical approach to the simulation of general quantum circuits based on neural-network quantum states (NQS) representations. Considering a set of universal quantum gates, we derive rules for exactly applying single-qubit and two-qubit Z rotations to NQS, whereas we provide a learning scheme to approximate the action of Hadamard gates. Results are shown for the Hadamard and Fourier transform of entangled initial states for systems sizes and total circuit depths exceeding what can be currently simulated with state-of-the-art brute-force techniques. The overall accuracy obtained by the neural-network states based on Restricted Boltzmann machines is satisfactory, and offers a classical route to simulating highly-entangled circuits. In the test cases considered, we find that our classical simulations are comparable to quantum simulations affected by an incoherent noise level in the hardware of about $10^{-3}$ per gate.