Action Principles for Quantum Automata and Lorentz Invariance of Discrete Time Quantum Walks
arXiv:1806.02313 · doi:10.1016/j.aop.2019.03.005
Abstract
A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space-time coordinates are introduced as new variables of the action and their equations of motion enforce energy and momentum conservation. This guarantees that the proposed action can be used to build future, DTQW-based self-consistent models of spinors interacting with gauge fields. A discrete stress-energy tensor for the DTQW is also obtained by functional differentiation of the action with respect to the gradients of the coordinates viewed as functions of the discrete grid points. The manifest covariance of the formulation highlights the special role played by the grid reference frame in the DTQW dynamics. The main discussion is complemented by three appendices.
14 pages
References in corpus (7)
- Quantum Walk in Position Space with Single Optically Trapped Atoms
- Realization of quantum walks with negligible decoherence in waveguide lattices
- Quantum Communication through Spin Chain Dynamics: an Introductory Overview
- Quantum walks and non-Abelian discrete gauge theory
- Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
- Quantum walks and gravitational waves
- Quantum Walks, Weyl equation and the Lorentz group
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