Structured near-optimal channel-adapted quantum error correction
Author(s)Fletcher, Andrew S.; Shor, Peter W.; Win, Moe Z.
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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.
DepartmentLincoln Laboratory; Massachusetts Institute of Technology. Department of Mathematics; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Physical Review A
American Physical Society
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.
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