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

TL;DR

This paper introduces quantum link models and D-theory as resource-efficient frameworks for simulating and computing gauge theories, leveraging finite-dimensional Hilbert spaces and dimensional reduction to connect higher-dimensional models to physically relevant lower-dimensional theories.

Contribution

It presents a novel approach combining quantum link models with D-theory to efficiently simulate gauge theories via dimensional reduction, enabling practical quantum computations.

Findings

Quantum link models have finite-dimensional Hilbert spaces.

Dimensional reduction connects higher-dimensional models to lower-dimensional gauge theories.

Quantum link models facilitate resource-efficient quantum simulations.

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.