Dirac Quantum Cellular Automaton from Split-step Quantum Walk

TL;DR

This paper demonstrates how a split-step quantum walk can be used to realize the Dirac Cellular Automaton, connecting quantum walks, cellular automata, and quantum field theory for improved quantum simulation.

Contribution

It introduces a method to derive the Dirac Cellular Automaton from a split-step quantum walk, enabling experimental implementation and better understanding of quantum field simulation.

Findings

Recovered DCA with fine oscillations in position space

Linked DH, DCA, and QW models coherently

Showed tunability of parameters affects Zitterbewegung and entanglement

Abstract

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.