Efficient and scalable branch-and-bound algorithm for exact qubit allocation

Qubit allocation is a central step in adapting abstract quantum circuits to noisy intermediate-scale quantum devices, yet exact approaches for solving it face severe scalability limitations. In this work, we revisit the formulation of qubit allocation as a permutation-based quadratic assignment problem and develop a branch-and-bound algorithm for its exact resolution. We first establish a refined sequential implementation that achieves significantly faster runtimes than previous exact approaches on most problem instances, thereby setting a new state-of-the-art for this formulation. Building on this foundation, we extend the approach to a performance-aware parallel implementation that exploits both intra-node and inter-node parallelism on High-Performance Computing (HPC) infrastructures. Our experimental evaluation demonstrates near-linear strong scaling at the intra-node level and substantial scalability in distributed settings across nodes. Leveraging these capabilities, we provide reference optimal solutions for challenging benchmark circuits of up to 26 qubits—significantly larger than previously reported instances. These results show that large-scale parallelization can effectively extend the reach of exact methods for qubit allocation, thereby advancing the integration of combinatorial optimization and HPC techniques in quantum computing.