Gate-based counterdiabatic driving with complexity guarantees

TL;DR

This paper introduces a fully gate-based quantum algorithm for counterdiabatic driving that provides rigorous complexity guarantees and improves efficiency based on the spectral gap.

Contribution

It presents a non-heuristic, regularized approach to counterdiabatic driving with proven quantum gate complexity bounds.

Findings

Worst-case gate complexity scales as  O(^{-(3 + o(1))} ^{-(1 + o(1))})

Gap dependence can be improved to quadratic in some cases

Provides a rigorous complexity upper bound for quantum counterdiabatic algorithms

Abstract

We propose a general, fully gate-based quantum algorithm for counterdiabatic driving. The algorithm does not depend on heuristics as in previous variational methods, and exploits regularisation of the adiabatic gauge potential to suppress only the transitions from the eigenstate of interest. This allows for a rigorous quantum gate complexity upper bound in terms of the minimum gap $\Delta$ around this eigenstate. We find that, in the worst case, the algorithm requires at most $\tilde O(\Delta^{-(3 + o(1))} \epsilon^{-(1 + o(1))})$ quantum gates to achieve a target state fidelity of at least $1 - \epsilon^2$, where $\Delta$ is the minimum spectral gap. In certain cases, the gap dependence can be improved to quadratic.