Fault-tolerant quantum computing (FTQC) requires fast and accurate decoding of quantum error correction 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 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.

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• Quantum error correction