Neighborhood-History Quantum Walk

TL;DR

This paper introduces the neighborhood-history quantum walk (NHQW), a generalized quantum walk model that incorporates neighborhood-dependent memory effects, enabling richer dynamics and potential applications in quantum computing and physics modeling.

Contribution

It extends existing history-dependent quantum walks by incorporating neighborhood interactions, realized as a single-particle sector of quantum cellular automata.

Findings

Constructed a one-dimensional NHQW with simple neighborhood.

Demonstrated NHQW as a single-particle sector of QCA.

Potential for richer walk strategies and physics modeling.

Abstract

History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhood-history quantum walk (NHQW), in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle's position are interdependent. To demonstrate it, we construct an NHQW on a one-dimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as single-particle sectors of quantum lattice gas automata (QLGA). In contrast, the NHQW constructed in this paper is realized as a single-particle sector of the more general quantum cellular automaton (QCA). The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.