Classical Benchmarks¶

The benchmark helpers provide small classical baselines for QSVT-oriented workflows. They are designed for reproducible notebook studies and advantage screening, not for claiming end-to-end quantum speedups.

Available Baselines¶

The public API is in qsvt.benchmarks:

dense_eigendecomposition_benchmark
dense_linear_solve_benchmark
conjugate_gradient_benchmark
polynomial_matrix_function_benchmark
spectral_matrix_function_benchmark
benchmark_summary_table
write_benchmark_summary_csv
plot_benchmark_timings
plot_qsvt_proxy_resources

Each benchmark report includes:

a truth_contract marking the report as a classical baseline, not a quantum runtime benchmark,
classical baseline algorithm and problem type
matrix dimension
best and mean wall-clock time across repeated runs
benchmark_environment metadata including Python, NumPy, platform, timer, and a stability note for timing snapshots
residual, condition-number, or matrix-function metadata where applicable
optional QSVT resource proxy metadata for polynomial workflows

Plot Abbreviations¶

Benchmark plots use compact legend labels:

abbreviation	meaning
DLS	dense linear solve
CGS	conjugate gradient solve
DSMF	dense spectral matrix function
PME	polynomial matrix evaluation

CLI Workflow¶

qsvt benchmark dense-solve \
  --matrix "4,1;1,3" \
  --rhs "1,2" \
  --qsvt-poly "0,1" \
  --output dense-solve-benchmark.json

qsvt benchmark cg-solve \
  --matrix "4,1;1,3" \
  --rhs "1,2" \
  --tolerance 1e-10 \
  --qsvt-poly "0,1"

qsvt benchmark polynomial \
  --matrix "0.5,0;0,-0.25" \
  --poly "0,0,1"

Benchmark Notebooks¶

Benchmark notebooks live in notebooks/benchmarks/:

notebook	output
`01_linear_system_classical_vs_qsvt_proxy.ipynb`	dense and CG Poisson-system baselines
`02_matrix_functions_spectral_baselines.ipynb`	spectral and polynomial matrix-function baselines
`03_scaling_sweeps.ipynb`	dimension and inverse-degree benchmark sweeps
`04_classical_baseline_assumptions.ipynb`	timed baseline assumptions versus QSVT proxy fields

The generated notebook outputs are published on the Benchmark notebook outputs page.

Committed Artifacts¶

The current benchmark notebooks write JSON reports under results/benchmarks/ and compact CSV tables under results/tables/. Algorithm comparison artifacts that are not wall-clock benchmarks live under results/algorithms/ and share the same compact table directory.

artifact	contents
`linear_system_dense_solve.json`	dense direct solve baseline with QSVT proxy
`linear_system_cg_solve.json`	conjugate-gradient baseline with QSVT proxy
`matrix_function_exponential_spectral.json`	dense spectral exponential baseline
`matrix_function_thermal_polynomial.json`	polynomial thermal matrix-function baseline
`matrix_function_filter_polynomial.json`	polynomial filter matrix-function baseline
`scaling_sweep_reports.json`	combined dense/CG scaling sweep reports
`linear_system_benchmark_summary.csv`	compact linear-system benchmark table
`matrix_function_benchmark_summary.csv`	compact matrix-function benchmark table
`benchmark_scaling_summary.csv`	compact scaling-sweep benchmark table
`benchmark_plot_manifest.csv`	generated plot manifest for benchmark notebooks
`linear_system_comparison.json`	dense, CG, and QSVT-style linear-system comparison report
`linear_system_comparison_summary.csv`	compact linear-system comparison rows

Interpretation¶

The QSVT proxy fields summarize polynomial degree, phase-count proxy, signal-call proxy, and encoding width. They do not include block-encoding construction, state preparation, amplitude amplification, error correction, hardware compilation, or data-loading costs.

Use these reports to compare regimes and identify where a quantum implementation would need favorable block encoding, state preparation, and scaling assumptions.

For per-baseline assumptions, see Classical baseline details. For the proxy quantities attached to QSVT comparisons, see QSVT resource model.