Simulating Lattice Gauge Theories with Virtual Rishons

TL;DR

This paper introduces a novel quantum simulation framework for lattice gauge theories using virtual rishons, enabling analysis of complex gauge models in multiple dimensions with promising results for classical and quantum computing.

Contribution

The authors develop a gauge-symmetry enforcing virtual rishon framework for lattice gauge theories applicable in multiple spacetime dimensions, bridging classical and quantum simulation methods.

Findings

Successfully simulated 1D Schwinger model with multiple flavors.

Extracted confining string tension in 2D gauge theory.

Framework is scalable and compatible with near-term quantum hardware.

Abstract

Classical tensor network and hybrid quantum-classical algorithms are promising candidates for the investigation of real-time properties of lattice gauge theories. We develop here a novel framework which enforces gauge symmetry via a quantum-link virtual rishon representation applied at intermediate steps. Crucially, the gauge and matter degrees of freedom are dynamical variables encoded in terms of qubits, enabling analysis of gauge theories in $d+1$ spacetime dimensions. We benchmark this framework in a U(1) gauge theory with and without matter fields. For $d = 1$, the multi-flavor Schwinger model with $1\leq N_f\leq3$ flavors is analyzed for arbitrary boundary conditions and nonzero topological angle, capturing signatures of the underlying Wess-Zumino-Witten conformal field theory. For $d = 2$, we extract the confining string tension in close agreement with continuum expectations. These results establish the virtual rishon framework as a scalable and robust approach for the simulation of lattice gauge theories using both classical tensor networks as well as near-term quantum hardware.