Understanding strongly interacting quantum field theories is a central challenge in theoretical physics, with direct relevance to nuclear, high-energy and condensed matter systems. Here we present a quantum algorithm for compact lattice Quantum Electrodynamics in 2+1 dimensions with dynamical fermionic matter. Using a variational quantum approach, we extract the static potential between charges across Coulomb, confinement, and string-breaking regimes. Our method employs a symmetry-preserving, resource-efficient circuit to prepare ground states, enabling accurate calculations on the Quantinuum H1-1 trapped-ion device and emulator, in agreement with noiseless simulations. Moreover, we visualize the electric field flux configurations that mainly contribute to the wave function of the quantum ground state, giving insights into the mechanisms of confinement and string-breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.
Understanding strongly interacting quantum field theories is a central challenge in theoretical physics, with direct relevance to nuclear, high-energy and condensed matter systems. Here we present a quantum algorithm for compact lattice Quantum Electrodynamics in 2+1 dimensions with dynamical fermionic matter. Using a variational quantum approach, we extract the static potential between charges across Coulomb, confinement, and string-breaking regimes. Our method employs a symmetry-preserving, resource-efficient circuit to prepare ground states, enabling accurate calculations on the Quantinuum H1-1 trapped-ion device and emulator, in agreement with noiseless simulations. Moreover, we visualize the electric field flux configurations that mainly contribute to the wave function of the quantum ground state, giving insights into the mechanisms of confinement and string-breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.
Understanding strongly interacting quantum field theories is a central challenge in theoretical physics, with direct relevance to nuclear, high-energy and condensed matter systems. Here we present a quantum algorithm for compact lattice Quantum Electrodynamics in 2+1 dimensions with dynamical fermionic matter. Using a variational quantum approach, we extract the static potential between charges across Coulomb, confinement, and string-breaking regimes. Our method employs a symmetry-preserving, resource-efficient circuit to prepare ground states, enabling accurate calculations on the Quantinuum H1-1 trapped-ion device and emulator, in agreement with noiseless simulations. Moreover, we visualize the electric field flux configurations that mainly contribute to the wave function of the quantum ground state, giving insights into the mechanisms of confinement and string-breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.
Abstract Understanding strongly interacting quantum field theories is a central challenge in theoretical physics, with direct relevance to nuclear, high-energy and condensed matter systems. Here we present a quantum algorithm for compact lattice Quantum Electrodynamics in 2+1 dimensions with dynamical fermionic matter. Using a variational quantum approach, we extract the static potential between charges across Coulomb, confinement, and string-breaking regimes. Our method employs a symmetry-preserving, resource-efficient circuit to prepare ground states, enabling accurate calculations on the Quantinuum H1-1 trapped-ion device and emulator, in agreement with noiseless simulations. Moreover, we visualize the electric field flux configurations that mainly contribute to the wave function of the quantum ground state, giving insights into the mechanisms of confinement and string-breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.
Compact lattice Quantum Electrodynamics is a complex quantum field theory with dynamical gauge and matter fields and it has similarities with Quantum Chromodynamics, in particular asymptotic freedom and confinement. We consider a (2+1)-dimensional lattice discretization of Quantum Electrodynamics with the inclusion of dynamical fermionic matter. We define a suitable quantum algorithm to measure the static potential as a function of the distance between two charges on the lattice and we use a variational quantum calculation to explore the Coulomb, confinement and string breaking regimes. A symmetry-preserving and resource-efficient variational quantum circuit is employed to prepare the ground state of the theory at various values of the coupling constant, corresponding to different physical distances, allowing the accurate extraction of the static potential from a quantum computer. We demonstrate that results from quantum experiments on the Quantinuum H1-1 trapped-ion device and emulator, with full connectivity between qubits, agree with classical noiseless simulations using circuits with 10 and 24 qubits. Moreover, we visualize the electric field flux configurations that mostly contribute in the wave-function of the quantum ground state in the different regimes of the potential, thus giving insights into the mechanisms of confinement and string breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.
String Breaking and Glueball Dynamics in 2+1D Quantum Link Electrodynamics
At the heart of quark confinement and hadronization, the physics of flux strings has recently become a focal point in the field of quantum simulation of high-energy physics (HEP). Despite considerable progress, a detailed understanding of the behavior of flux strings in quantum simulation-relevant lattice formulations of gauge theories has remained limited to the lowest truncations of the gauge field, which are severely limited in their ability to draw conclusions about the quantum field theory limit. Here, we employ tensor network simulations to investigate the behavior of flux strings in a quantum link formulation of 2+1D quantum electrodynamics (QED) with a spin-1 representation of the gauge field. We first map out the ground-state phase diagram of this model in the presence of two spatially separated static charges, revealing distinct microscopic processes responsible for string breaking, including a two-stage breaking mechanism not possible in the spin-21 formulation. Starting in different initial product state string configurations, we then explore far-from-equilibrium quench dynamics across various parameter regimes, demonstrating genuine 2+1D real-time string breaking and glueball-like bound state formation, with the latter not possible in the spin-21 formulation. In and out of equilibrium, we consider different values and placements of the static charges. Finally, we provide efficient qudit circuits for a quantum simulation experiment in which our results can be observed in state-of-the-art ion-trap setups. Our findings lay the groundwork for quantum simulations of flux strings towards the quantum field theory limit.
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.
Observation of glueball excitations and string breaking in a 2+1D Z2 lattice gauge theory on a trapped-ion quantum computer
A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a Z2 lattice gauge theory in 2+1D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a 6×5 matter-site square lattice utilizing all 56 available qubits to execute over 1000 entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine 2+1D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to 1+1D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.