Strategies for Overcoming Gradient Troughs in the ADAPT-VQE Algorithm

TL;DR

This paper addresses the gradient trough problem in ADAPT-VQE, proposing heuristics and protocols to detect and escape these troughs, resulting in faster convergence and reduced measurement costs while maintaining low circuit complexity.

Contribution

It introduces novel heuristics and operator insertion protocols to mitigate gradient troughs in ADAPT-VQE, enhancing convergence speed and efficiency.

Findings

Gradient troughs are more likely with repeated operator insertions at the same locations.

New insertion protocols effectively escape gradient troughs and improve convergence.

The proposed methods reduce measurement costs without increasing circuit depth.

Abstract

The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.