Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes

Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes

21 June 2024 | Stasiu Wolanski, Ben Barber
Ambiguity Clustering (AC) is a new decoding algorithm for quantum low-density parity-check (qLDPC) codes, offering significant speed improvements over the state-of-the-art BP-OSD decoder. AC divides the measurement data into clusters that can be decoded independently, reducing computational complexity. It achieves accuracy comparable to BP-OSD while being up to three orders of magnitude faster, particularly for the bivariate bicycle codes. AC's CPU implementation is already fast enough to decode the 144-qubit Gross code in real time for neutral atom and trapped ion systems. Quantum error correction is essential for fault-tolerant quantum computing, where logical qubits are encoded in physical qubits to withstand errors. The surface code is a widely studied qLDPC code, but more general qLDPC codes offer better efficiency. AC works by performing incomplete Gaussian elimination with modified pivot selection and stopping criteria, creating a block structure in the parity check matrix that allows for efficient decoding. This block structure enables independent decoding of clusters, significantly reducing the search space. AC is tested on bivariate bicycle codes, where it matches BP-OSD's accuracy with a speedup of 30x to 150x. The algorithm's performance is validated through Monte Carlo simulations, showing that it can decode the 144-qubit Gross code in 280 microseconds per round without loss of logical fidelity. AC's block structure allows for efficient decoding by breaking the problem into smaller, manageable clusters, making it suitable for real-time decoding in quantum systems. The algorithm's efficiency and accuracy make it a promising candidate for improving the performance of qLDPC codes in practical quantum computing applications.Ambiguity Clustering (AC) is a new decoding algorithm for quantum low-density parity-check (qLDPC) codes, offering significant speed improvements over the state-of-the-art BP-OSD decoder. AC divides the measurement data into clusters that can be decoded independently, reducing computational complexity. It achieves accuracy comparable to BP-OSD while being up to three orders of magnitude faster, particularly for the bivariate bicycle codes. AC's CPU implementation is already fast enough to decode the 144-qubit Gross code in real time for neutral atom and trapped ion systems. Quantum error correction is essential for fault-tolerant quantum computing, where logical qubits are encoded in physical qubits to withstand errors. The surface code is a widely studied qLDPC code, but more general qLDPC codes offer better efficiency. AC works by performing incomplete Gaussian elimination with modified pivot selection and stopping criteria, creating a block structure in the parity check matrix that allows for efficient decoding. This block structure enables independent decoding of clusters, significantly reducing the search space. AC is tested on bivariate bicycle codes, where it matches BP-OSD's accuracy with a speedup of 30x to 150x. The algorithm's performance is validated through Monte Carlo simulations, showing that it can decode the 144-qubit Gross code in 280 microseconds per round without loss of logical fidelity. AC's block structure allows for efficient decoding by breaking the problem into smaller, manageable clusters, making it suitable for real-time decoding in quantum systems. The algorithm's efficiency and accuracy make it a promising candidate for improving the performance of qLDPC codes in practical quantum computing applications.
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