Quantum Entanglement in Dirac Dynamics via Continuous-Time Quantum Walks in a Quantum Circuit Framework

TL;DR

This paper introduces a continuous-time quantum walk model simulating one-dimensional Dirac dynamics, exploring how spacetime size influences quantum entanglement and relativistic effects like Zitterbewegung, with implications for quantum information and algorithms.

Contribution

It establishes a novel CTQW framework for Dirac dynamics that connects with Dirac Cellular Automata using Quantum Fourier Transform, revealing spacetime size impacts on entanglement and relativistic phenomena.

Findings

Time interval variations affect site transition ranges.

Position space size influences transition amplitude.

Spacetime size significantly impacts entanglement and Zitterbewegung.

Abstract

We propose a Continuous-Time Quantum Walks (CTQW) model for one-dimensional Dirac dynamics simulation with higher-order approximation. Our model bridges CTQW with a discrete-time model called Dirac Cellular Automata (DCA) via Quantum Fourier Transformation (QFT). From our continuous-time model, we demonstrate how varying time intervals and position space sizes affect both quantum entanglement between the internal space and external (position) space of the quantum state and the relativistic effect called Zitterbewegung. We find that the time interval changes the transition range for each site, and the position space sizes affect the value of transition amplitude. Therefore, it shows that the size of spacetime plays a crucial role in the observed quantum entanglement and relativistic phenomena in quantum computers. These results enhance the understanding of the interplay between internal and external spaces in Dirac dynamics through the insights of quantum information theory and enrich the application of the quantum walks-based algorithm.