Séminaire de groupe
Quantum Error Correction and Classical Spin Models: A Fruitful Relationship 
Ruben Andrist 
ETH Zurich (Suisse) 
mardi 12 avril 2011 , 10h25 
Salle de séminaire du groupe de Physique Statistique 
A prospective quantum computer promises exponential speedups for specific tasks, such as factorization and search algorithms. Unfortunately, sensitivity to noise makes most of the current quantum computing schemes prone to errors and nonscalable. Topological quantum computing solves this problem and prevents decoherence effects at the hardware level by encoding quantum states in topological properties of the system. The combination of this robust setup with an active error correction scheme could make quantum computation feasible. <br> It has been shown by Dennis et al.[1] that the resulting error correction process can be mapped to a classical statistical spin model with disorder. In this relation, the disorder follows from the error rate and the ability to correct for all local errors in the quantum computer corresponds to finding a stable ordered phase in the spin system. Hence this connection is instrumental in determining the maximum tolerable error rate of the quantum setup  all we need to do is analyzing the corresponding phase diagram. The details of the mapping depend on the topological code used and the types of errors considered. Our recent publications include individual qubit and phase flips for Topological Color Codes, as well as work on the Depolarizing Channel. The results were obtained by means of large scale replica exchange Monte Carlo simulations to detect the orderdisorder phase transition for each of the classical statistical models. With the reasonably high error thresholds of ~12% and ~19%, respectively, error correction is feasible. <br> [1] E. Dennis et al., J. Math. Phys. 43, 4452 (2002) 
