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

TL;DR

The paper addresses the challenge of simulating real-time dynamics of lattice gauge theories by proposing a hybrid qubit–qumode architecture that assigns fermionic matter to qubits and gauge fields to continuous-variable qumodes. It develops two complementary compactness-enforcement strategies for the non-compact qumodes, a detailed mapping of the lattice Hamiltonian to a hardware-friendly gate set, and a CV extension of Quantum Imaginary Time Evolution to prepare ground states while preserving gauge invariance. The authors demonstrate the approach on a minimal single-plaquette model, deriving analytic spectra and validating them against exact diagonalization, and they show scalable resource estimates and polynomial gate complexity for larger lattices. The work provides a near-term pathway for Abelian lattice gauge theory simulations on hybrid quantum devices and lays groundwork for extending to non-Abelian gauges and real-time dynamics in more complex settings.

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.

Figures (13)

• Figure 1: One plaquette system for the pure $U(1)$ gauge theory before (left) and after (right) the selection of the dynamical degrees of freedom.
• Figure 2: Comparison of the perturbative analysis (PT) in Eq. \ref{['eq:grndE']} with exact diagonalization (ED). We show the ground state energy (left) and the energy gap (right) for different values of the mass $m_0$.
• Figure 3: Circuit implementing the non-Gaussian unitary $\mathcal{D}_\mu (s)$ given in Eq. \ref{['eq:ds']}.
• Figure 4: The quantum circuit that creates the state $\ket{\psi^{(Q)} }$, see Eq. \ref{['eq:82']}, from a given input two-qumode state $\ket{\Psi}$, where D is a displacement gate (see Table \ref{['table:1']}) and $\mathcal{D}$ is defined in Eq. \ref{['eq:ds']}.
• Figure 5: Path for the Jordan-Wigner transformation from fermions to spin degrees of freedom.