Quantum Simulation of Markov Chains

TL;DR

This paper explores how quantum systems can intrinsically simulate stochastic processes, specifically proposing two methods to simulate Markov Chains through quantum measurements.

Contribution

It introduces two novel quantum measurement-based methods for simulating Markov Chains, advancing quantum simulation techniques for stochastic processes.

Findings

Proposed two quantum measurement schemes for Markov Chain simulation

Demonstrated the feasibility of quantum-based stochastic process simulation

Lays groundwork for quantum algorithms in stochastic modeling

Abstract

The possibility of simulating a stochastic process by the intrinsic randomness of quantum system is investigated. Two simulations of Markov Chains by the measurements of quantum systems are proposed.