Problem-Size Independent Angles for a Grover-Driven Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces a method to analytically compute expectation values in a Grover-driven QAOA that are independent of problem size, aiding in understanding and predicting QAOA performance for large combinatorial problems.

Contribution

It presents a novel analytical approach to calculate QAOA expectations based on the probability density function, independent of problem size, especially for the number partitioning problem.

Findings

Expectation calculations are size-independent when using the probability density function.

The method provides insights into QAOA performance and angle predictability for large problems.

Applicable to problems like number partitioning, enhancing scalability understanding.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either costly outer-loop optimization procedures and repeated calls to a quantum computer or, alternatively, via analytical means. In this work we demonstrate that if one knows the probability density function describing how the objective function of a problem is distributed, that the calculation of the expectation of such a problem Hamiltonian under a Grover-driven, QAOA-prepared state can be performed independently of system size. Such calculations can help deliver insights into the performance of and predictability of angles in QAOA in the limit of large problem sizes, in particular, for the number partitioning problem.