Anomaly inflow, foliation, and measurement-based quantum simulation of abelian lattice gauge theories

Lattice gauge theory has been a fundamental formulation in theoretical physics, with relevance to quantum information science, high-energy physics, and condensed matter physics. Motivated by Measurement-Based Quantum Computation, we explore a family of custom-designed resource states for Ising/gauge theories, employing adaptive measurement on bulk qubits. We demonstrate that the sequential measurement drives the Hamiltonian quantum simulation of lattice Ising/gauge theories at the boundary of resource states. The tailor-made entanglers for the resource state result in symmetry-protected topological orders concerning higher-form symmetries. I will discuss the connections of our setup to concepts in high-energy and condensed matter physics, including anomaly inflow, dualities, and the foliation of quantum error-correcting codes.