Scalable quantum computation of Quantum Electrodynamics beyond one spatial dimension

TL;DR

This paper introduces a scalable quantum algorithm for simulating Quantum Electrodynamics in higher dimensions, maintaining gauge invariance and demonstrating feasibility on current quantum hardware for large-scale dynamics.

Contribution

A novel, scalable quantum algorithm for higher-dimensional QED that preserves gauge invariance and is suitable for implementation on near-term quantum computers.

Findings

Gauge invariance is maintained throughout discretisation and digitisation.

Benchmarking shows effective quantum error mitigation techniques.

Implementation on current hardware demonstrates feasibility for 2+1 and 3+1 dimensions.

Abstract

In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian quantisation, bosonic fields introduce the additional challenge of an infinite-dimensional Hilbert space. We present a scalable quantum algorithm for Quantum Electrodynamics (QED), an Abelian gauge field theory in higher than one spatial dimensions, designed to address this limit while preserving gauge invariance. In our formulation, Gauss's law is automatically satisfied when the implementation remains fully gauge invariant. We demonstrate how gauge invariance is maintained throughout the lattice discretisation, digitisation, and qubitisation procedures, and identify the most efficient representation for extending to large Hilbert space dimensions. Within this framework, we benchmark several quantum error mitigation techniques and find the calibration method to perform most effectively. The approach scales naturally to larger lattices, and we implement and test the 2+1 and 3+1 dimensional setups on current quantum hardware. Our results indicate that next-generation quantum platforms could enable reliable, fully quantum simulations of large-scale QED dynamics.