Native Spinach propagation benchmark

Completed native-route experiment. Exact source, raw repeats, validation data, and launch records accompany this report.

ODC4 is accurate, but is not the fastest implementation in this experiment. Across 24 case/target comparisons using maximum physical checkpoint error, CF4 wins 5, CF4-3 wins 3, and CF6-5 wins 16. Their best measured medians improve on the fastest qualifying pre-existing route by 1.78 to 67.79 times. ODC4 takes 3.00 to 11.43 times the winning time.

What was measured

The sweep contains 1,204 method/grid cases and 6,020 timed full solves, with five interleaved repetitions per point. All 28 routes were compared on the common two-spin fixtures. Six- and eight-spin fixtures cover 25 routes; native amplitude/frequency phase-grid routes were limited to two spins.

Each solve propagates four reproducible orthonormal complex state columns for a 1 ms pulse under the same spin-chain Hamiltonian. The drift contains site offsets and nearest-neighbour ZZ interactions. RF acts along X and Y with boundary-flat, nonflat, or chirped analytic controls. The state dimension is 2ⁿ. Static setup and independent reference costs are recorded separately.

Timed calls include waveform sampling, generator construction, requested derivatives and onsite jets, native exponential actions, endpoint processors, and final physical decoding. No trajectory is requested during timing. Accuracy is checked separately at 17 equally spaced physical checkpoints, without phase alignment or renormalisation. Errors are Frobenius differences divided by the initial block norm, which is 2.

Equal-error comparison

Median complete solve times at maximum checkpoint error 1e-8

All eight fixtures at the strictest selected target. Whiskers show observed min-max across five repeats, not confidence intervals. Each method uses its fastest measured qualifying grid.

Fastest measured qualifying grid

Primary criterion: maximum error over the 17 checkpoints. Selection uses the lowest measured median among grids meeting each target, without interpolation or extrapolation. The archive also includes final-state-only selections and every method’s qualification status.

Spins / pulse	Target	Winner (steps)	Time, ms	Best older route (steps)	Speedup	ODC4 / winner
2 / flat	1e-04	CF4 (16)	1.347	isergen-three (32)	2.12	6.57
2 / flat	1e-06	CF6-5 (16)	3.244	isergen-three (128)	3.18	5.32
2 / flat	1e-08	CF6-5 (32)	5.976	RKMK-DP8 (16)	2.49	5.58
2 / nonflat	1e-04	CF4 (16)	1.344	isergen-three (32)	2.09	6.49
2 / nonflat	1e-06	CF6-5 (16)	3.068	isergen-three (128)	3.37	5.56
2 / nonflat	1e-08	CF6-5 (32)	5.778	RKMK-DP8 (16)	2.63	5.76
2 / chirp	1e-04	CF4-3 (16)	1.899	isergen-three (64)	2.63	4.49
2 / chirp	1e-06	CF6-5 (16)	2.961	RKMK-DP5 (32)	4.59	10.90
2 / chirp	1e-08	CF6-5 (32)	5.553	RKMK-DP8 (32)	4.95	11.43
6 / flat	1e-04	CF4 (16)	7.584	isergen-three (32)	1.87	4.85
6 / flat	1e-06	CF6-5 (16)	16.677	isergen-three (128)	2.91	4.27
6 / flat	1e-08	CF6-5 (32)	29.231	isergen-three (512)	6.05	4.77
6 / nonflat	1e-04	CF4 (16)	8.001	isergen-three (32)	1.78	4.55
6 / nonflat	1e-06	CF6-5 (16)	16.817	isergen-three (128)	2.88	4.21
6 / nonflat	1e-08	CF6-5 (32)	29.482	isergen-three (512)	5.92	4.70
6 / chirp	1e-04	CF4-3 (16)	10.853	isergen-three (64)	2.35	6.47
6 / chirp	1e-06	CF6-5 (16)	16.622	isergen-three (256)	5.46	8.23
6 / chirp	1e-08	CF6-5 (64)	53.025	RKMK-DP8 (32)	9.33	5.05
8 / nonflat	1e-04	CF4 (16)	35.540	isergen-three (32)	2.07	3.50
8 / nonflat	1e-06	CF6-5 (16)	76.633	step-three (128)	3.44	3.00
8 / nonflat	1e-08	CF6-5 (32)	134.953	RKMK4 (256)	13.84	3.31
8 / chirp	1e-04	CF4-3 (16)	48.690	isergen-three (64)	2.90	4.66
8 / chirp	1e-06	CF6-5 (16)	75.389	step-three (256)	6.15	5.88
8 / chirp	1e-08	CF6-5 (64)	238.165	RKMK-RKF45 (128)	67.79	3.66

“Older route” excludes the six methods added by this branch: GM4, CF4, CF4-3, CF6-5, BP4, and ODC4. This does not mean their mathematical formulas are all new. Five-repeat medians and recorded min/max spreads are descriptive, not formal confidence intervals.

Work-precision curves

Grey lines show pre-existing native routes; coloured lines show additions to this branch. Points are measured grids; connecting lines guide the eye. Raw tables retain points outside the plotted error range.

