Hamiltonian methods from Quantum Information Technologies: A Unified Program from Z2 String Dynamics to Continuous U(1) Electrodynamics with Superconducting Circuits

Real-time, non-perturbative dynamics of gauge theories, from string formation and fragmentation to thermalization and jet production, lie largely beyond the reach of standard Euclidean Monte Carlo methods. Hamiltonian formulations of lattice gauge theories, combined with tools from quantum information science, offer a complementary route that provides direct access to time evolution, avoids the sign problem, and enforces gauge invariance at the level of the physical Hilbert space.

In this colloquium, I present three interconnected works that systematically develop this program, using the Z2 and U(1) gauge groups as a ladder of increasing complexity. In the first, we use matrix product state (MPS) methods to study the roughening transition of an electric flux string in a (2+1)-dimensional Z2 lattice gauge theory. Working in the Hamiltonian framework, we obtain the universal Lüscher correction to the confining potential, extract a central charge c = 1 consistent with an effective free-boson description of the rough string, confirm the restoration of rotational symmetry, and reveal qualitatively distinct real-time entanglement dynamics in the roughening and strongly-confined regimes, which are inaccessible to Euclidean approaches. In the second, we extend to the Z2-Higgs model with dynamical matter and implement it on a superconducting quantum processor with up to 144 qubits and a circuit depth of 192 two-qubit layers. Exploiting local gauge symmetry for error suppression and mitigation, we resolve a dynamical hierarchy between longitudinal string oscillations and transverse endpoint-bending modes, precursors to hadronization and meson rotational spectra, and observe multi-string fragmentation and recombination. In the third work, we propose an analog superconducting-circuit architecture that realizes compact U(1) lattice gauge theory using the intrinsic infinite-dimensional Hilbert space of Josephson-junction phase and charge variables. Gauss's law follows exactly from Kirchhoff's current conservation, with no truncation, penalty terms, or auxiliary stabilizers, and numerical diagonalization confirms the emergence of compact electrodynamics and coherent vortex excitations. Together, these results establish a complementary triad of classical tensor networks, digital NISQ hardware, and analog circuit design as a viable and scalable strategy for probing non-perturbative gauge dynamics in real time.