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Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

A simple approach to approximate quantum error correction

Hui Khoon Ng, Caltech

joint work with Prabha Mandayam 

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. This analytical result is compared with earlier work that relies on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity.  For the practically more relevant case of codes encoding a single qubit of information, our algorithm is particularly easy to implement.