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From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
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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.
Forward citations
Cited by 4 Pith papers
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Non-Abelian dynamics on a cube: improving quantum compilation through qudit-based simulations
A qudit-based circuit for SU(2) lattice gauge theory on a cube, with improved decompositions for uniformly-controlled rotations and new elementary-gate resource estimates.
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Scaling and Luescher Term in a non-Abelian (2+1)d SU$(2)$ Quantum Link Model
In an SU(2) quantum link model on a hexagonal lattice, the static quark potential shows a coupling-dependent Lüscher term and logarithmically growing string width, indicating a rough confining string with no continuum limit.
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Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
Exact diagonalization shows 1+1D SU(2) lattice gauge theory with dynamical fermions satisfies ETH, including for non-local string operators that display a memory peak.
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Quantum computation of hadron scattering in a lattice gauge theory
On a trapped-ion quantum computer, the authors prepared multiple meson wave packets and simulated their early-time collisions in a 1+1D Z2 lattice gauge theory.
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