Quantum simulation of lattice gauge theory is expected to become a major application of near-term quantum devices. In this presentation, I will talk about a quantum simulation scheme for lattice gauge theories motivated by Measurement-Based Quantum Computation [1], which we call Measurement-Based Quantum Simulation (MBQS). In MBQS, we consider preparing a resource state whose entanglement structure reflects the spacetime structure of the simulated gauge theory. We then consider sequentially measuring qubits in the resource state in a certain adaptive manner, which drives the time evolution in the Hamiltonian lattice gauge theory. It turns out that the resource states we use for MBQS of Wegner’s models possess topological order protected by higher-form symmetries. These higher-form symmetries are also practically useful for error correction to suppress contributions that violate gauge symmetries. We also discuss the relation between the resource state and the partition function of Wegner’s model. This presentation is based on my work with Takuya Okuda [2].
[1] R. Raussendorf and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett. 86, 5188 (2001)
[2] H. Sukeno and T. Okuda, Measurement-based quantum simulation of Abelian lattice gauge theories, arXiv:2210.10908