IQIM Postdoctoral and Graduate Student Seminar

Abstract: We investigate the protection and recovery of quantum information stored in the ground-state manifold of deformed toric codes, particularly as they are pushed towards a quantum critical point. Our focus is on the toric code perturbed by transverse and longitudinal fields, whose ground states are described by the three-dimensional classical Fradkin-Shenker model via the quantum-classical mapping. Using an effective replica field theory approach in the vicinity of the topological-to-trivial phase transition, we show quite generally that the intrinsic error threshold for local Pauli decoherence remains finite as the critical point is approached. Moreover, we demonstrate that this class of nonstabilizer codes can be simply and efficiently decoded by measuring the stabilizers of the unperturbed model. This property follows from the stoquastic nature of the deformed toric code Hamiltonians, which in turn allows us to formulate an optimal decoder for the postmeasurement states in terms of a constrained three-dimensional statistical physics model. We numerically implement the optimal decoder for the transverse-field toric code subjected to bit-flip decoherence and stabilizer measurements, and we find that the error threshold for this decoder remains finite throughout the topological phase.

Following the talk, lunch will be provided on the lawn outside East Bridge.