Relating the multi-angle quantum approximate optimization algorithm and continuous-time quantum walks on dynamic graphs

Abstract

In this work, we show that ma-QAOA is equivalent to a restriction of continuous-time quantum walks on dynamic graphs. We then show it is universal for computation by finding the appropriate $B$ and $C$ operators and angles that implement the universal gate set consisting of the Hadamard, $\pi/8$ and Controlled-Not gates in the ma-QAOA framework. This result begins to bridge the gap between the continuous-time quantum walk model and gate model of quantum computation.