Generalized toric codes coupled to thermal baths

Abstract

© 2012 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We acknowledge support from the Spanish MICINN grant no. FIS2009-10061, the CAM research consortium QUITEMAD S2009-ESP-1594, the European Commission PICC: FP7 2007-2013, grant no. 249958 and UCM-BS grant no. GICC-910758.We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code’s degrees of freedom to a thermal bath. We find that in the case of qutrits, new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension d of the qudits. While we provide an explicit proof that the system relaxes to the Gibbs state for arbitrary qudits, we also prove that above a certain crossover temperature the qutrits’ initial decay rate is smaller than the original case for qubits. Surprisingly, this behavior only happens for qutrits and not for other qudits with d > 3.Spanish MICINNCAM, SpainEuropean Commission PICC: FP7 2007-2013UCM-BSDepto. de Física TeóricaFac. de Ciencias FísicasTRUEpu