A relativistic discrete spacetime formulation of 3+1 QED

Abstract

This work provides a relativistic, digital quantum simulation scheme for both $2+1$ and $3+1$ dimensional quantum electrodynamics (QED), based on a discrete spacetime formulation of theory. It takes the form of a quantum circuit, infinitely repeating across space and time, parametrised by the discretization step ${\Delta }_t={\Delta }_x$. Strict causality at each step is ensured as circuit wires coincide with the lightlike worldlines of QED; simulation time under decoherence is optimized. The construction replays the logic that leads to the QED Lagrangian. Namely, it starts from the Dirac quantum walk, well-known to converge towards free relativistic fermions. It then extends the quantum walk into a multi-particle sector quantum cellular automata in a way which respects the fermionic anti-commutation relations and the discrete gauge invariance symmetry. Both requirements can only be achieved at cost of introducing the gauge field. Lastly the gauge field is given its own electromagnetic dynamics, which can be formulated as a quantum walk at each plaquette.

37 pages, 8 figures. V2: typos corrected, precisions added. V3: changed license, added ref doi. v4: 3D transport corrected

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• A massless interacting Fermionic Cellular Automaton exhibiting bound states
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• A perturbative approach to the solution of the Thirring quantum cellular automaton
• The Dirac Vacuum in Discrete Spacetime
• Renormalisation of Quantum Cellular Automata
• Bounds on QCA Lattice Spacing from Data on Lorentz Violation
• Classification of qubit cellular automata on hypercubic lattices
• Recurrence Time for Finite Quantum Systems
• Fermion Doubling in Dirac Quantum Walks