Native-route coverage

shaped_pulse_xy: expv-pwc, expv-pwl, expm-pwc, expm-pwl, evol-pwc, and evol-pwl.
step: midpoint, two-point, and three-point calls, plus explicit two-point and three-point isergen calls.
iserstep through step and iserblock: PWCL, LG2, LG4, LG4A, RKMK4, RKMK-DP5, RKMK-DP8, RKMK-RKF45, GM4, CF4, CF4-3, CF6-5, BP4, and ODC4.
shaped_pulse_af: expv, expm, and evolution, including phase-grid construction and physical folding.

The candidate methods use Spinach’s native step action. BP4 and ODC4 telescope internal processors through iserblock; physical output decoding is charged. Competing solvers are not standalone ports.

Accuracy and verification

The reference independently integrates the Schrodinger equation with ode113, then tightens tolerances and maximum step. Its largest refinement difference in the timing fixtures is 4.47e-13. The correctness sweep contains 625 method/grid comparisons, including strong and zero interactions, plus 36 amplitude/frequency checks. All numerical calls completed successfully.

The six new methods passed block/single-step parity, reversibility, superposition, long-run Gram preservation, and Hilbert density-matrix checks. Their largest long-run Gram defect is 8.69e-14. Density tests cover unitary conjugation, trace, Hermiticity, and minimum eigenvalue.

ODC4 order is conditional

With zero coupling, nonflat-pulse ODC4 errors at 32, 64, and 128 steps are 1.78e-8, 2.77e-10, and 4.33e-12, consistent with sixth-order onsite cancellation. For four spins with the coupling multiplier raised to 20, the errors are 2.34e-6, 1.46e-7, and 9.13e-9, consistent with fourth order. The interacting method is not generally sixth order.

Regression and source checks

kernel/dynamic_propagation_frontends: PASS
kernel/step_zero_time: PASS
kernel/step_matches_expm: PASS
kernel/shaped_pulse_rotation: PASS
kernel/dynamic_shaped_pulses_deep: PASS
kernel/dynamic_iserstep_highorder: PASS
kernel/processed_iser: PASS
Source hashes were unchanged during resumed timing. Postflight verified exact preservation of all 779 original rows.

The focused house-style checker passed. Git whitespace checking passed with the repository-required trailing blank lines exempted.

Remaining code-analyser diagnostics are retained in postflight/quality.json:

native_af_check.m: {'id': 'AGROW', 'message': 'Variable appears to change size on every loop iteration. Consider preallocating for speed.', 'fix': 0, 'line': 26, 'column': [47, 50]}
native_benchmark.m: {'id': 'AGROW', 'message': 'Variable appears to change size on every loop iteration. Consider preallocating for speed.', 'fix': 0, 'line': 101, 'column': [47, 50]}
native_validate.m: {'id': 'AGROW', 'message': 'Variable appears to change size on every loop iteration. Consider preallocating for speed.', 'fix': 0, 'line': 50, 'column': [47, 50]}

Timing exit status: 0. Postflight exit status: 0. Focused house-checker and chart outcomes are recorded in postflight_console.log.

Interpretation and limits

At six and eight spins, errors are measured on four reproducible state columns, not as a worst-case operator-norm bound. Reference refinement is a numerical consistency check, not an interval-arithmetic error certificate.
ODC4 constructs onsite defect commutators from full-basis embedded matrices. Its measured cost includes this work; no reduced local-action implementation was benchmarked.
This is coherent Hamiltonian wavefunction propagation with supplemental density-matrix validation. Dissipative dynamics, nonlinear generators, every Spinach formalism, and GPU backends are outside this timing sweep.
Grids are 16, 32, 64, 128, 256, and 512 for two and six spins; eight spins stop at 256. Eight-spin timing covers nonflat and chirped RF, not the boundary-flat pulse. An unqualified method only failed to meet that target on the sampled grids.
The run spans two sessions on the same machine. A broken output stream interrupted the first after 779 complete rows. Continuation resumed missing grid blocks without combining partial repeat sets.
A continuation startup using MATLAB’s -singleCompThread flag failed before timing. The preserved log documents it. The successful run retained the original one-thread-after-construction policy.
The full repository test suite, online wiki checks, and other hardware configurations were not run. No remote publication or merge is implied.

Environment and reproducibility

Branch: research/odc4-native-benchmark-20261114. Local source commit: dc0f6c3d384c1f7ca3b38e5fa09d835f1ddb7676. No push or merge was performed.

Intel Xeon w9-3595X, 60 physical / 120 logical cores; Windows Server 2025 Standard; MATLAB 26.2.0.3320248 (R2026b) Prerelease Update 2. The fixture requests one native process worker and sets the client to one computational thread after construction. Spinach warns that the worktree is on ReFS and recommends NTFS for locking and performance.

Use examples/benchmarks/native_propagation/README.md to reproduce the sweep. Keep numerical sources unchanged between resumed segments. The archive retains MAT/CSV/JSON evidence, raw repeats, achieved-error selections, hashes, tests, completion logs, and coefficient reconstruction.

Coefficient attribution

CF4-3 and CF6-5 are CF4:3Opt and CF6:5Opt from Alvermann and Fehske, Journal of Computational Physics 230 (2011), 5930-5956, Tables 5 and 6. Reconstructing their Gauss-node coefficients using Eq. 60 matches this branch within 1.11e-16 and 8.33e-17. Primary paper; open manuscript.

These are measured implementation results, not universal or hardware-independent speed claims.