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This research aims to experimentally validate the prime-gap fidelity formula on quantum hardware.

June 2, 20260 citationsOpen Access

Experimental Validation of Prime Harmonic Modulation: Quantum State Tomography and Prime-Gap Indistinguishability

Key Points

This research aims to experimentally validate the prime-gap fidelity formula on quantum hardware.
Conducted single-qubit state tomography on IBM Fez.
Analyzed fidelity formula across 6 patent primes.
Reported additional experiments on decoherence, entropy, quantum bit error rate, and fingerprints.
Validated the prime-gap fidelity formula within 2.49% accuracy.
Measured Bloch angles with a mean error of 0.66°.
Completed five supplementary experiments demonstrating various quantum characteristics.

Abstract

We report continous experimental validation of the prime-gap fidelity formula Fₖ = cos² (pi*gₖ/ (2*pₖ*p₊+₁) ) on real IBM quantum hardware. Single-qubit state tomography on IBM Fez confirms the formula within 2. 49% for all 6 patent primes. Bloch angles match pi/p within 0. 66° mean error. Five additional experiments (decoherence, entropy, QBER, fingerprints) are reported. IBM Quantum job IDs: d8e3v607jphs739k6kig (primary, ibmfez), d8e3s5ro3njc73eu773g, d8e3sijo3njc73eu77h0, d8e3t73o3njc73eu7880, d8e3tj87jphs739k6img, d8e3u007jphs739k6j50.

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