Hidden Quantum Markov Models and Open Quantum Systems with Instantaneous Feedback

TL;DR

This paper explores Hidden Quantum Markov Models (HQMMs), demonstrating their ability to generate complex stochastic sequences and highlighting their application in open quantum systems with instantaneous feedback, advancing quantum simulation techniques.

Contribution

The paper introduces the connection between HQMMs and open quantum systems with feedback, revealing a new application of quantum feedback control in modeling stochastic processes.

Findings

HQMMs can produce more complex sequences than classical models.

Open quantum systems with feedback are examples of HQMMs.

Quantum feedback control has novel applications in stochastic modeling.

Abstract

Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines --- so-called Hidden Quantum Markov Models (HQMMs). Using the properties of Quantum Physics, HQMMs are able to generate more complex random output sequences than their classical counterparts, even when using the same number of internal states. They are therefore expected to find applications as quantum simulators of stochastic processes. Here, we emphasise that open quantum systems with instantaneous feedback are examples of HQMMs, thereby identifying a novel application of quantum feedback control.