  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.
