Notebooks

The repository includes notebook-first examples that introduce QSVT and QSP concepts step by step, followed by real physics workflows and classical benchmark notebooks that reuse the package APIs.

Notebook outputs

The rendered results pages are generated from the embedded outputs of these notebooks:

notebook set	generated output page	source directory
tutorials	Tutorial notebook outputs	notebooks/tutorials/
real physics examples	Real-example notebook outputs	notebooks/real_examples/
benchmarks	Benchmark notebook outputs	notebooks/benchmarks/

Benchmark notebooks are package-client workflows that write JSON/CSV artifacts under results/benchmarks/ and results/tables/; their plots are extracted to results/plots/benchmarks/.

For the compact result summary and regeneration commands, see Results.

Tutorial notebooks

Tutorial notebooks live in notebooks/tutorials/.

notebook	focus
tutorials/01_QSVT_Scalar_and_Diagonal_Matrix.ipynb	scalar and diagonal QSVT transforms
tutorials/02_QSVT_Singular_Value_Filter.ipynb	singular-value filtering
tutorials/03_QSP_Polynomial_Demo.ipynb	QSP polynomial behaviour
tutorials/04_QSVT_Linear_Solver_2x2.ipynb	small linear-solver intuition
tutorials/05_QSVT_Linear_Solver_4x4.ipynb	larger diagonal linear-solver experiment
tutorials/06_QSVT_Linear_Solver_Approximate.ipynb	approximate inverse-like transforms
tutorials/07_QSVT_Polynomial_Design_and_Approximation.ipynb	polynomial design and approximation
tutorials/08_QSVT_Matrix_Functions_Powers_and_Roots.ipynb	matrix functions, powers, and roots
tutorials/09_QSVT_Sign_Function_and_Projectors.ipynb	sign functions and projectors
tutorials/10_QSVT_Design_and_Templates.ipynb	design helpers and templates
tutorials/11_QSVT_Algorithm_Workflows.ipynb	QSVT algorithm workflow diagnostics
tutorials/12_QSVT_Reports_CLI_and_Artifacts.ipynb	QSVT reports, CLI output, and reproducible artifacts
tutorials/13_QSVT_Design_Tradeoffs.ipynb	QSVT design degree/error/boundedness tradeoffs
tutorials/14_QSVT_Resource_Proxy_Limits.ipynb	block-encoding assumptions and QSVT resource-proxy limits
tutorials/15_Block_Encoded_QSVT_Workflow.ipynb	finite block-encoded QSVT workflow
tutorials/16_Sparse_Oracle_Assumptions.ipynb	sparse operators, oracle assumptions, and omitted costs
tutorials/17_QSVT_Compatibility_Failure_Cases.ipynb	boundedness, parity, and QSVT compatibility failures
tutorials/18_QSVT_Linear_System_Comparisons.ipynb	dense, CG, and QSVT-style linear-system comparison rows
tutorials/19_HHL_Linear_System_Solver.ipynb	finite simulator-scale HHL linear-system solver

Benchmark notebooks

Benchmark notebooks live in notebooks/benchmarks/.

notebook	focus
benchmarks/01_linear_system_classical_vs_qsvt_proxy.ipynb	dense and CG linear-system baselines with QSVT inverse-polynomial resource proxies
benchmarks/02_matrix_functions_spectral_baselines.ipynb	dense spectral and polynomial matrix-function baselines for thermal/filter workflows
benchmarks/03_scaling_sweeps.ipynb	dimension, conditioning, and inverse-degree sweeps for compact benchmark tables
benchmarks/04_classical_baseline_assumptions.ipynb	what classical benchmark helpers time versus what QSVT proxy fields estimate

Real physics examples

Real physics examples live in notebooks/real_examples/. Each notebook now starts with a short orientation block that identifies the physical system, the QSVT-style implementation used, and the classical reference or quantum-relevance context for the toy-scale example.

notebook	focus
01_ground_state_filtering.ipynb	ground-state filtering
02_tight_binding_band_filter.ipynb	tight-binding band filters
03_imaginary_time_filtering.ipynb	imaginary-time filtering
04_heat_equation_pde.ipynb	heat-equation PDE workflow
05_poisson_equation_pde.ipynb	Poisson-equation PDE workflow
06_hamiltonian_simulation_schrodinger_dynamics.ipynb	Hamiltonian simulation
07_quantum_chemistry_h2_toy_solver.ipynb	H2 toy chemistry solver
08_greens_function_response.ipynb	Green’s-function response
09_spectral_density_estimation.ipynb	spectral density estimation
10_gibbs_state_thermal_weights.ipynb	Gibbs-state thermal weights
11_transport_physics_landauer_chain.ipynb	transport physics and Landauer chains
12_tensor_network_hybrid_filtering.ipynb	tensor-network hybrid filtering
13_heat_equation_2d_pde.ipynb	2D heat-equation PDE workflow
14_advection_diffusion_pde.ipynb	advection-diffusion PDE workflow
15_wave_equation_dynamics.ipynb	wave-equation dynamics
16_helmholtz_equation_pde.ipynb	Helmholtz-equation PDE workflow
17_quantum_walk_search_toy.ipynb	quantum-walk search toy model
18_ssh_chain_edge_state_filtering.ipynb	SSH-chain edge-state filtering
19_anderson_localization.ipynb	Anderson localization
20_schrodinger_bound_states.ipynb	Schrödinger bound states
21_quantum_harmonic_oscillator_grid.ipynb	harmonic-oscillator grid spectrum
22_electrostatic_green_function_poisson.ipynb	electrostatic Green’s function
23_coupled_oscillator_normal_modes.ipynb	coupled-oscillator normal modes
24_ising_phase_transition_filtering.ipynb	Ising phase-transition filtering
25_diffusion_heat_treatment_slab.ipynb	diffusion-limited heat treatment
26_graphene_nanoribbon_density_of_states.ipynb	graphene nanoribbon density of states
27_fermi_dirac_electronic_occupations.ipynb	Fermi-Dirac electronic occupations
28_photonic_crystal_band_gap_filtering.ipynb	photonic-crystal band-gap filtering
29_topological_band_projector_chern_marker.ipynb	topological band projectors and Chern markers
30_block_encoded_laplacian_smoothing.ipynb	block-encoded QSVT Laplacian smoothing

See the repository notebook directory for executable files: notebooks.