Entropic property of randomized QAOA circuits

TL;DR

This paper investigates the entropic properties of randomized QAOA circuits, showing they produce higher entropy distributions and have a greater likelihood of reaching global optima compared to uniform random sampling.

Contribution

It provides analytical and numerical analysis of QAOA with random angles, revealing enhanced entropy and success probabilities over traditional sampling methods.

Findings

Randomized QAOA circuits yield higher entropy in energy distributions.

Sampling with random angles increases the probability of finding global optima.

Analytical equations describe probabilities for unweighted Max-Cut on connected graphs.

Abstract

Quantum approximate optimization algorithm (QAOA) aims to solve discrete optimization problems by sampling bitstrings using a parameterized quantum circuit. The circuit parameters (angles) are optimized in the way that minimizes the cost Hamiltonian expectation value. Recently, general statistical properties of QAOA output probability distributions have begun to be studied. In contrast to the conventional approach, we analyse QAOA circuits with random angles. We provide analytical equations for probabilities and the numerical evidence that for unweighted Max-Cut problems on connected graphs such sampling always gives higher entropy of energy distribution than uniform random sampling of bitstrings. We also analyse the probability to obtain the global optima, which appears to be higher on average than for random sampling.