Convergence of Digitized-Counterdiabatic QAOA: circuit depth versus free parameters

TL;DR

This paper investigates Digitized-Counterdiabatic QAOA for solving MaxCut problems, showing higher-order corrections improve convergence speed but do not increase the number of free parameters needed.

Contribution

It critically analyzes the impact of higher-order CD corrections on QAOA convergence and parameter complexity for MaxCut problems.

Findings

Higher-order CD corrections enable faster convergence.

The total number of free parameters remains constant across variants.

Complexity of the variational cost function increases with correction order.

Abstract

Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed.