We propose a parametrized quantum circuit (PQC) with the same real-device-performable optimal structure as in the previous work [Satzinger et al., Science 374, 1237 (2021)] to represent quantum loop gas states with adjustably weighted loop configurations (see the left panel in the above figure). Combining such a PQC with the variational quantum eigensolver, we obtain the accurate quantum circuit representation for the toric code model in an external magnetic field with any field strength, where the system is not exactly solvable (for the variational energy comparison, see the right panel in the above figure). The The details of this studied have been published in the following journal.

Journal reference: Rong-Yang Sun, Tomonori Shirakawa, and Seiji Yunoki, “Parametrized quantum circuit for weight-adjustable quantum loop gas” Phys. Rev. B 107, L041109.
DOI: https://doi.org/10.1103/PhysRevB.107.L041109