Simple approach to approximate quantum error correction based on the transpose channel
Open accessAbstract
We demonstrate that there exists a universal, near-optimal recovery map---the transpose channel---for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.
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A variant of the Petz map defined over a codespace C rather than a specific state ρ has been shown to be a universal, near-optimal recovery map in terms of worst-case fidelity.
“Subsequently, a variant of the Petz map -defined over a codespace C, rather than a specific state ρ -has been shown to be a universal, nearoptimal recovery map in terms of the worst-case fidelity [190].”
From Holographic spacetime, black holes and quantum error correcting codes: a review (2022) · cites this paper as [190]
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- Authors
- Ng, H. K., & Mandayam, P.
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- California Institute of Technology (US)
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- 1050-2947
- 1094-1622
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- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0803371)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- approximate quantum error correction, recovery maps, entanglement fidelity, quantum error-correcting codes, code construction algorithm
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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