Parametrized quantum circuit for weight-adjustable quantum loop gas

TL;DR

This paper introduces a parametrized quantum circuit capable of representing weighted quantum loop gas states, enabling simulation of the toric code model under external magnetic fields and observing topological phase transitions.

Contribution

It presents a novel parametrized quantum circuit structure for weight-adjustable quantum loop gases, extending the simulation capabilities to non-exactly solvable models.

Findings

Accurate quantum circuit representation of the toric code in magnetic fields.

Observation of topological phase transition via optimized circuits.

Measurement of magnetization and entanglement entropy confirms phase change.

Abstract

Motivated by the recent success of realizing the topologically ordered ground state of the exactly solvable toric code model by a quantum circuit on the real quantum device [K. J. Satzinger {\it et al}., Science \textbf{374}, 1237 (2021)], here we propose a parametrized quantum circuit (PQC) with the same real-device-performable optimal structure to represent quantum loop gas states with adjustably weighted loop configurations. 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. The topological quantum phase transition in this system is further observed in the optimized circuits by measuring the magnetization and topological entanglement entropy.