Simulating Lattice Gauge Theories with Virtual Rishons

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 1leq N_fleq3 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.