Efficient Quantum Computation of Floquet Hamiltonians

The Floquet formalism describes the control over quantum systems using external periodic fields. With recent advances in ultrafast spectroscopy of solid-state systems, Floquet engineering, that is, a targeted design of quantum systems driven by laser pulse, has led to an increasing interest in computational methods that can simulate light-matter interactions. Although the perturbative regime, in which the fundamental driving frequency is much larger than the energy bandwidth of the quantum system, shows interesting phenomena, it is the non-perturbative regime that presents the most exciting opportunity to study the interplay with strong correlations and which remains largely unexplored. Here we describe hybrid quantum algorithms that make use of quantum computers to tackle this problem. The required quantum resources are within reach for current day NISQ devices and allow the efficient computation of Floquet Hamiltonians. We demonstrate applications of these algorithms and discuss their performance for small scale driven quantum systems.