Quantum Walks via Quantum Cellular Automata

TL;DR

This paper introduces a partitioned quantum cellular automata model that can simulate quantum walks efficiently, leveraging local qubit interactions, which may enhance experimental realizations of quantum algorithms.

Contribution

It presents a novel partitioned model of quantum cellular automata capable of simulating quantum walks with equivalent resource efficiency.

Findings

Quantum cellular automata can simulate quantum walks.

The model uses local qubit interactions.

Potential for improved experimental implementation.

Abstract

Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with the same amount of resources (in terms of effective Hilbert space dimension), various models of quantum walks. All the algorithms developed within quantum walk models are thus directly inherited by the quantum cellular automata. The latter, however, has its structure based on local interactions between qubits, and as such it can be more suitable for present (and future) experimental implementations.