A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry. Recent advancements in the experimental realizations of large-scale LGTs have been impressive, albeit mostly restricted to Abelian gauge groups. Guided by this requirement for gauge protection, we propose an experimentally feasible approach to implement large-scale non-Abelian SU ( N ) and U ( N ) LGTs with dynamical matter in d + 1 D , enabled by two-body spin-exchange interactions realizing local emergent gauge-symmetry stabilizer terms. We present two concrete proposals for 2 + 1 D SU ( 2 ) and U ( 2 ) LGTs, including dynamical bosonic matter and induced plaquette terms, that can be readily implemented in current ultracold-molecule and next-generation ultracold-atom platforms. We provide numerical benchmarks showcasing experimentally accessible dynamics, and demonstrate the stability of the underlying non-Abelian gauge invariance. We develop a method to obtain the effective gauge-invariant model featuring the relevant magnetic plaquette and minimal gauge-matter coupling terms. Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators. Published by the American Physical Society 2024
Quantum simulation of lattice gauge theories (LGTs) provides a powerful framework for understanding nonperturbative phenomena. However, to realize the hope of answering challenging physics questions on near-term devices it is crucial to develop resource-efficient formulations, in particular for non-Abelian LGTs and beyond (1+1) dimensions. In this work, we address this issue by focusing on the difficulty of simulating fermionic degrees of freedom and on mitigating the Hilbert space redundancy, i.e., the presence of exponentially many nonphysical states that do not obey gauge invariance. First, we show a procedure that removes the matter and improves the hardware-resource efficiency. We demonstrate it for the simplest non-Abelian group addressable with this procedure, D 8 , in the cases of both one and two spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the D 8 LGT onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem, and reducing the amount of quantum resources. This approach can serve as a way of simulating LGTs in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.
Efficient quantum simulation protocols for any quantum theories demand efficient protection protocols for its underlying symmetries. This task is nontrivial for gauge theories as it involves local symmetry/invariance. For non-Abelian gauge theories, protecting all the symmetries generated by a set of mutually noncommuting generators, is particularly difficult. In this paper, a global symmetry-protection protocol is proposed. Using the novel loop-string-hadron formalism of non-Abelian lattice gauge theory, we numerically demonstrate that all of the local symmetries get protected even for large time by this global symmetry protection scheme. With suitable protection strength, the dynamics of a (
1+1)-dimensional SU(2) lattice gauge theory remains confined in the physical Hilbert space of the theory even in presence of explicit local symmetry violating terms in the Hamiltonian that may occur in both analog and digital simulation schemes as an error. The whole scheme holds for SU(3) gauge theory as well.
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice gauge theories in tabletop experiments. However, the realization of non-Abelian models remains challenging. Here, we employ a coherent quantum control scheme to enforce non-Abelian gauge invariance, and discuss this idea in detail for a one-dimensional SU(2) lattice gauge system. We comment on how to extend our scheme to other non-Abelian gauge symmetries and higher spatial dimensions. Because of its wide applicability, the presented coherent control scheme provides a promising route for the quantum simulation of non-Abelian lattice gauge theories.
Abstract Quantum simulation of a lattice gauge theory demands imposing on-site constraints. Ideally, the dynamics remain confined within the physical Hilbert space, where all the states satisfy those constraints. For a non-Abelian gauge theory, implementing these local Gauss’ law constraints is non-trivial. The presence of noise in current quantum devices further complicates efforts to confine the theory to the physical Hilbert space. The SU(3) gauge theory, describing the strong interaction of nature contains 8 mutually non-commuting local constraints. An efficient Hamiltonian simulation for the same should preserve all of these simultaneously - which stands as a notoriously difficult task. In this work, we explore two symmetry protection protocols for simulating SU(3) gauge theory in 1+1 dimensions. The first protocol does not require the imposition of any local symmetry but relies on protecting global symmetries, which are Abelian within the preferred choice of framework, namely the loop-string-hadron framework. The second protocol employs a protection scheme that is local, Abelian, and generalizable to higher dimensions. The symmetry protection schemes presented here are important steps towards quantum simulating the full theory of Quantum Chromodynamics.
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.