Entropic property of randomized QAOA circuits

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.