Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.
Gauge theories like lattice QCD present a complex problem for quantum simulation. In a basis where the electric part of the Hamiltonian is simple, the magnetic part, generally expressed as a sum over the plaquette operators of the lattice, is quite complicated, producing correlated transitions between several link and...
Gauge theories describe fundamental interactions in the standard model of particle physics and build effective theories in condensed matter physics. Being notoriously hard to simulate, these theories are commonly regularized as lattice gauge theories which can be evaluated with high precision through Monte Carlo algori...
Eloic Vall'ee, Ariel Kelman, Julius Mildenberger et al.· 0 citations
We investigate the perturbative renormalization of Noether currents associated with chiral symmetry and supersymmetry transformations in $\mathcal{N}=1$ supersymmetric Yang-Mills theory, regularized on the lattice using improved discretizations. In particular, we study the chiral current and the supercurrent operator f...
Marios Costa, Elias Antoniou, S. Dimou et al.· 0 citations
Quantum computers offer the potential to directly probe the dynamics of strongly coupled quantum field theories. As a step towards reaching this potential, local Krylov-based truncations of a pure SU(2) lattice gauge theory on a triangular lattice are constructed. Adjoint strings connected to dynamical gluons are const...
Anthony N. Ciavarella, R. de Putter, Ed Younis et al.· 3 citations
Transitions out of non-Abelian topological order are difficult to describe in microscopic quantum models with numerical methods that remain tractable at large scales. We develop a sign-free path-integral framework for Kitaev quantum doubles $\mathcal D(G)$ by organizing single-link perturbations in terms of non-inverti...
R. Flores-Calderón, F. Pollmann, M. Knap· 0 citations
We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees...
Xiaojun Yao· 3 citations
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