Stroboscopic Hamiltonian engineering in the low-frequency regime with a one-dimensional quantum processor

Abstract

We propose a scheme to perform stroboscopic Hamiltonian engineering in the low frequency regime using a quantum system with one-dimensional nearest-neighbor coupling that are commonly available in the NISQ era. Computational problems are encoded in the effective Hamiltonian of the quantum systems under the effect of external driving. Our approach is nonperturbative and it does not rely on high-frequency expansions, which are a common tool in Floquet engineering. In our paper, the effective Hamiltonian that we want to engineer is fully tailored through designing the periodic driving. We illustrate how this quantum computation proceeds with two examples, an instance from the 3-SAT problem and the LiH molecule quantum chemistry simulation. In the case of the 3-SAT Hamiltonian, we show that by starting from the ground state of the trivial Hamiltonian, the quantum systems go through an adiabatic process in the stroboscopic picture towards the target Hamiltonian of the problem.