English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We analyze the long time behavior of a quantum computer running a quantumerror correction (QEC) code in the presence of a correlated environment.Starting from a Hamiltonian formulation of realistic noise models, and assumingthat QEC is indeed possible, we find formal expressions for the probability ofa faulty path and the residual decoherence encoded in the reduced densitymatrix. Systems with non-zero gate times (``long gates'') are included in ouranalysis by using an upper bound on the noise. In order to introduce the localerror probability for a qubit, we assume that propagation of signals throughthe environment is slower than the QEC period (hypercube assumption). Thisallows an explicit calculation in the case of a generalized spin-boson modeland a quantum frustration model. The key result is a dimensional criterion: Ifthe correlations decay sufficiently fast, the system evolves toward astochastic error model for which the threshold theorem of fault-tolerantquantum computation has been proven. On the other hand, if the correlationsdecay slowly, the traditional proof of this threshold theorem does not hold.This dimensional criterion bears many similarities to criteria that occur inthe theory of quantum phase transitions.

Hamiltonian Formulation of Quantum Error Correction and Correlated Noise: The Effects Of Syndrome Extraction in the Long Time Limit