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
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C
P
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models emerge by dimensional reduction from
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quantum spin ladders, the
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confining
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gauge theory emerges from the Abelian Coulomb phase of a
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quantum link model, and
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QCD arises from a non-Abelian Coulomb phase of a
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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’.
From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories
