Optimal Hamiltonian simulation for time-periodic systems

The implementation of time-evolution operators U(t), called Hamiltonian simulation, is one the most promising usage quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization stretchy="false">)=e−iHt, with achieving optimal computational resource both in time xmlns:mml="http://www.w3.org/1998/Math/MathML">t and an allowable error xmlns:mml="http://www.w3.org/1998/Math/MathML">ε. In contrast, those for time-dependent systems require larger cost due to difficulty handling time-dependency. this paper, we establish optimal/nearly-optimal simulation generic time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped auxiliary states labeling Fourier indices, develop way certainly obtain target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, query complexity, which measures implementing time-evolution, nearly-optimal dependency respectively inverse xmlns:mml="http://www.w3.org/1998/Math/MathML">ε, becomes sufficiently close that qubitization. Thus, our protocol tells us that, among systems, time-periodic provides class accessible efficiently despite existence As also provide applications nonequilibrium phenomena adiabatic preparation, results will shed light condensed matter physics chemistry, tasks yielding time-dependency computation.