Spectral Arithmetic Drift Detection in Entangled Qubits: A Measurement-Free Experiment
Bibliographic record
Abstract
We introduce a measurement-free protocol (avoiding projective collapse) to detect decoherence (’drift’) in entangled qubit registers, using the conserved arithmetic structure predicted by Spectral Quantum Mechanics (SQM). In SQM, computational basis states |n⟩ map directly to prime-exponent vectors ⟨aj(n)⟩, causing quantum superpositions to inhabit a prime-logarithmic ”spectral space.” We show that low-order spectral arithmetic moments, defined as invariants Ik = j fk,jˆaj, commute with the SQM Hamiltonian HLKO. The combination of these invariants with an ancilla oscillator through a dispersive interaction Hint = gIk⊗ˆnanc imprints the spectral moments as measurable Ramsey phases, allowing continuous drift monitoring without projective measurement and thus preserving entanglement. Numerical simulations of two entangled SQM qubits subjected to pure dephasing noise demonstrate that invariant I1 reliably flags drift at the 10−4 level while maintaining Bell state fidelity greater than 0.99. Verified experiments conducted on IBM quantum platforms (ibm brisbane, ibm sherbrooke) confirm the predictive precision of our spectral arithmetic drift detection protocol, closely matching theoretical predictions. Additionally, we uncover Spectral Sympathetic Resonance (SSR), a coherent oscillatory effect in spectrally aligned qubits, further supporting SQM’s predictive scope. We outline concrete implementation pathways in trapped-ion, circuit-QED, and photonic time-bin architectures, showing that current coherence times and coupling strengths are sufficient for resolving Ik well within typical qubit lifetimes. The proposed protocol defines a new class of ”spectral arithmetic stabilizers,” offering an experimentally validated signature of SQM and a scalable pathway toward drift-tolerant quantum computation
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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; both teacher heads agree on what is shown here.
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".