From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories

Abstract

Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way (1+1)-d CP(N-1) models emerge by dimensional reduction from (2+1)-d SU(N) quantum spin ladders, the (2+1)-d confining U(1) gauge theory emerges from the Abelian Coulomb phase of a (3+1)-d quantum link model, and (3+1)-d QCD arises from a non-Abelian Coulomb phase of a (4+1)-d SU(3) quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories.

Comments: 14 pages, 7 figures, invited manuscript for Philosophical Transactions A