Year: 2026
Type: article
Abstract: Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.
Authors: Shouzhen Gu, Mehdi Soleimanifar
Institutions: Yale University, California Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1938338418, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, Center: Institute for Quantum Information and Matter: IQIM, The Institute for Quantum Information and Matter: Advancing the Entanglement Frontier, G5616713406, G585908603, CAREER: The Role of Classical Cryptography in Quantum Computing, G86560745, G969889393
OpenAlex ID: W7169851400