High Energy / Nuclear Theory / RIKEN Seminars
# [Hybrid RBRC seminar] Measurement-based quantum simulation of Abelian lattice gauge theories

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US/Eastern

2-160 (https://bnl.zoomgov.com/j/1606067399?pwd=am02b0xIUXZ6TDR3d1dWL05TTDdaUT09)
### 2-160 (https://bnl.zoomgov.com/j/1606067399?pwd=am02b0xIUXZ6TDR3d1dWL05TTDdaUT09)

Description

Quantum simulation of lattice gauge theory is expected to become a major application of near-term quantum devices. In this talk, I present 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. After discussing the procedure of MBQS, we investigate aspects of symmetries in our formulation. We demonstrate that the resource states we use for MBQS of Wegner’s models — a class of spin systems that includes the Ising model and the discrete gauge theories — possess topological order protected by higher-form symmetries. These higher-form symmetries turn out to be practically useful for error correction to suppress contributions that violate gauge symmetries. We also present a formula that relates the wave function of the resource state and the partition function of the Wegner’s model. This presentation is based on Ref. [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

Organized by

Nobuyuki Matsumoto

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