Framework for simulating gauge theories with dipolar spin systems

Abstract

Gauge theories appear broadly in physics, ranging from the standard model of particle physics to long-wavelength descriptions of topological systems in condensed matter. However, systems with sign problems are largely inaccessible to classical computations and also beyond the current limitations of digital quantum hardware. In this work, we develop an analog approach to simulating gauge theories with an experimental setup that employs dipolar spins (molecules or Rydberg atoms). We consider molecules fixed in space and interacting through dipole-dipole interactions, avoiding the need for itinerant degrees of freedom. Each molecule represents either a site or gauge degree of freedom, and Gauss law is preserved by a direct and programmatic tuning of positions and internal state energies. This approach can be regarded as a form of analog systems programming and charts a path forward for near-term quantum simulation. As a first step, we numerically validate this scheme in a small-system study of U(1) quantum link models in (1+1) dimensions with link spin S = 1/2 and S = 1 and illustrate how dynamical phenomena such as string inversion and string breaking could be observed in near-term experiments. Our work brings together methods from atomic and molecular physics, condensed matter physics, high-energy physics, and quantum information science for the study of nonperturbative processes in gauge theories.

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• High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED
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• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories
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• Gauge Theory Couplings on Anisotropic Lattices
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Gluon Digitization via Character Expansion for Quantum Computers
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• Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Randomized measurement protocols for lattice gauge theories
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• (1+1)-d U(1) Quantum link models from effective Hamiltonians of dipolar molecules