NT Seminar - Tommaso Rainaldi, Stony Brook University

Abstract: Quantum simulation can reach real-time and finite-density dynamics of gauge theories that Euclidean lattice methods cannot. Since gauge fields are continuous and live on group manifolds, they map naturally onto the bosonic modes of continuous-variable (CV) hardware, while fermions and the ancillas used to synthesize and read out bosonic gates are carried by qubits. We present a hybrid CV-DV (qumode-qubit) framework for simulating lattice gauge theories, giving the explicit CV gate content for each encoding. For compact U(1), where the gauge field is a rotor, we encode it in a single bosonic mode with a GKP-type stabilizer, resolve Gauss's law before encoding and quantify the finite-energy errors of the physical finite-energy encoded states. This rotor construction has no non-Abelian analogue, so for SU(2) we instead use a frame embedding with four modes per link, and sketch how the strategy extends toward SU(N). We close with an outlook toward real-time dynamics and state preparation on near-term hardware.