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.
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.
A bstract 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.
Classical tensor network and hybrid quantum-classical algorithms are promising candidates for the investigation of real-time properties of lattice gauge theories. We develop here a novel framework which enforces gauge symmetry via a quantum-link virtual rishon representation applied at intermediate steps. Crucially, the gauge and matter degrees of freedom are dynamical variables encoded in terms of qubits, enabling analysis of gauge theories in d+1 spacetime dimensions. We benchmark this framework in a U(1) gauge theory with and without matter fields. For d=1, the multi-flavor Schwinger model with 1≤Nf≤3 flavors is analyzed for arbitrary boundary conditions and nonzero topological angle, capturing signatures of the underlying Wess-Zumino-Witten conformal field theory. For d=2, we extract the confining string tension in close agreement with continuum expectations. These results establish the virtual rishon framework as a scalable and robust approach for the simulation of lattice gauge theories using both classical tensor networks as well as near-term quantum hardware.
This thesis investigates advances in quantum simulation methods for lattice gauge theories, with a focus on (2+1)-dimensional quantum electrodynamics (QED), which shares important features with (3+1)-dimensional quantum chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first project investigates the ongoing coupling in a compact pure U(1) gauge theory using a step-scaling function approach. A quantum variational method allows calculations over a wide range of couplings. Plaquette expectation value results are compared with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can potentially be extended to the study of QED, which also includes fermionic matter. The second project investigates the static potential between two charges, analyzing the Coulomb, confining, and string-breaking regimes. It involves the development of a tailored variational approach that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device agree well with classical simulations, validating the method. Furthermore, this work evaluates superconducting quantum devices, noting issues with noise but also demonstrating improvements in hardware and potential through error limitation. Overall, this work underscores the feasibility of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computers. This thesis explores advancements in quantum simulation methods for lattice gauge theories, focusing on (2+1)-dimensional Quantum Electrodynamics (QED), which shares key features with (3+1)-dimensional Quantum Chromodynamics (QCD), such as confinement and asymptotic freedom. Two main projects are developed. The first investigates the running coupling in a compact U(1) pure gauge theory using a step scaling function approach. A quantum variational method enables computation across a wide range of couplings. The plaquette expectation value is matched with classical Monte Carlo simulations to obtain, in principle, the physical value of the lattice spacing. This method can be eventually extended to study QED, where fermionic matter is included. The second project examines the static potential between two charges, analyzing Coulomb, confining, and string-breaking regimes. It involves developing a custom variational Ansatz that incorporates system symmetries and mutual information to represent fermionic degrees of freedom. Results from a trapped-ion quantum device align well with exact classical simulations, validating the method. Additionally, the thesis evaluates superconducting devices, identifying noise challenges but noting improvements in hardware and the potential of error mitigation. Overall, this work highlights the viability of variational quantum algorithms for lattice gauge theory simulations and demonstrates their promise for advancing theoretical physics with quantum computing.
Recent advancements in the field of quantum simulation have significantly expanded the potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a central challenge, especially for large-scale non-Abelian LGTs with dynamical matter, which are particularly complex in terms of engineering for experiments. Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs) and controlling the magnitude of its effect is an open challenge. Here we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature. Second, we present a proposal for a gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian U ( 2 ) LGTs with dynamical fermionic matter in ( 2 + 1 ) dimensions on large scales. Due to the simplicity of the gauge protection mechanism, based on a Zeeman shift in combination with superexchange interactions, our scheme can be naturally included in other rishon-based quantum simulation protocols. Third, we extend our approach to a fully scalable, hybrid digital-analog simulator for U ( N ) LGTs based on Rydberg AELA with variable rishon number. The proposed general mechanism for gauge protection provides a promising path towards the simulation of non-Abelian LGTs relevant to particle physics.
Aharonov–Bohm interference in a Z2 lattice gauge theory on a hybrid qubit–oscillator quantum computer
Abstract Lattice gauge theories, which have both dynamical matter and gauge fields, are strongly coupled problems that lie beyond the reach of classical computation. Quantum simulations may provide a tractable approach for studying lattice gauge theories, but implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here we demonstrate a resource-efficient encoding of a Z2 Z 2 lattice gauge theory using a hybrid qubit–oscillator trapped-ion quantum device, with the qubits representing the gauge fields and the vibrational modes of the ions encoding the bosonic matter fields. We use synthetic dimensions to construct higher dimensional lattice geometries, and we combine digital and analogue techniques to prepare the initial states, realize the gauge-invariant real-time evolution and measure the relevant observables. After observing dynamics obeying Gauss’s law in a Z2 Z 2 link, we extend this approach to a loop geometry formed by two qubits and two oscillators. In this quasi-two-dimensional set-up, we observe Aharonov–Bohm interference with dynamical gauge fields encoding the magnetic flux, thereby demonstrating the interplay between charge and flux. Our results establish a path for scalable quantum simulations of lattice gauge theories in higher dimensions.
Quantum simulation provides a promising framework for studying non-perturbative phenomena in lattice gauge theories that are difficult to access using classical computational methods. In particular, classical Monte Carlo approaches suffer from the sign problem, limiting their applicability to real-time dynamics and finite-density regimes. Quantum computers, by directly encoding quantum dynamics, offer a natural pathway to overcoming these limitations. In this thesis, we study quantum simulations of a truncated SU(2) lattice gauge theory using a Hamiltonian formulation, representing an important non-Abelian step toward quantum chromodynamics. We focus on three-dimensional gauge-theory simulations in the noisy intermediate-scale quantum (NISQ) era, where limited qubit resources pose a significant challenge. To address this, we introduce the triamond lattice, a three-dimensional lattice geometry that enforces local gauge invariance while providing an economical encoding of gauge degrees of freedom, thereby reducing qubit overhead compared to conventional lattice constructions. We derive the corresponding Hamiltonian, construct physical gauge-invariant states, and implement quantum simulations using quantum imaginary time evolution to prepare ground states, alongside real-time evolution methods to study dynamical behavior. Error-mitigation techniques are employed to extract reliable physical observables from noisy quantum hardware. Our results demonstrate that the triamond lattice enables resource-efficient three-dimensional quantum gauge simulations and represents a practical step toward scalable quantum simulations of non-perturbative gauge theories.