A Novel Quantum Circuit for Integer Factorization: Evaluation via Simulation and Real Quantum Hardware
Bibliographic record
Abstract
This work tests the hypothesis that a Quantum Number Theoretic Transform (QNTT) circuit, here named Jesse-Victor-Gharabaghi (JVG) algorithm, can perform better than the Shor’s algorithm, in terms of number of required gates and qubits. This methodology replaces the Quantum Fourier Transform (QFT) with a Quantum Number Theoretic Transform (QNTT) circuit to predict periodicity in the number theory and factor integer numbers, which serve as keys in cryptographic methods, like RSA and ECC. Several composite numbers were evaluated through both simulation and real quantum hardware to verify feasibility and performance. Performance was assessed across runtime, memory consumption, and gate counts. Simulation results showed that the JVG can reduce the growth in CX gates by 30.3%, circuit depth by 33.5%, memory by 9.6%, and runtime by 14.7% relative to the Shor’s algorithm. On quantum hardware, JVG reduces growth in runtime by 26% and X-gate counts by 44.4%, achieving consistently lower coefficients of variation across metrics. Projection curves derived from the fitted trends predict the eventual JVG advantage, over Shor ,in runtime, gates, and depth as the number of qubits increases, including RSA-scale configurations. These results support JVG as a more hardware-compatible and robust noise-tolerant substitute for the Shor’s framework, offering a viable path toward practical quantum integer factorization on near-term Noisy Intermediate-Scale Quantum (NISQ) devices.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".