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RESEARCH PRODUCT
A Perturbative Approach to Continuous-Time Quantum Error Correction
Matteo IppolitiMatteo RizziLeonardo MazzaVittorio Giovannettisubject
PhysicsQuantum PhysicsNumerical analysisFOS: Physical sciencesNoise (electronics)Atomic and Molecular Physics and OpticsAction (physics)Condensed Matter - Other Condensed MatterTheoretical physicsQuantum error correctionState spaceLimit (mathematics)Statistical physicsTransient (oscillation)Error detection and correctionQuantum Physics (quant-ph)Perturbative approach to continuous-time quantum error correctionOther Condensed Matter (cond-mat.other)description
We present a novel discussion of the continuous-time quantum error correction introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame features a short initial transient in which error correction is ineffective, followed by a slow decay of the information content consistent with the known facts about discrete-time error correction in the limit of fast operations. This behavior is explained in the two case studies through a geometric description of the continuous transformation of the state space induced by the combined action of noise and error correction.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-11-09 |