Quantum mean value approximator for hard integer value problems

TL;DR

This paper introduces a quantum mean value approximator that enhances the efficiency of solving hard integer value problems by using approximation techniques combined with classical sampling, reducing quantum gate requirements.

Contribution

It proposes a novel quantum approximation method for expectation values that improves optimization efficiency for integer problems like SVP.

Findings

Approximate quantum expectation evaluation reduces quantum gate count.

Combining classical sampling with quantum algorithms enhances problem-solving efficiency.

Method is applicable to problems like the shortest vector problem (SVP).

Abstract

Evaluating the expectation of a quantum circuit is a classically difficult problem known as the quantum mean value problem (QMV). It is used to optimize the quantum approximate optimization algorithm and other variational quantum eigensolvers. We show that such an optimization can be improved substantially by using an approximation rather than the exact expectation. Together with efficient classical sampling algorithms, a quantum algorithm with minimal gate count can thus improve the efficiency of general integer-value problems, such as the shortest vector problem (SVP) investigated in this work.