Quantum Structural Benchmark (QSB): Evaluating Quantum Devices via π-Reconstruction Fidelity

Quantum Structural Benchmark (QSB): Evaluating Quantum Devices via π-Reconstruction Fidelity Overview We propose a novel quantum device benchmark—the Quantum Structural Benchmark (QSB)—based on the reconstruction accuracy of π from GHZ state measurements. Unlike conventional benchmarks (T₁/T₂, gate error rates, etc.), QSB measures how faithfully a quantum device reproduces fundamental geometric structure constants embedded in quantum mechanics. Key Metric: Structural Constant Fidelity (SCF) SCF = 1 - |π̂ - π| / π Where π̂ = √(3/2λ₃) is derived from Mermin inequality measurements on GHZ states. SCF Value Interpretation 1.000 Perfect (ideal simulator) 0.99+ Excellent (best hardware) 0.95-0.99 Good (typical NISQ) < 0.95 Structural degradation Main Results Measurement Value Mermin violation >700σ above classical bound Structure constant λ₃ 0.1482 ± 0.0006 Reconstructed π 3.181 SCF 0.9875 Platform IBM Quantum ibm_torino Paradigm Shift Aspect Conventional QSB/SCF Evaluates Gate quality Structural fidelity Question "How fast/quiet?" "How faithful to reality?" Type Engineering metric Physics metric Companion Paper This work builds upon: Quantum Buffon's Needle: Deriving π from the GHZ Structure Constant λ₃*DOI: 10.5281/zenodo.17855223 Files Included quantum_structural_benchmark.pdf — Full manuscript qsb.py — Complete QSB library (Python) README.md — Documentation Significance SCF could become the "LINPACK of quantum computing" — a universal metric for comparing quantum devices by their ability to reproduce fundamental physical constants. This represents a paradigm shift from hardware-centric to physics-centric quantum device evaluation.