Efficient simulation of non-Markovian system-environment interaction

Simulation of Non-Markovian Systems

A generalized semi-Markov process provides a stochastic process model for a discrete-event simulation. This representation is particularly useful for non-Markovian systems where it is nontrivial to obtain recurrence properties of the underlying stochastic processes. We develop ‘geometric trials” arguments which can be used to obtain results on recurrence and regeneration in this setting. Such p...

Efficient simulation of sparse Markovian quantum dynamics

Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lind...

Entropy production in a non-Markovian environment.

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian appr...

Perfect simulation and non-monotone Markovian systems

Perfect simulation, or coupling from the past, is an efficient technique for sampling the steady state of monotone discrete time Markov chains. Indeed, one only needs to consider two trajectories corresponding to minimal and maximal state in the system. We show here that even for non-monotone systems one only needs to compute two trajectories: an infimum and supremum envelope. Since the sequenc...

Efficient Transient Simulation of Failure/Repair Markovian Models