Yoshihiko Abe

Time-dependent Hamiltonian simulation is one of the most important applications of quantum computing, but existing approaches based on Dyson-series or Magnus-expansion constructions can require complicated circuits and large hardware overhead. In this work, we propose a cost-aware variant of continuous-qDrift that incorporates implementation cost into the sampling probabilities through importance sampling. We prove that, under the same diamond-norm error requirement as standard continuous-qDrift, the expected total cost of the cost-weighted algorithm is no larger than that of the original method. To assess practical performance, we numerically simulate a Floquet-driven Rydberg system with multi-body interaction terms and use CNOT counts as the cost metric. The results show that the proposed method achieves a similar error distribution to standard continuous-qDrift while significantly reducing total cost.