Quantum electrodynamics in 1 + 1 D (QED2) shares intriguing properties with quantum chromodynamics (QCD), including confinement, string breaking, and interesting phase diagram when the nontrivial topological θ -term is considered. Its lattice regularization is a commonly used toy model for quantum simulations of gauge theories on near-term quantum devices. In this work, we address algorithms for adiabatic state preparation in digital quantum simulations of QED2. We demonstrate that, for specific choices of parameters, the existing adiabatic procedure leads to level crossing between states of different charge sectors, preventing the correct preparation of the ground state. We further propose a new adiabatic Hamiltonian and verify its efficiency in targeting systems with a nonzero topological θ -term and in studying string breaking phenomena.
Quantum electrodynamics in 1 + 1 D (QED2) shares intriguing properties with quantum chromodynamics (QCD), including confinement, string breaking, and interesting phase diagram when the nontrivial topological θ -term is considered. Its lattice regularization is a commonly used toy model for quantum simulations of gauge theories on near-term quantum devices. In this work, we address algorithms for adiabatic state preparation in digital quantum simulations of QED2. We demonstrate that, for specific choices of parameters, the existing adiabatic procedure leads to level crossing between states of different charge sectors, preventing the correct preparation of the ground state. We further propose a new adiabatic Hamiltonian and verify its efficiency in targeting systems with a nonzero topological θ -term and in studying string breaking phenomena.
We perform digital quantum simulation to study screening and confinement in a gauge theory with a topological term, focusing on (1+1)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for non-integer charges and a non-linear behavior for integer charges, consistently with the expected confinement (screening) behavior for non-integer (integer) charges.
We perform digital quantum simulation, using a classical simulator, to study screening and confinement in a gauge theory with a topological term, focusing on (1+1)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for noninteger charges and a nonlinear behavior for integer charges, consistently with the expected confinement (screening) behavior for noninteger (integer) charges.
Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising alternative, but present-day devices are limited in qubit count and circuit depth, so efficient formulations and algorithms are key to scaling toward experimentally relevant QCD simulations. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, where the charge distribution and energy loss are measured. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. Digitizing the continuous gauge fields with as few as three qubits per plaquette reproduces low-energy observables with 10−3 precision. Scaling to larger systems is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in basis-operator contributions. Demonstrated on the adiabatic preparation of the λφ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. All simulations in this dissertation are validated on quantum hardware against classical benchmarks. These studies advance quantum simulations of real-time QCD dynamics.
Simulating quantum-mechanical systems is a very challenging issue due to the high computational costs. The main reason for this is related to the dimension of the Hilbert space that grows exponentially with the number of degrees of freedom, making an exact implementation impossible even for the most powerful today’s supercomputers. \nOn this ground it appears clear the need of a new simulation method, i.e. quantum simulation. The general idea is very simple: using a controllable quantum system, called quantum simulator, to emulate and to analyze another quantum system that usually results less controllable or accessible. Quantum simulation is currently a growing and multidisciplinary physical area that involves theoretical and experimental research. From the theoretical side, the main focus is on the study of simulation-models that create a mapping between the target physics and the simulator. \nIn the first two parts of this thesis, we explore these ideas by studying the ground-state properties and the real-time dynamics of a class of Zn lattice gauge theories in 1+1 dimensions, in which the gauge fields are coupled to fermionic matter. These models can be considered as quantum simulation-models of lattice 1+1 Quantum Electrodynamics (QED), which is the simplest gauge theory that shows non-trivial phenomena, like confinement, that are also observed in more complicated gauge theories, such as 3+1 Quantum Chromodynamics (QCD). \nIn the third part of this thesis, we unveil an interesting interplay of symmetry and topology by demonstrating the existence of symmetry-protected topological (SPT) phases in the presence of gauge interactions. More specifically, we introduce an alternative discretization of the Schwinger model leading to a new type of topological-QED. We use bosonization and Density-Matrix Renormalization Group (DMRG) techniques to analyze the phase diagram of the model, opening an interesting route to study topological phases of matter in the context of gauge theories.
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.
We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on 1+1 dimensional quantum electrodynamics with the θ-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation is already useful tool to explore non-perturbative aspects of gauge theories with real time and topological terms.