Quantum Simulation of Markov Chains

量化马尔可夫链耦合以生成Q样本

Quantized Markov Chain Couplings that Prepare Qsamples

该研究提出了一种通过量化马尔可夫链耦合方法生成量子样本的新技术，其收敛时间与耦合时间直接相关。

Quantum Markov chains associated with open quantum random walks

In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such as reducibility/irreducibility, recurrence/transience, accessibility, ergodicity, etc, of the underlying dynamics. Here we focus on the discussion of the reducibility and irreducibility of open quantum random walks via the corresponding quantum Markov chains. Particularly we show that the concept of reducibility/irreducibility of open quantum random walks i…

Zeon Algebra, Fock Space, and Markov Chains

Fock spaces over zeons are introduced. Trace identities and a noncommutative "integration-by-parts" formula are developed. As an application, we find a new criterion, without involving powers of the transition matrix, for a Markov chain to be ergodic.

On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three

In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two now quasi equivalent QMC for the given family of interaction operators $\{K_{<x,y>}\}$.