Simple approach to approximate quantum error correction based on the transpose channel
- Creators
- Ng, Hui Khoon
- Mandayam, Prabha
Abstract
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.
Additional Information
© 2010 The American Physical Society. Received 12 April 2010; published 28 June 2010. We thank David Poulin for introducing us to the problem of approximation quantum error correction and for many insightful discussions. This work is supported by NSF under Grant No. PHY-0803371.Attached Files
Published - Ng2010p10790Phys_Rev_A.pdf
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Additional details
- Eprint ID
- 19110
- Resolver ID
- CaltechAUTHORS:20100719-132549667
- PHY-0803371
- NSF
- Created
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2010-07-23Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field