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Lecture notes in networks and systems

Towards Scalable Exact Qubit Allocation Using Parallel Tree Search

Jean-Philippe Valois, Guillaume Helbecque, Nouredine Melab

Published Oct 6, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-34564-6_30

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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.
The scaling of quantum processors is currently limited by technical challenges such as decoherence and cross- talk. As the number of qubits grows, the interference between them adds more noise to the computations. Distributed quantum computing addresses this limitation by interconnecting smaller, easier-to-handle quantum cores, but it introduces the challenge of minimizing slow, error-prone inter-core communication. The task of distributing quantum circuits across cores to minimize communication costs is known as the Qubit Allocation problem. This work is centered on finding a deep learning approach to this problem, focusing on scalability and improving the state-of-the-art performance. Classical algorithms like the Hungarian Qubit Allocation (HQA) currently represent the state of the art, but they suffer from poor scalability with circuit size. In contrast, existing Deep Learning optimizations like Reinforcement Learning (RL) approaches often lack flexibility, requiring retraining if hardware configurations change, and are far from the solution quality of classical methods. However, these are worth exploring due to the good scalability and execution times. To overcome these limitations, this thesis proposes a flexible, transformer-based architecture capable of handling arbitrary numbers of qubits and cores without retraining. The policy is trained using a combination of REINFORCE and Group Relative Policy Optimization, two well-known RL algorithms. Furthermore, to explore the test-time compute paradigm applied to this problem, we introduce QAllocZero, an AlphaZero-inspired tree search algorithm we implemented in C++ that utilizes the trained policy as a heuristic. The results show that the trained policy achieves up to 33% improvement in allocation cost with respect to the state of the art (HQA) for the Cuccaro Adder and narrows the gap between RL and HQA for the most common circuits while maintaining scalable execution time. These findings show that learning-based approaches can effectively break the computational bottlenecks of classical algorithms, a crucial step for managing future systems with millions of qubits. All the code is open source and can be found in the porject's repository (https://github.com/Vicara12/MAI-TFM_RL_Qubit_Allocation).