2007/05/31 by Ognyan Oreshkov, Todd A. Brun · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #quant-ph
paper · pdf · doi:10.1103/physreva.76.022318
published as Phys. Rev. A 76, 022318 (2007) · 16 pages, 4 figures, minor typos corrected, references updated
openalex publication_date 2007/08/20 · arxiv created 2007/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.