Quantum computing Floquet energy spectra

TL;DR

This paper introduces two quantum algorithms for efficiently computing Floquet energy spectra in periodically driven quantum systems, overcoming classical limitations especially in strongly correlated regimes.

Contribution

The paper presents novel quantum algorithms that leverage parametrized quantum circuits to determine Floquet modes and spectra, addressing classical computational challenges.

Findings

Algorithms successfully benchmarked on quantum hardware.

Effective in low-frequency and strongly correlated regimes.

Show potential for near-term quantum applications.

Abstract

Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing ground state properties or single time-dependent trajectories, and scales exponentially with the Hilbert space dimension. Especially for strongly correlated systems in the low frequency limit, classical approaches based on truncation break down. Here, we present two quantum algorithms to determine effective Floquet modes and energy spectra. We combine the defining properties of Floquet modes in time and frequency domains with the expressiveness of parametrized quantum circuits to overcome the limitations of classical approaches. We benchmark our algorithms and provide an analysis of the key properties relevant for near-term quantum hardware.