Floquet ADAPT-VQE: Quantum Algorithm to Simulate Non-Equilibrium Physics in a Periodically Driven System

We propose a hybrid quantum-classical algorithm, Floquet ADAPT-VQE, to simulate the non-equilibrium physics of periodically driven quantum systems. We utilize the Floquet-Hilbert space to transform the Hamiltonian to be time-independent and present methods to decompose it into Pauli strings for arbitrary qubit truncation. We introduce a suitable initial state ansatz, which leads to better convergence with fewer ADAPT iterations. Moreover, we present a framework to calculate the time-dependent expectation value of an observable in a Floquet state on a quantum computer. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field.