The development of quantum technology and the advent of quantum computation have renewed interest in Hamiltonian formulations of lattice gauge theories. In contrast to Euclidean Monte Carlo calculations, Hamiltonian simulation requires a direct representation of the physical Hilbert space, an efficient treatment of enforcing Gauss' law as constraints, and a formulation of real-time dynamics in terms of degrees of freedom that can be encoded on quantum or quantum-inspired classical platforms. The starting point corresponds to finding a suitable basis for Hamiltonian lattice gauge theories. The existing literature focuses on several complementary approaches: electric basis, magnetic basis, gauge-fixed, quantum-link, qubit-regularised, finite-group, and orbifold formulations. This article primarily focuses on the prepotential and loop--string--hadron formulations, where non-Abelian Gauss laws are solved locally and the dynamics is written directly in terms of gauge-invariant loop, string and hadron excitations. The discussion covers the SU(2) and SU(3) constructions in one spatial dimension, the role of residual Abelian Gauss laws, and the extension to higher dimensions through point splitting. We conclude by highlighting its direct applications: eliminating redundant gauge degrees of freedom makes exact diagonalisation and tensor network calculations feasible for studying real-time dynamics, provides insights into thermalisation properties, enables mapping of physical degrees of freedom onto analog and digital quantum hardware, and enables quantum simulation of dynamics.
Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for
Zl LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.
We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time.
We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic properties. The unusual physics of these systems is due to local constraints on the degrees of freedom which are variables localized on the links of the lattice. We discuss two types of constraints that become equivalent after a duality transformation for Abelian theories but are qualitatively different for non-Abelian ones. We emphasize highly nontrivial topological properties of the excitations (fluxons and charges) in these non-Abelian discrete lattice gauge theories. We show that an implementation of these models may provide one with the realization of an ideal quantum computer, that is, the computer that is protected from the noise and allows a full set of precise manipulations required for quantum computations. We suggest a few designs of the Josephson-junction arrays that provide the experimental implementations of these models and discuss the physical restrictions on the parameters of their junctions.
We study the ground-state properties of a class of
Zn lattice gauge theories in
1+1 dimensions, in which the gauge fields are coupled to spinless fermionic matter. These models, stemming from discrete representations of the Weyl commutator for the U(1) group, preserve the unitary character of the minimal coupling and have, therefore, the property of formally approximating lattice quantum electrodynamics in one spatial dimension in the large-
n limit. The numerical study of such approximated theories is important to determine their effectiveness in reproducing the main features and phenomenology of the target theory, in view of implementations of cold-atom quantum simulators of QED. In this paper, we study the cases $n=2\textdiv{}8$ by means of a DMRG code that exactly implements Gauss's law. We perform a careful scaling analysis and show that, in absence of a background field, all
Zn models exhibit a phase transition which falls in the Ising universality class, with spontaneous symmetry breaking of the
CP symmetry. We then perform the large-
n limit and find that the asymptotic values of the critical parameters approach the ones obtained for the known phase transition of the zero-charge sector of the massive Schwinger model, which occurs at negative mass.
Hamiltonian formulation of lattice gauge theories provides the natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It is therefore important to identify the most accurate, while computationally economic, Hamiltonian formulation(s) of lattice gauge theories along with necessary truncation imposed on the Hilbert space of gauge bosons for any finite computing resources. We report a study toward addressing this question in the case of non-Abelian lattice gauge theories that require the imposition of non-Abelian Gauss's laws on the Hilbert space.