  Noise in quantum devices is generally considered detrimental to computational
accuracy. However, the recent proposal of noise-assisted simulation has
demonstrated that noise can be an asset in digital quantum simulations of open
systems on Noisy Intermediate-Scale Quantum (NISQ) devices. In this context, we
introduce an optimized decoherence rate control scheme that can significantly
reduce computational requirements by multiple orders of magnitude, in
comparison to the original noise-assisted simulation. We further extend this
approach to encompass Lindblad equations with time-dependent coefficients,
using only quantum error characterization and mitigation techniques. This
extension allows for the perturbative simulation of non-Markovian dynamics on
NISQ devices, eliminating the need for ancilla qubits or mid-circuit
measurements. Our contributions are validated through numerical experiments on
an emulated IBMQ device. Overall, our work offers valuable optimizations that
bring current quantum processors closer to effectively simulating realistic
open systems.
