A Formulation of Lattice Gauge Theories for Quantum Simulations

Abstract

We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete $D_3$ gauge group, are presented.

13 pages, 1 figure

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Cited by in corpus (15)

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• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• How many quantum gates do gauge theories require?
• Gauge Theories with Ultracold Atoms
• Classification of Matrix Product States with a Local (Gauge) Symmetry
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• Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Half a state, half an operator: a general formulation of stators
• Towards Quantum Simulating Non-Abelian Gauge Theories