Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination

• URL: http://arxiv.org/abs/2206.00685v3
• Date: Tue, 8 Aug 2023 10:29:12 GMT
• Title: Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
• Authors: Guy Pardo, Tomer Greenberg, Aryeh Fortinsky, Nadav Katz, Erez Zohar
• Abstract summary: We focus on two important bottlenecks that make developing such simulators hard. The redundancy of the Hilbert space leads to a waste of experimental resources and the need to impose and monitor the local constraints of gauge theories. We show an alternative procedure for dealing with these problems, which removes the matter symmetry space, and is valid for higher space dimensions.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulation of Lattice Gauge Theories has been proposed and used as a method to overcome theoretical difficulties in dealing with the non-perturbative nature of such models. In this work we focus on two important bottlenecks that make developing such simulators hard: one is the difficulty of simulating fermionic degrees of freedom, and the other is the redundancy of the Hilbert space, which leads to a waste of experimental resources and the need to impose and monitor the local symmetry constraints of gauge theories. This has previously been tackled in one dimensional settings, using non-local methods. Here we show an alternative procedure for dealing with these problems, which removes the matter and the Hilbert space redundancy, and is valid for higher space dimensions. We demonstrate it for a $\mathbb{Z}_2$ lattice gauge theory and implement it experimentally via the IBMQ cloud quantum computing platform.

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