Observation of Emergent $\mathbb{Z}_2$ Gauge Invariance in a Superconducting Circuit

Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations. Here we experimentally investigate the emergent $\mathbb{Z}_2$ gauge invariance in a 1D superconducting circuit with 10 transmon qubits. By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing an LGT and gauge-broken terms. The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectation value can retain nonzero for a long time in low-energy regimes. The above localization can be regarded as the confinement of matter fields, and the 3-body operator is the $\mathbb{Z}_2$ gauge generator. These experimental results demonstrate that, despite the absence of gauge structure in the effective Hamiltonian, $\mathbb{Z}_2$ gauge invariance can still emerge in low-energy regimes. Our work provides a method for both theoretically and experimentally studying the rich physics in quantum many-body systems with emergent gauge invariance.