From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of...

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 [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] 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. This article is part of the theme issue 'Quantum technologies in particle physics'.