Title

Hamiltonian formulation of quantum error correction and correlated noise: Effects of syndrome extraction in the long-time limit

Authors

Authors

E. Novais; E. R. Mucciolo;H. U. Baranger

Comments

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Abbreviated Journal Title

Phys. Rev. A

Keywords

CODES; COMPUTATION; DECOHERENCE; SYSTEMS; COHERENCE; THRESHOLD; Optics; Physics, Atomic, Molecular & Chemical

Abstract

We analyze the long-time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a given syndrome history and the associated residual decoherence encoded in the reduced density matrix. Systems with nonzero gate times ("long gates") are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.

Journal Title

Physical Review A

Volume

78

Issue/Number

1

Publication Date

1-1-2008

Document Type

Article

Language

English

First Page

18

WOS Identifier

WOS:000258180300059

ISSN

1050-2947

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