Simulating quantum electrodynamics in 2+1 dimensions with qubits and qumodes

TL;DR

This paper presents a hybrid quantum simulation framework combining qubits and qumodes to model 2+1 dimensional quantum electrodynamics, enabling scalable and gauge-invariant simulations on near-term quantum devices.

Contribution

It introduces a novel hybrid qubit-qumode approach with constraint strategies for simulating lattice gauge theories with fermionic matter and gauge fields.

Findings

Successfully reproduces gauge-invariant dynamics.

Constructs experimentally feasible hybrid Hamiltonian.

Demonstrates ground-state preparation using continuous-variable QITE.

Abstract

We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions. In this approach, fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic modes whose canonical quadratures capture the electric and vector-potential components of the theory. To reconcile the non-compact phase space of the qumodes with the compact U(1) gauge symmetry, we introduce and compare two complementary constraint-enforcement strategies: (i) a squeezing-based projection that confines qumode states to the unit circle through an effective modification of the inner product, and (ii) a method that dynamically enforces compactness via a penalty Hamiltonian term. We construct the corresponding hybrid Hamiltonian, derive its decomposition into experimentally accessible qubit-qumode gates, and analyze its spectrum in the analytically tractable single-plaquette limit. The hybrid formulation reproduces the correct gauge-invariant dynamics and provides a scalable route toward simulating Abelian lattice gauge theories coupled to fermionic matter on near-term hybrid quantum architectures. Ground-state preparation and convergence are demonstrated using a continuous-variable extension of the Quantum Imaginary Time Evolution (QITE) algorithm, establishing a general framework for hybrid discrete-continuous quantum simulations of lattice gauge theories.