Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata

Abstract

We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the first-order-only covariance of the Dirac QW. We then introduce the Clock QW and the Clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for non-homogeneous Lorentz transforms, between non-inertial frames.

21 pages, 15 figures

References in corpus (2)

• Reversible quantum cellular automata
• Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics

Cited by in corpus (7)

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• Chirality from quantum walks without quantum coin
• Quantum State Transfer through Noisy Quantum Cellular Automata
• Reversibility in one-dimensional quantum cellular automata in the presence of noise
• Quantum Coherence in Noisy Cellular Automata