Abstract
Quantum processors are inherently noisy, so the prepared quantum states are mixed and deviate from the pure ground state of the target model. Z2 gauge models provide a natural testing ground for understanding how such noisy quantum ensembles can still encode thermodynamic information. We show that this deviation can be characterized by an effective temperature Teff, inferred from measured stabilizer (plaquette) violations and the average energy of the prepared state. As a paradigmatic example, we consider the Kitaev honeycomb model relevant to candidate materials such as RuCl3, which maps to free Majorana fermions coupled to a static Z2 gauge field. Within this free-fermion framework, we compute the thermal energy of the canonical ensemble across flux sectors and compare it to the measured energy of the quantum-prepared state to extract Teff. A noisy ground-state preparation of such a model exhibits low plaquette violations, consistent with low-T behavior of the Kitaev model, and an average energy consistent with a finite, low effective temperature matching the expected flux excitation statistics. This approach provides a route for connecting noisy quantum data to finite-temperature behavior in Z2 gauge and quantum spin-liquid materials.
*A.A., K.K, V.M, B.X., P.K., G.B.H., A.B., and P.C.L. were supported by the Quantum Science Center (QSC), a National Quantum Science Initiative of the Department of Energy (DOE), managed by Oak Ridge National Laboratory (ORNL). J.G. was supported with funding from AWE. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DEAC05-00OR22725. A.A., K.K., and V.M. additionally acknowledge funding by the Center for Quantum Technologies, an Industry–University Cooperative Research Center funded by NSF Grant No. 2224960.
