Restricted Simon Algorithm on 56-Slot Physical Circuits
We evaluate the scalability of constant-depth Simon oracles on IBM Heron across register sizes up to \(N = 28\) qubits (requiring up to 56 physical slots, Job da1a0piein7c73bd5beg, 24,576 shots). Physical measurement recovered secret periods on 6/12 instances with polynomial query reductions relative to classical sampling. However, two-qubit gate error accumulation at larger register sizes caused secret recovery failures on the remaining 6 instances. The hypothesis of asymptotic physical quantum speedup is INCONCLUSIVE.
1. Protocol & Physical Results
Secret reconstruction succeeded consistently on smaller registers (\(N=8, 12\)), achieving \(O(N)\) linear system reconstruction with high confidence. For \(N \ge 18\), multi-qubit cross-talk and measurement errors degraded the orthogonal subspace sampling purity below classical solvability thresholds.
2. Scientific Boundaries
Asymptotic quantum advantage for Simon's algorithm on physical NISQ hardware requires fault-tolerant error correction or active mitigation. Unconditional asymptotic advantage is not claimed.