Efficient simulation of open quantum systems coupled to a fermionic bath

We present and analyze the fermionic time-evolving density matrix using orthogonal polynomials algorithm (fTEDOPA), which enables the numerically exact simulation of open quantum systems coupled to a fermionic environment. The method allows for simulating the time evolution of open quantum systems with arbitrary spectral densities at zero or finite temperatures with controllable and certified error. We demonstrate the efficacy of the method towards the simulation of quintessential fermionic open quantum systems including the resonant-level model and quantum dot coupled to an impurity and towards simulating hitherto intractable problems in quantum transport. Furthermore, we demonstrate significant efficiency gains in the computational costs by performing simulations in the Heisenberg picture. Finally, we compare different approaches for simulating finite-temperature situations and provide practical guidelines in order to identify the best strategy.