Constraint-Optimal Driven Allocation for Scalable QEC Decoder Scheduling

TL;DR

This paper introduces CODA, an optimization-based scheduling algorithm for quantum error correction decoders that significantly improves resource efficiency and scalability in large-scale fault-tolerant quantum computing systems.

Contribution

CODA leverages global circuit structure to optimize decoder scheduling, surpassing heuristic methods and enabling scalable, resource-efficient quantum error correction.

Findings

CODA reduces the longest undecoded sequence length by 74% on average.

Scheduling time scales linearly with the number of qubits, not the combinatorial search space.

CODA effectively bypasses exponential growth in the search space, ensuring scalability.

Abstract

Fault-tolerant quantum computing (FTQC) requires fast and accurate decoding of Quantum Error Correction (QEC) syndromes. However, in large-scale systems, the number of available decoders is much smaller than the number of logical qubits, leading to a fundamental resource shortage. To address this limitation, Virtualized Quantum Decoder (VQD) architectures have been proposed to share a limited pool of decoders across multiple qubits. While the Minimize Longest Undecoded Sequence (MLS) heuristic has been introduced as an effective scheduling policy within the VQD framework, its locally greedy decision-making structure limits its ability to consider global circuit structure, causing inefficiencies in resource balancing and limited scalability. In this work, we propose Constraint-Optimal Driven Allocation (CODA), an optimization-based scheduling algorithm that leverages global circuit structure to minimize the longest undecoded sequence length. Across 19 benchmark circuits, CODA achieves an average 74\% reduction in the longest undecoded sequence length. Crucially, while the theoretical search space scales exponentially with circuit size, CODA effectively bypasses this combinatorial explosion. Our evaluation confirms that the scheduling time scales linearly with the number of qubits, determined by physical resource constraints rather than the combinatorial search space, ensuring robust scalability for large-scale FTQC systems. These results demonstrate that CODA provides a global optimization-based, scalable scheduling solution that enables efficient decoder virtualization in large-scale FTQC systems.