Systematic time-coarse graining for driven quantum systems

Fidelity requirements on quantum devices necessitate faster and stronger drives, pushing into regimes where the rotating-wave approximation (RWA) is no longer adequate. In those regimes, high-frequency processes generated by counter-rotating terms can significantly modify the long-term dynamics of a quantum system. Exploring these regimes is difficult even numerically, since system dynamics exhibiting disparate time-scales are often stiff and unstable. In this work, we present a systematic time-coarse graining (STCG) framework that addresses these issues by directly providing a Quantum Master Equation (QME) for the time-coarse grained density matrix of a driven quantum system. STCG allows the perturbative calculation of effective unitary and non-unitary generators describing the relevant slow dynamics at any given order of truncation beyond the RWA, and is accompanied by a complete software framework written in Julia, QuantumGraining.jl, for efficient implementation. We present three case studies examining the numerical stability, convergence and the interpretive utility of the coarse-grained QME at high orders. These examples illustrate two key results: observables measured by finite bandwidth apparatus can differ significantly from exact dynamics due to the effect of the counter-rotating terms, and that this can be captured by solving the STCG QME with basic low-order ODE solvers.