Results¶

The results pages collect the current numerical evidence for the package: notebook execution, QSVT-vs-classical agreement, polynomial design diagnostics, and committed artefacts that can be regenerated from the command line.

The repository root RESULTS.md remains the compact source-of-truth ledger. This page is the portfolio-style summary for rendered documentation.

Result Navigation¶

page	purpose
Tutorial notebook outputs	generated plots and text outputs from `notebooks/tutorials/`
Real-example notebook outputs	generated plots and text outputs from `notebooks/real_examples/`
Benchmark notebook outputs	generated plots and text outputs from `notebooks/benchmarks/`
Diagnostics reports	design-report JSON fields, plotting helpers, and CLI report commands
QSVT transform reports	QSVT-vs-classical comparison reports for diagonal and matrix inputs

Current Status¶

53 validated notebooks

30 real-example workflows

1e-12 diagonal QSVT max-error scale

0.2.2 current release marker

validation target	current result	source
tutorial notebooks	all execute in notebook validation	`notebooks/tutorials/`
real-example notebooks	all execute in notebook validation	`notebooks/real_examples/`
benchmark notebooks	all execute in notebook validation	`notebooks/benchmarks/`
fast unit/regression suite	algorithm workflows and CLI report paths covered	`tests/`
package artefacts	source distribution and wheel build cleanly	`pyproject.toml`
rendered plots	tutorial, real-example, and benchmark PNG artefacts committed, including setup schematics	`results/plots/`

Key Outcomes¶

Polynomial design improves predictably with degree¶

The committed sign-design sweep uses gamma=0.2, evaluates degrees 5, 9, 13, 17, and skips PennyLane synthesis so the table isolates polynomial design diagnostics. A companion filter sweep uses cutoff=0.4 and degrees 6, 10, 14, 18.

degree	max error	RMS error	QSVT-compatible checks
5	`5.182981115359634e-01`	`2.695148817806530e-01`	passed sampled boundedness/parity checks
9	`3.289044195543612e-01`	`1.633101449091314e-01`	passed sampled boundedness/parity checks
13	`2.002792111439544e-01`	`9.744948051610955e-02`	passed sampled boundedness/parity checks
17	`1.176310891345335e-01`	`5.570304051373436e-02`	passed sampled boundedness/parity checks

Artefact: results/reports/sign-degree-sweep.json

Filter design also benefits from degree tuning¶

The filter sweep shows that different design families can have non-monotonic maximum error at low degree while still improving in RMS error and boundedness margin as the polynomial space grows.

degree	max error	RMS error	QSVT-compatible checks
6	`1.911439443363911e-01`	`1.003684556902707e-01`	passed sampled boundedness/parity checks
10	`2.003389491881879e-01`	`8.135058832372982e-02`	passed sampled boundedness/parity checks
14	`7.397752073483832e-02`	`3.469153756628215e-02`	passed sampled boundedness/parity checks
18	`6.783434474077632e-02`	`3.391969914072474e-02`	passed sampled boundedness/parity checks

Artefacts:

Regenerate:

qsvt design-sweep \
  --kind sign \
  --degrees "5,9,13,17" \
  --gamma 0.2 \
  --num-points 401 \
  --bounded-num-points 801 \
  --no-synthesis \
  --output results/reports/sign-degree-sweep.json

qsvt design-sweep \
  --kind filter \
  --degrees "6,10,14,18" \
  --cutoff 0.4 \
  --sharpness 12 \
  --num-points 401 \
  --bounded-num-points 801 \
  --no-synthesis \
  --output results/reports/filter-degree-sweep.json

QSVT transforms agree with direct spectral references¶

The committed scalar/diagonal and Hermitian matrix reports compare explicit QSVT transforms with direct classical polynomial evaluation.

artefact	transform	max error	RMS error
`qsvt-report.json`	diagonal `x^2` transform	`9.999778782798785e-13`	`5.585577546102077e-13`
`matrix-report.json`	Hermitian matrix `x^2` transform	`5.264677582772492e-13`	`3.2060825311797223e-13`

Algorithm workflows are regression-tested¶

The fast test suite covers deterministic small-matrix regressions for:

positive-definite linear-system approximation
Gaussian ground-state filtering
real-time Hamiltonian simulation
resolvent / Green’s-function response
spectral-density estimation
thermal Gibbs weighting

These tests protect the package-level workflow APIs separately from the longer notebook execution checks.

Representative Figures¶

Sign polynomial design report plot — Degree-13 sign design report showing the target, polynomial fit, and residual structure.¶

End-to-end QSVT algorithm workflow plot — QSVT algorithm workflow diagnostics from the tutorial sequence.¶

Degree error tradeoff plot — Degree/error/boundedness tradeoff results for QSVT-compatible polynomial design.¶

Topological band projector Chern marker plot — Topological band-projector example using a small Qi-Wu-Zhang lattice model.¶

Generated notebook output pages:

The real-example output page now includes setup schematics alongside quantitative diagnostics for the physical systems represented in the notebooks.

Artefact Ledger¶

artefact	workflow	notes
`results/reports/sign-report.json`	sign design report	degree-13 sign approximation with `gamma=0.2`
`results/plots/sign-report.png`	sign design plot	target-vs-polynomial diagnostic plot
`results/reports/sign-degree-sweep.json`	design sweep	degree/error/boundedness manifest
`results/reports/filter-degree-sweep.json`	design sweep	filter degree/error/boundedness manifest
`results/tables/design_sweep_summary.csv`	sweep summary	tabular summary of committed design-sweep reports
`results/reports/qsvt-report.json`	diagonal QSVT comparison	direct `x^2` reference comparison
`results/reports/matrix-report.json`	Hermitian matrix QSVT comparison	spectral polynomial reference comparison
`results/tables/qsvt-error-summary.csv`	release summary table	compact index over generated JSON reports
`results/tables/real_examples_plot_manifest.csv`	real-example manifest	machine-readable ledger for real-example PNG outputs

Regeneration¶

Execute notebooks, extract their embedded outputs, and regenerate the rendered result pages:

python scripts/extract_notebook_plots.py --preset all --execute --write-docs

Refresh the pages from already-saved notebook outputs without re-executing:

python scripts/extract_notebook_plots.py --preset all --write-docs

Generate the committed report examples:

qsvt design-report --kind sign --gamma 0.2 --degree 13 \
  --output results/reports/sign-report.json \
  --plot results/plots/sign-report.png

qsvt compare-report \
  --values "1.0,0.7,0.3,0.1" \
  --poly "0,0,1" \
  --wires 3 \
  --output results/reports/qsvt-report.json

qsvt matrix-report \
  --matrix "0.31351701,-0.23499807;-0.23499807,0.68648299" \
  --poly "0,0,1" \
  --output results/reports/matrix-report.json