Clean Two-Dimensional Floquet Time Crystal Stabilized for 5000+ Periods by a Purely Imaginary Spiral-Twist Phase
Bibliographic record
Abstract
We demonstrate a clean, disorder-free two-dimensional Floquet time crystal on a $30\times30$ square lattice with periodic boundaries that achieves full wavefunction fidelity $>0.9996$ after 50 periods and $>0.9957$ after 5000 periods ($\sim$4 minutes of evolution at 20~Hz drive frequency). The system is driven by a globally uniform transverse field $h(t)\sum_i\sigma^x_i$ and a purely imaginary spiral-twist interaction $iJ\sum_{\langle ij\rangle}\sin(\theta_{ij})\sigma^z_i\sigma^z_j$, with $\theta_{ij}(t)$ a slow, center-origin spiral phase profile of maximum amplitude $\pi/512$. Mean-field product-state evolution in the 1800-dimensional amplitude space, integrated with fourth-order Runge--Kutta (200 steps/period), accurately captures the dynamics and reveals that the imaginary twist passively suppresses Floquet heating for thousands of cycles without disorder, measurement feedback, or long-range interactions. An attempted hardware validation on a 9-qubit patch of IBM Sherbrooke (1.05~million physical gates, 50 periods) yielded only classical readout noise (Bhattacharyya fidelity $0.305\pm0.018$ on four marked qubits, no detectable subharmonic response), confirming that individual addressing and mid-circuit measurement destroy the required coherence. The Hamiltonian maps directly to a single global RF beam plus one static linear magnetic gradient on existing 2D trapped-ion arrays, providing a scalable route to ultra-stable logical qubits and low-frequency (~10--200~Hz) isotope and chiral separation.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".