In this paper, we show the application of the quantum Metropolis sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group
D4 in (
2+1)-dimensions, discussing in general how some components of hybrid quantum-classical algorithms should be adapted in the case of gauge theories. In particular, we discuss the construction of random unitary operators which preserve gauge invariance and act transitively on the physical Hilbert space, constituting an ergodic set of quantum Metropolis moves between gauge invariant eigenspaces, and introduce a protocol for gauge invariant measurements. Furthermore, we show how a finite resolution in the energy measurements distorts the energy and plaquette distribution measured via QMS, and propose a heuristic model that takes into account part of the deviations between numerical results and exact analytical results, whose discrepancy tends to vanish by increasing the number of qubits used for the energy measurements.
In this paper, we show the application of the Quantum Metropolis Sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group
D4 in (2+1)-dimensions, discussing in general how some components of hybrid quantum-classical algorithms should be adapted in the case of gauge theories. In particular, we discuss the construction of random unitary operators which preserve gauge invariance and act transitively on the physical Hilbert space, constituting an ergodic set of quantum Metropolis moves between gauge invariant eigenspaces, and introduce a protocol for gauge invariant measurements. Furthermore, we show how a finite resolution in the energy measurements distorts the energy and plaquette distribution measured via QMS, and propose a heuristic model that takes into account part of the deviations between numerical results and exact analytical results, whose discrepancy tends to vanish by increasing the number of qubits used for the energy measurements.
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.
Aiming at evading the notorious sign problem in classical Monte-Carlo approaches to lattice quantum chromodynamics, we present an approach for quantum computing finite-temperature lattice gauge theories at non-zero density. Based on the thermal pure-quantum-state formalism of statistical mechanics when extended to gauge-theory systems, our approach allows for sign-problem-free quantum computations of thermal expectation values and non-equal time correlation functions. By taking a simple lattice gauge theory for which classical benchmarks are possible, namely
Z2 lattice gauge theory in 1+1 dimensions at finite chemical potential, we discuss resource requirements and robustness to algorithmic and hardware imperfections for near-term quantum-hardware realizations.
Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2 + 1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.
Lattice gauge theories provide a first-principles, non-perturbative formulation of the fundamental interactions of the Standard Model, and their Hamiltonian reformulation on a quantum simulator offers a promising route to regimes---real-time dynamics, finite baryon density---that lie beyond the reach of Euclidean Monte Carlo methods. With the ultimate goal of overcoming these shortcomings, over the last decade, quantum simulations of Abelian lattice gauge theories have expanded from the first proofs of principle to the experimental study of confinement and string breaking by pair production. One of the next frontiers lies in the simulation of non-Abelian theories, which are significantly more demanding both in local Hilbert space dimension and in symmetry-protection requirements, and ultimately essential for addressing open problems in high-energy physics. In this thesis, we investigate dihedral non-Abelian lattice gauge theories
DN---whose small order and finite local dimension make
D3 and
D4 natural targets for near-term quantum platforms---as a minimal yet physically rich arena for the study of non-Abelian gauge dynamics. After introducing dihedral groups and the associated lattice gauge theories, we propose a gauge-fixed ladder model that reduces the effective dimensionality while preserving the essential physics. We use it to show that the
D3 theory on a ladder displays a smooth crossover---rather than a sharp phase transition---between electric- and magnetic-dominated regimes, with the nonstabilizerness peaking in the crossover region. Furthermore, we introduce a formulation of the model compatible with the analysis of the Eigenstate Thermalization Hypothesis. We then study string breaking in pure-gauge
DN ladders in the presence of static charges through tensor-network DMRG simulations in the rishon formalism. We show that for odd
N static charges are screened by gluelumps---charge-glueball bound states enabled by the trivial centre of the group---while for even
N a fundamental flux string persists. Turning to the quantum-simulation side, we introduce a dynamical post-selection (DPS) protocol in which the local gauge charges are tested by mid-circuit measurements on auxiliary registers, and we show that gauge protection emerges through a sharp quantum Zeno transition in the spectrum of an associated Liouvillian. We verify the generality of this picture on
Z2,
Z3, and truncated
U(1) gauge groups, identifying an optimal window of measurement frequencies that survives also in the presence of noisy measurements. Finally, we benchmark DPS against an alternative post-processed symmetry verification scheme on a two-plaquette
D3 model designed for state-of-the-art qudit hardware. We find that both protocols significantly improve the reconstructed dynamics, with DPS tracking the exact evolution over longer times. Taken together, the results of this thesis position dihedral gauge theories as a concrete stepping stone from Abelian proofs of principle toward genuinely non-Abelian quantum simulation on near-term devices.