Scaling Quantum Optimization to the Thousand-Qubit Scale with Distributed Quantum Sampling

2026-10-07

AI Summary

This study addresses the bottleneck of current quantum hardware in solving thousand-scale minimum Birkhoff decompositions by proposing a distributed quantum sampling framework that integrates single-layer QAOA, spectral graph partitioning, and classical repair algorithms. The core innovation lies in introducing a synergistic mechanism combining spectral partitioning with spatial circuit packing, enabling efficient mapping of large-scale problems while preserving substantial quantum advantage. Experiments conducted on IBM superconducting processors and matrix product state (MPS) simulators using the PEGASE-1354 benchmark demonstrate that repaired QAOA samples yield lower errors than simulated annealing baselines, while reducing hardware execution time by approximately threefold. These results establish a viable quantum deployment pathway for large-scale constrained optimization.

Abstract

The Minimum Birkhoff Decomposition (MBD) seeks a sparse weighted sum of matchings and is a challenging optimization problem with applications in network scheduling and energy trading. We scale a quantum-assisted decomposition method by combining single-layer QAOA sampling with Extended Fully-Corrective Frank-Wolfe (E-FCFW) optimization, spectral graph partitioning, and greedy feasibility repair. We demonstrate the pipeline on the 1,354-node PEGASE bus test case (representing a 1,354-bus transmission grid with 1,710 transmission lines), whose 1,710 edges define a native 1,710-variable matching optimization problem requiring 1,710 qubits in the unpartitioned encoding. Partitioning enables distributed execution on IBM superconducting quantum processors. The best reported hardware result uses a 50-qubit partition bound, while reducing partitions to 20 qubits degrades convergence in the partition-size comparison. Larger partitions are more demanding for matrix product state (MPS) simulation, and bond-dimension tests show that truncating quantum correlations reduces candidate quality. The results therefore motivate retaining a substantive quantum sampling task within each partition as the overall problem scales. On the PEGASE-1354 benchmark, repaired QAOA samples achieve lower residual decomposition error than both simulated annealing and uniform random sampling baselines, while spatial circuit packing reduces hardware execution time by approximately a factor of three. These results demonstrate that combining spectral partitioning, spatial circuit packing, and classical feasibility repair provides an executable path for deploying gate-based quantum sampling on thousand-variable constrained optimization problems on current hardware.

Problem

• Minimum Birkhoff Decomposition
• Quantum Optimization
• Constrained Optimization
• Network Scheduling
• Energy Trading

Innovation

• Distributed Quantum Sampling
• QAOA
• Spectral Graph Partitioning
• Minimum Birkhoff Decomposition
• Spatial Circuit Packing