A relativistic discrete spacetime formulation of 3+1 QED

TL;DR

This paper introduces a relativistic quantum simulation scheme for 3+1 QED using a discrete spacetime quantum circuit that respects causality, gauge invariance, and incorporates electromagnetic dynamics, enabling digital quantum simulation of QED.

Contribution

It presents a novel quantum circuit framework for simulating 3+1 dimensional QED based on a discrete spacetime formulation, extending quantum walks to include gauge fields and electromagnetic dynamics.

Findings

Circuit respects strict causality with lightlike worldlines.

Simulation scheme is optimized for decoherence.

Framework extends to 3+1 dimensions with gauge invariance.

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.