Suppressing unwanted fluctuations in QAOA and approximate quantum annealing

TL;DR

This paper introduces techniques using Pauli X measurements in QAOA to suppress unwanted fluctuations, improving success probabilities and robustness in quantum optimization, even at low circuit depths.

Contribution

The authors develop a method to mitigate fluctuation effects in QAOA by leveraging Pauli X measurements to adjust mixer angles, enhancing performance and compatibility with other innovations.

Findings

Mitigation techniques improve success probabilities in distorted energy landscapes.

Fluctuation effects are observable on IonQ Harmony QPU.

Methods are effective at low circuit depths (p=10-20).

Abstract

The quantum approximate optimisation algorithm (QAOA) was partially inspired by digitising quantum annealing. Based on this inspiration, we develop techniques to use the additional flexibility of a universal gate-model quantum computer to mitigate fluctuation effects which are known to distort the search space within quantum annealing and lead to false minima. We find that even just the added ability to take Pauli X measurements allows us to modify the mixer angles to counteract these effects by scaling mixer terms in a way proportional to the diagonal elements of the Fubini-Study metric. We find that mitigating these effects can lead to higher success probabilities in cases where the energy landscape is distorted and that we can use the same Pauli X measurements to target which variables are likely to be susceptible to strong fluctuations. The effects of the methods we introduce are relevant even at relatively low depth of $p=10-20$, suggesting that the techniques we are developing are likely to be relevant in the near term. Furthermore, since these methods rely on controlling a degree of freedom which is not typically modified in QAOA, our methods will be compatible with a wide range of other QAOA innovations. We further verify that these fluctuation effects can be observed on an IonQ Harmony QPU.