A practical, unitary simulator for non-Markovian complex processes
Stochastic processes are as ubiquitous as they are notorious for being difficult to simulate and predict. In this letter we propose a unitary quantum simulator for discrete-time, discrete-valued, stationary stochastic processes
which requires less memory than its classical analogues throughout the simulation. It extends previous works in two important aspects. First, the proposed quantum simulator forgoes a trade-off between small memory
requirement and exponentially increasing Hilbert space dimension which in the case of previous models only reached optimal memory savings in the limit of an infinite-dimensional Hilbert space. Instead, the quantum simulator’s memory requirement equals the best previous models but only requires a (small) finite-dimensional Hilbert space. Second, since the proposed simulator operates unitarily throughout, information loss inherent to previous measure-and-prepare schemes is avoided. Moreover, its unitary operation directly opens the possibility for experimental implementations. The results are illustrated for an example process.