Universal Decoding of Quantum Stabilizer Codes via Classical Guesswork

Abstract

A universal decoding scheme is conceived for quantum stabilizer codes (QSCs) by appropriately adapting the ‘guessing random additive noise decoding’ (GRAND) philosophy of classical domain codes. We demonstrate that the generalized quantum decoder conceived is eminently suitable for different QSC decoding paradigms, namely for both stabilizer-measurement-based as well as the inverse-encoder-based decoding. We then harness the resultant decoder for both quantum Bose-Chaudhuri-Hocquenghem (BCH) codes and quantum polar codes and quantify both their quantum block error rate (QBLER), and QBLER per logical qubits as well as their decoding complexity. Furthermore, we provide a parametric study of the associated design trade-offs and offer design guideline for the implementation of GRAND-based QSC decoders.

Keywords

• Quantum error correction codes
• quantum stabilizer codes
• quantum noise
• decoding