Weighted Feedback-Based Quantum Algorithm for Excited States Calculation

TL;DR

This paper introduces a novel weighted feedback-based quantum algorithm inspired by Lyapunov control to efficiently calculate excited states in quantum systems, extending previous ground state algorithms.

Contribution

The paper proposes a new weighted feedback quantum algorithm for excited states, inspired by the weighted subspace-search variational quantum eigensolver, with demonstrated effectiveness in quantum chemistry applications.

Findings

Successfully prepares specific excited states through weight and feedback design.

Effective in quantum chemistry simulations for excited state calculation.

Extends feedback-based algorithms from ground to excited states.

Abstract

Drawing inspiration from the Lyapunov control technique for quantum systems, feedback-based quantum algorithms have been proposed for calculating the ground states of Hamiltonians. In this work, we consider extending these algorithms to tackle calculating excited states. Inspired by the weighted subspace-search variational quantum eigensolver algorithm, we propose a novel weighted feedback-based quantum algorithm for excited state calculation. We show that depending on how we design the weights and the feedback law, we can prepare the $p$th excited state or lowest energy states up to the $p$th excited state. Through an application in quantum chemistry, we show the effectiveness of the proposed algorithm, evaluating its efficacy via numerical simulations.