Quantum restricted Boltzmann machine universal for quantum computation

TL;DR

This paper introduces a quantum restricted Boltzmann machine (QRBM) based on a 2-local Hamiltonian, demonstrating its universality for quantum computation and practical implementation on NISQ devices to compute complex quantum states.

Contribution

It designs a universal single-layer quantum neural network (QRBM) based on a 2-local Hamiltonian, capable of quantum computation and efficient on NISQ hardware.

Findings

Proves QRBM's universality for quantum tasks

Successfully computes ground and thermal states of molecules on quantum chip

Demonstrates acceptable error rates in practical quantum state computations

Abstract

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the many-body wave functions with high complexity. Quantum neural network provides a powerful tool to represent the large-scale wave function, which has aroused widespread concern in the quantum superiority era. A significant open problem is what exactly the representational power boundary of the single-layer quantum neural network is. In this paper, we design a 2-local Hamiltonian and then give a kind of Quantum Restricted Boltzmann Machine (QRBM, i.e. single-layer quantum neural network) based on it. The proposed QRBM has the following two salient features. (1) It is proved universal for implementing quantum computation tasks. (2) It can be efficiently implemented on the Noisy Intermediate-Scale Quantum (NISQ) devices. We successfully utilize the proposed QRBM to compute the wave functions for the notable cases of physical interest including the ground state as well as the Gibbs state (thermal state) of molecules on the superconducting quantum chip. The experimental results illustrate the proposed QRBM can compute the above wave functions with an acceptable error.