Dynamical kickback and non commuting impurities in a spin chain

TL;DR

This paper investigates the dynamics of a two-walker continuous time quantum walk on a graph, focusing on interactions with noncommuting operators and analyzing its behavior using Markov process concepts.

Contribution

It introduces a framework for analyzing two interacting quantum walkers with noncommuting primitives, extending the understanding of quantum walk dynamics.

Findings

Interaction with noncommuting primitives affects walk behavior

Trajectory notions help understand quantum walk dynamics

Sample path analysis provides new insights into quantum processes

Abstract

In an interacting continuous time quantum walk, while the walker (the cursor) is moving on a graph, computational primitives (unitary operators associated with the edges) are applied to ancillary qubits (the register). The model with one walker was originally proposed by R. Feynman, who thus anticipated many features of the Continuous Time Quantum Walk (CTWQ) computing paradigm. In this note we examine the behaviour of an interacting CTQW with two walkers and examine the interaction of the walkers with noncommuting primitives. We endow such a walk with a notion of trajectory, in the sense of sample path of an associated Markov process, in order to use such notions as sojourn time and first passage time as heuristic tools for gaining intuition about its behaviour.