Predictive modelling of quantum stochastic processes

Abstract

In this paper, predictive modelling involving non-orthogonal emissions upon state transitions of Hidden Markov Model is studied. Mixed-State Presentation (MSP) is used to unifilarise the process in order to keep track of the state of knowledge over underlying machine states after each measurement. It is then incorporated into a work extraction protocol for the formulation of a predictive work extraction protocol. The MSP-enhanced prediction as well as the work extraction protocol are then applied to two energy-degenerate processes, the perturbed coin and golden mean process. When limited to the task of identifying the most likely next observation, it is found that the MSP-enhanced predictive protocol does not significantly improve pattern prediction. The MSP-enhanced predictive work extraction protocol, however, performs significantly better than the non-MSP protocols, owing to its ability to precisely track the evolution of state of knowledge over time.