Monte Carlo simulations in open quantum systems.

Jyrki Piilo, Sabrina Maniscalco, Kalle‐Antti Suominen

Various Monte Carlo methods allow the simulation of the dynamics of open quantum systems. We highlight the central features a commonly used method for Markovian systems, i.e., Monte Carlo Wave Function method and another one used for non-Markovian systems, i.e., the doubled Hilbert space method. One of the open problems in the field has been the lack of the existence of Monte Carlo method with quantum jumps for non-Markovian systems. We characterize the key problems that should be solved in this context and give indications for the way towards the development of quantum jump method without auxiliary states for non-Markovian systems.

H. DeRaedt, Ad Lagendijk, Pedro de Vries

Matthias Troyer, Philipp Werner, Adolfo Avella +1 more

Jyrki Piilo, Sabrina Maniscalco, A. Messina +1 more

We demonstrate a scaling method for Monte Carlo wave-function simulations used to study the dynamics of non-Markovian open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo simulations. In the optimal case, the scaling method can be used, within the weak coupling approximation, to reduce the size of the generated Monte Carlo ensemble by several orders of magnitude. Thus, the developed method allows faster simulations and makes it possible to solve the dynamics of the certain class of non-Markovian systems whose simulation would be otherwise too tedious because of the requirement for large computational resources.

Ryan Sweke

Alexander Sturges, Hugo Smith, Matteo Marcuzzi

Inspired by previous works on epidemic-like processes in open quantum systems, we derive an elementary quantum epidemic model that is simple enough to be studied via Quantum Jump Monte Carlo simulations at reasonably large system sizes. We show how some weak symmetries of the Lindblad equation allow us to map the dynamics onto a classical Kinetic Monte Carlo; this simplified, effective dynamics can be described via local stochastic jumps coupled with a local deterministic component. Simulations are then used to reconstruct a phase diagram which displays stationary features completely equivalent to those of completely classical epidemic processes, but richer dynamics with multiple, recurrent waves of infection.