Strategies for optimizing double-bracket quantum algorithms

TL;DR

This paper introduces optimization strategies for double-bracket quantum algorithms, improving their efficiency in approximating eigenstates by selecting optimal evolutions and parameters, with practical implementations for current quantum hardware.

Contribution

It proposes novel methods to optimize double-bracket quantum algorithms, including generator and duration selection, and offers practical gate-based parametrizations suitable for current quantum devices.

Findings

Optimized evolution parameters improve eigenstate approximation.

Adaptive and variational approaches enhance convergence.

Gate-based parametrizations facilitate implementation on existing hardware.

Abstract

Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal evolutions. Here, we present strategies to optimize the choice of the double-bracket evolutions to enhance the diagonalization efficiency. This can be done by finding optimal generators and durations of the evolutions. We present numerical results regarding the preparation of double-bracket iterations, both in ideal cases where the algorithm's setup provides analytical convergence guarantees and in more heuristic cases, where we use an adaptive and variational approach to optimize the generators of the evolutions. As an example, we discuss the efficacy of these optimization strategies when considering a spin-chain Hamiltonian as the target. To propose algorithms that can be executed starting today, fully aware of the limitations of the quantum technologies at our disposal, we finally present a selection of diagonal evolution parametrizations that can be directly compiled into CNOTs and single-qubit rotation gates. We discuss the advantages and limitations of this compilation and propose a way to take advantage of this approach when used in synergy with other existing methods.