Streamlined Krylov construction and classification of ergodic Floquet systems

TL;DR

This paper introduces a faster Krylov-based method for analyzing periodically driven quantum systems, mapping their dynamics to a one-dimensional chain and classifying their chaos or integrability based on chain parameters.

Contribution

It generalizes Krylov construction to Floquet systems using orthogonal polynomials on the unit circle, enabling efficient simulation and new classification of quantum chaos.

Findings

Method outperforms existing approaches in speed.

Effective mapping to a one-dimensional Krylov chain.

Classification of Floquet systems based on chain parameters.

Abstract

We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a one-dimensional tight-binding Krylov chain, which is efficiently simulated on both classical and quantum computers. We also suggest a classification of chaotic and integrable Floquet systems based on the asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients). We illustrate this classification with random matrix ensembles, kicked top, and kicked Ising chain.