Structured Near-Optimal Channel-Adapted Quantum Error Correction

Abstract

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 (CPTP) 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.

18 pages, 13 figures Update: typos corrected in Appendix

References in corpus (2)

• Optimum Quantum Error Recovery using Semidefinite Programming
• Suboptimal quantum-error-correcting procedure based on semidefinite programming

Cited by in corpus (3)

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• Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
• Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem