Nadarasa · experiment · G20 · gate 0.4.5e
G20 — Floquet native port: subharmonic peak under H2-class noise
A native Guppy/Selene reimplementation of the mixed-field Ising Floquet magnet studied in G19 (Leviatan et al. 2026). Two six-qubit lattices are driven for eight Floquet cycles at four kick imperfections, across an ideal control and a five-rung depolarizing ladder anchored on Quantinuum's published H2 error rates, then corrected with Richardson zero-noise extrapolation.
Verdicts
Period-doubled peak is full height at eps=0 and monotonically collapses as the kick imperfection grows, in both exact diagonalization and ideal Selene.
Worst ideal-cell deviation from exact diagonalization is 0.0495 against a 4-sigma shot-noise threshold of 0.1250.
At published H2-2 rates the peak retains at least 93.8 percent of its ideal height, and quadratic Richardson extrapolation lands within 2.0 percent of ideal in the worst cell.
The qualitative structure reported on a 74-qubit heavy-hex superconducting device reproduces on an all-to-all trapped-ion compiler with an independent noise model. This is corroboration of the mechanism, not a numerical match of the published values.
Subharmonic peak across the noise ladder
Peak height of the period-two component of the staggered magnetization, per lattice and kick imperfection. Values are absolute peak heights; the bracketed number is retention against that row's ideal control.
| Lattice | eps | Exact | ideal | h2_1x | h2_2x | h2_5x | h2_10x | h2_20x |
|---|---|---|---|---|---|---|---|---|
| 1D chain (n=6) | 0.00 | 1.000 | 1.000 | 0.969 (97%) | 0.950 (95%) | 0.881 (88%) | 0.763 (76%) | 0.606 (61%) |
| 1D chain (n=6) | 0.04 | 0.969 | 0.969 | 0.940 (97%) | 0.918 (95%) | 0.847 (87%) | 0.736 (76%) | 0.583 (60%) |
| 1D chain (n=6) | 0.08 | 0.856 | 0.863 | 0.825 (96%) | 0.813 (94%) | 0.744 (86%) | 0.633 (73%) | 0.507 (59%) |
| 1D chain (n=6) | 0.12 | 0.644 | 0.650 | 0.625 (96%) | 0.601 (93%) | 0.557 (86%) | 0.492 (76%) | 0.381 (59%) |
| Heavy-hex cell (n=6) | 0.00 | 1.000 | 1.000 | 0.960 (96%) | 0.930 (93%) | 0.846 (85%) | 0.730 (73%) | 0.530 (53%) |
| Heavy-hex cell (n=6) | 0.04 | 0.987 | 0.987 | 0.947 (96%) | 0.914 (93%) | 0.829 (84%) | 0.709 (72%) | 0.510 (52%) |
| Heavy-hex cell (n=6) | 0.08 | 0.937 | 0.942 | 0.893 (95%) | 0.863 (92%) | 0.765 (81%) | 0.654 (69%) | 0.453 (48%) |
| Heavy-hex cell (n=6) | 0.12 | 0.835 | 0.836 | 0.784 (94%) | 0.765 (91%) | 0.657 (79%) | 0.558 (67%) | 0.386 (46%) |
Zero-noise extrapolation
Each row fits peak height against the noise multiplier over the five noisy rungs and extrapolates to zero. The quadratic Richardson fit beats the linear fit everywhere, and both beat the unmitigated 20x value by a wide margin.
| Lattice | eps | Ideal | Worst noisy | Unmitigated err | Linear (err) | Quadratic (err) |
|---|---|---|---|---|---|---|
| 1D chain (n=6) | 0.00 | 1.000 | 0.606 | 0.394 | 0.980 (0.0195) | 1.000 (0.0003) |
| 1D chain (n=6) | 0.04 | 0.969 | 0.583 | 0.387 | 0.948 (0.0208) | 0.969 (0.0006) |
| 1D chain (n=6) | 0.08 | 0.863 | 0.507 | 0.356 | 0.834 (0.0283) | 0.858 (0.0045) |
| 1D chain (n=6) | 0.12 | 0.650 | 0.381 | 0.269 | 0.627 (0.0228) | 0.637 (0.0124) |
| Heavy-hex cell (n=6) | 0.00 | 1.000 | 0.530 | 0.470 | 0.970 (0.0298) | 0.987 (0.0126) |
| Heavy-hex cell (n=6) | 0.04 | 0.987 | 0.510 | 0.477 | 0.955 (0.0319) | 0.975 (0.0122) |
| Heavy-hex cell (n=6) | 0.08 | 0.942 | 0.453 | 0.488 | 0.900 (0.0415) | 0.922 (0.0195) |
| Heavy-hex cell (n=6) | 0.12 | 0.836 | 0.386 | 0.450 | 0.789 (0.0469) | 0.817 (0.0186) |
Magnetization trajectories
Staggered magnetization cycle by cycle, comparing exact diagonalization, ideal Selene, and the two extreme noise rungs. The sign alternation is the period doubling; noise damps its amplitude without shifting its period.
