Effects of Different Noise Environments on the Coherence Time of Open Quantum Systems

The use of Stochastic Schrödinger Equations (SSE) to describe open quantum systems is a well-known class of methods, that can be used as an unravelling scheme of associated Quantum Master Equations and as a starting point to derive new ones. From the perspective of simulating quantum systems in Quantum Computers (QC), one can exploit stochastic averages to implement intrinsically contractive mappings into unitary-gates bases QC since each trajectory is a unitary evolution of the system [1,2] and harnesses the repeated noisy measures in lieu of classical parallelization. Recent studies have shown the ability to engineer environmental effects, in particular concerning non-Markovian environments [3,4]. Such noises can be detrimental to or enhance the coherence time and the transport properties of the system. Here, we present a theoretical description of the differences between using a stochastic process and its derived noise as sources of fluctuations in the stochastic formulation of the dynamics of an open quantum system, and their associated QME.

The starting point is the model presented in [6], leading to non-Markovian quantum evolution in small model systems. Showing the different interpretations, we remark the differences with respect to the usual memoryless approximations and the effects on initial coherence time and stationary distributions.

[1] Lloyd, S. (1996), Science, 273(5278)

[2] Hu, Z., Xia, R., Kais, S. (2020), Scientific Reports, 10(1)

[3] Cialdi, S., Benedetti, C., Tamascelli, D., Olivares, S., Paris, M. G. A., Vacchini, B. (2019), Physical Review A, 100(5)

[4] Carmele, A., Parkins, S., Knorr, A. (2020), Physical Review A, 102(3)

[6] Barchielli, A., Pellegrini, C., Petruccione, F. (2010), Europhysics Letters, 91(2)