Progress on measurement-based quantum simulation of lattice gauge theories

Measurement-based quantum simulation offers a framework for studying gauge-theory dynamics through adaptive local measurements on entangled resource states. This approach unifies concepts from measurement-based quantum computation, lattice gauge theory, and recent insights into the role of mid-circuit measurements in transforming topological orders. We present a theoretical scheme for simulating the real-time dynamics of discrete Hamiltonian gauge models, illustrating how gauge invariance and topological orders emerge within the measurement-based setting. We further discuss strategies to protect gauge invariance against noise. Ongoing progress toward experimental realization on the Quantinuum trapped-ion device will be reported.