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 |
| Ideal Selene | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 |
| H2 1x | -0.99 | +0.99 | -0.98 | +0.97 | -0.96 | +0.96 | -0.96 | +0.95 |
| H2 20x | -0.85 | +0.78 | -0.68 | +0.60 | -0.56 | +0.50 | -0.45 | +0.42 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.99 | +0.97 | -0.97 | +0.96 | -0.97 | +0.96 | -0.96 | +0.96 |
| Ideal Selene | -0.99 | +0.97 | -0.97 | +0.96 | -0.98 | +0.96 | -0.97 | +0.96 |
| H2 1x | -0.98 | +0.97 | -0.95 | +0.93 | -0.93 | +0.92 | -0.92 | +0.91 |
| H2 20x | -0.84 | +0.76 | -0.65 | +0.58 | -0.54 | +0.47 | -0.42 | +0.40 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.97 | +0.90 | -0.86 | +0.84 | -0.84 | +0.81 | -0.81 | +0.81 |
| Ideal Selene | -0.97 | +0.90 | -0.88 | +0.84 | -0.83 | +0.83 | -0.83 | +0.82 |
| H2 1x | -0.96 | +0.88 | -0.83 | +0.81 | -0.82 | +0.78 | -0.77 | +0.76 |
| H2 20x | -0.82 | +0.69 | -0.58 | +0.49 | -0.44 | +0.37 | -0.34 | +0.32 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.93 | +0.78 | -0.69 | +0.61 | -0.58 | +0.53 | -0.53 | +0.51 |
| Ideal Selene | -0.92 | +0.76 | -0.70 | +0.65 | -0.58 | +0.58 | -0.48 | +0.52 |
| H2 1x | -0.93 | +0.77 | -0.66 | +0.61 | -0.57 | +0.50 | -0.51 | +0.46 |
| H2 20x | -0.79 | +0.61 | -0.44 | +0.31 | -0.28 | +0.24 | -0.20 | +0.17 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 |
| Ideal Selene | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 | -1.00 | +1.00 |
| H2 1x | -0.99 | +0.98 | -0.97 | +0.96 | -0.96 | +0.95 | -0.94 | +0.93 |
| H2 20x | -0.84 | +0.71 | -0.61 | +0.52 | -0.46 | +0.41 | -0.37 | +0.32 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.99 | +0.98 | -0.98 | +0.99 | -0.99 | +0.99 | -0.99 | +0.98 |
| Ideal Selene | -0.99 | +0.98 | -0.99 | +0.99 | -0.99 | +0.99 | -0.98 | +0.98 |
| H2 1x | -0.98 | +0.97 | -0.96 | +0.95 | -0.95 | +0.95 | -0.92 | +0.90 |
| H2 20x | -0.83 | +0.69 | -0.59 | +0.51 | -0.45 | +0.39 | -0.35 | +0.28 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.97 | +0.92 | -0.92 | +0.94 | -0.95 | +0.95 | -0.94 | +0.91 |
| Ideal Selene | -0.97 | +0.91 | -0.93 | +0.93 | -0.95 | +0.97 | -0.95 | +0.93 |
| H2 1x | -0.96 | +0.90 | -0.89 | +0.90 | -0.89 | +0.91 | -0.86 | +0.84 |
| H2 20x | -0.81 | +0.64 | -0.53 | +0.44 | -0.40 | +0.33 | -0.26 | +0.21 |
| Series | t1 | t2 | t3 | t4 | t5 | t6 | t7 | t8 |
|---|---|---|---|---|---|---|---|---|
| Exact | -0.93 | +0.82 | -0.81 | +0.81 | -0.83 | +0.83 | -0.84 | +0.82 |
| Ideal Selene | -0.92 | +0.83 | -0.81 | +0.78 | -0.82 | +0.83 | -0.86 | +0.83 |
| H2 1x | -0.93 | +0.80 | -0.78 | +0.75 | -0.77 | +0.77 | -0.75 | +0.73 |
| H2 20x | -0.79 | +0.56 | -0.46 | +0.35 | -0.30 | +0.25 | -0.18 | +0.19 |
What this shows, and what it does not
It shows that the subharmonic response and its collapse under kick imperfection are not artefacts of one hardware platform or one mitigation stack. The same mechanism appears on an all-to-all trapped-ion compiler with an independently parameterized depolarizing model, and simple Richardson extrapolation over a noise ladder is enough to recover the ideal peak to about one percent.
It does not reproduce the published numbers. Six qubits over eight cycles is far inside the classically simulable regime; the interesting claim in the original work is finite-size scaling toward 74 qubits, which this port cannot address. The noise model is depolarizing plus measurement error, not a device-characterized quasiprobability model, so the ZNE performance here is an upper bound on what PEC-free extrapolation achieves on hardware.