Structured near-optimal channel-adapted quantum error correction
We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), w...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2011
|
| Online Access: | http://hdl.handle.net/1721.1/67444 https://orcid.org/0000-0002-8573-0488 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1826202403520643072 |
|---|---|
| author | Fletcher, Andrew S. Shor, Peter W. Win, Moe Z. |
| author2 | Lincoln Laboratory |
| author_facet | Lincoln Laboratory Fletcher, Andrew S. Shor, Peter W. Win, Moe Z. |
| author_sort | Fletcher, Andrew S. |
| collection | MIT |
| description | We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace-preserving constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality. |
| first_indexed | 2024-09-23T12:06:54Z |
| format | Article |
| id | mit-1721.1/67444 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:06:54Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/674442022-10-01T08:16:22Z Structured near-optimal channel-adapted quantum error correction Fletcher, Andrew S. Shor, Peter W. Win, Moe Z. Lincoln Laboratory Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Fletcher, Andrew S. Fletcher, Andrew S. Shor, Peter W. Win, Moe Z. We present a class of numerical algorithms which adapt a quantum error correction scheme to a channel model. Given an encoding and a channel model, it was previously shown that the quantum operation that maximizes the average entanglement fidelity may be calculated by a semidefinite program (SDP), which is a convex optimization. While optimal, this recovery operation is computationally difficult for long codes. Furthermore, the optimal recovery operation has no structure beyond the completely positive trace-preserving constraint. We derive methods to generate structured channel-adapted error recovery operations. Specifically, each recovery operation begins with a projective error syndrome measurement. The algorithms to compute the structured recovery operations are more scalable than the SDP and yield recovery operations with an intuitive physical form. Using Lagrange duality, we derive performance bounds to certify near-optimality. National Science Foundation (U.S.) (Grant No. CCF-0431787) United States. Dept. of the Air Force (AF Contract No. FA8721-05-C-0002) 2011-12-05T20:41:53Z 2011-12-05T20:41:53Z 2008-01 2007-08 Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/67444 Fletcher, Andrew, Peter Shor, and Moe Win. “Structured near-optimal channel-adapted quantum error correction.” Physical Review A 77.1 012320 (2008) [16 pages]. © 2008 The American Physical Society. https://orcid.org/0000-0002-8573-0488 https://orcid.org/0000-0003-4626-5648 en_US http://dx.doi.org/10.1103/PhysRevA.77.012320 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Fletcher, Andrew S. Shor, Peter W. Win, Moe Z. Structured near-optimal channel-adapted quantum error correction |
| title | Structured near-optimal channel-adapted quantum error correction |
| title_full | Structured near-optimal channel-adapted quantum error correction |
| title_fullStr | Structured near-optimal channel-adapted quantum error correction |
| title_full_unstemmed | Structured near-optimal channel-adapted quantum error correction |
| title_short | Structured near-optimal channel-adapted quantum error correction |
| title_sort | structured near optimal channel adapted quantum error correction |
| url | http://hdl.handle.net/1721.1/67444 https://orcid.org/0000-0002-8573-0488 https://orcid.org/0000-0003-4626-5648 |
| work_keys_str_mv | AT fletcherandrews structurednearoptimalchanneladaptedquantumerrorcorrection AT shorpeterw structurednearoptimalchanneladaptedquantumerrorcorrection AT winmoez structurednearoptimalchanneladaptedquantumerrorcorrection |