Structured Near-Optimal Channel-Adapted Quantum Error Correction

TL;DR

This paper introduces scalable algorithms for designing structured, near-optimal quantum error recovery operations tailored to specific channels, improving computational efficiency over previous SDP-based methods.

Contribution

It develops methods to generate structured, channel-adapted quantum error correction operations that are more scalable and physically interpretable than prior optimal but unstructured approaches.

Findings

Algorithms produce structured recovery operations with physical intuition.

Methods are more scalable than semidefinite programming.

Performance bounds certify near-optimality of the recovery operations.

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.