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

We report continous experimental validation of the prime-gap fidelity formula F_k = cos^2(pi*g_k/(2*p_k*p_{k+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, ibm_fez), d8e3s5ro3njc73eu773g, d8e3sijo3njc73eu77h0, d8e3t73o3njc73eu7880, d8e3tj87jphs739k6img, d8e3u007jphs739k6j50.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-31
DOI
https://doi.org/10.5281/zenodo.20477311
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

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

Will Daoud
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

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

Will Daoud
preprint en

Abstract

We report continous experimental validation of the prime-gap fidelity formula F_k = cos^2(pi*g_k/(2*p_k*p_{k+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, ibm_fez), d8e3s5ro3njc73eu773g, d8e3sijo3njc73eu77h0, d8e3t73o3njc73eu7880, d8e3tj87jphs739k6img, d8e3u007jphs739k6j50.

Zenodo (CERN European Organization for Nuclear Research)
University of South Florida (US)
Decent work and economic growth
Quantum Computing Algorithms and Architecture
DOIOpen Access PDFOpenAlex
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