Método Kernel Polinomial aplicado a uma rede de spins em ambiente correlacionado

Abstract

Quantum bits, or qubits, are highly fragile due to interactions with the environment. The search for good protocols for protecting quantum information from decoherence is mandatory in order to make large-scale quantum computation possible. Most of the models proposed for this assume that correlations in the environment do not exist. Correlations can induce a time dependent error probability thus seriously damaging the quantum information over the time even if a quantum correction code is avaliable. In this way, we must taking into consideration possible physical limitations to fault-tolerant quantum computing. In this work we apply the Kernel Polynomial Method (KPM) to evaluate the density of states and fidelity decay of a L = 3 toric code without taking the lattice spin dynamics into account. The Hamiltonian model is based in a free bosonic environment and a spin-boson coupling, with two decoherence channels X and Z. A long-range, anisotropic interaction between spin pairs is then proposed as a correlated model. This correlation is directly related to the interaction strengh and range between spins. We show that the fidelity decay time scale depends on these parameters.