History Dependent Quantum Random Walks as Quantum Lattice Gas Automata

TL;DR

This paper demonstrates that various history-dependent quantum random walks can be understood as one-particle sectors of quantum lattice gas automata, providing a unified geometric framework for these models and their role in studying quantum-to-classical transitions.

Contribution

It introduces a unifying framework linking history-dependent quantum walks to quantum lattice gas automata, revealing geometric degrees of freedom for history storage.

Findings

History-dependent QRWs are identified as sectors of QLGA.

Provides a geometric interpretation for history storage in quantum walks.

Facilitates analysis of quantum-to-classical transition mechanisms.

Abstract

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.