qsvt-pennylane 0.2.21

Educational utilities and examples for Quantum Singular Value Transformation (QSVT) using PennyLane.

Quantum Singular Value Transformation (QSVT)

Lightweight tools for experimenting with Quantum Singular Value Transformation (QSVT) and bounded polynomial transforms using PennyLane.

This repository combines:

• a notebook-first introduction to QSVT and QSP
• a reusable Python package for polynomial design, spectral transforms, and small PennyLane QSVT checks where the backend can synthesize the transform
• explicit polynomial realizability classification and phase-synthesis reports
• block-encoding specifications for matrices, PennyLane operators, and user-provided circuit factories
• reproducible examples for scalar, matrix, PDE, and small physics workflows

The focus is spectral intuition and reproducible validation: how bounded polynomials transform singular values or eigenvalues, what approximation error they incur on concrete finite instances, and which extra quantum assumptions would be needed to turn the polynomial core into a complete algorithm.

Links

• PyPI: qsvt-pennylane
• Website: project documentation
• Usage guide: USAGE.md
• Cookbook examples: examples/
• Theory notes: THEORY.md
• Results index: RESULTS.md
• Roadmap: ROADMAP.md
• Release checklist: RELEASING.md
• API reference: docs/qsvt/api_reference.md

Installation

Install from PyPI:

pip install qsvt-pennylane

Install from source:

git clone https://github.com/SidRichardsQuantum/Quantum_Singular_Value_Transformation.git
cd Quantum_Singular_Value_Transformation
pip install -e .

Requirements:

• Python >= 3.10
• PennyLane >= 0.42, < 0.46
• NumPy >= 1.23, < 3

Plotting helpers are optional:

pip install "qsvt-pennylane[plot]"

Quick Example

Apply a scalar polynomial transform:

from qsvt.qsvt import qsvt_scalar_output

result = qsvt_scalar_output(
    x=0.5,
    poly=[0, 0, 1],  # x^2
    encoding_wires=[0],
)

Design a bounded sign polynomial and keep the diagnostics:

from qsvt.stable import design_workflow

result = design_workflow(
    kind="sign",
    gamma=0.25,
    degree=13,
)

coeffs = result.coeffs
report = result.as_report()

Plan from a finite problem and a requested error instead of choosing a degree manually:

from qsvt.stable import QSVTProblemSpec, QSVTTransformSpec, plan_qsvt

plan = plan_qsvt(
    QSVTProblemSpec(np.diag([1.0, 2.0]), rhs=np.ones(2)),
    QSVTTransformSpec(
        "linear_system", tolerance=0.4, min_degree=3, max_degree=9
    ),
)

Run a finite problem workflow with a uniform report:

import numpy as np
from qsvt import qsvt_problem_workflow

result = qsvt_problem_workflow(
    "linear_system",
    np.diag([1.0, 2.0]),
    rhs=np.array([1.0, 1.0]),
    degree=12,
)

report = result.as_report()

Use the command line interface:

qsvt scalar --x 0.5 --poly "0,0,1"
qsvt phase-synthesis --poly "0,1,0,-0.5,0,0.333333"
qsvt boundedness-certificate --poly "0.996,0.1,-0.5"
qsvt phase-solver-benchmark --poly "0,1" --solvers root-finding --repeats 3
qsvt mixed-parity-synthesis --poly "0.5,0.5"
qsvt design-workflow --kind sign --gamma 0.2 --degree 13
qsvt design-sweep --kind sign --degrees "5,9,13,17" --gamma 0.2 \
  --no-synthesis --output sign-degree-sweep.json
qsvt resource-report --poly "0,0,1" --matrix-dimension 4 --no-synthesis
qsvt problem-workflow --target linear_system --matrix "2,0;0,1" \
  --rhs "1,1" --degree 8 --no-synthesis --no-qsvt
qsvt plan-workflow --target linear_system --matrix "2,0;0,1" \
  --rhs "1,1" --tolerance 0.2 --no-execute
qsvt degree-search --kind sign --gamma 0.2 --tolerance 0.05
qsvt spectral-filter-qsvt --pauli-terms "0.4:ZI,0.3:IZ,0.2:XI" \
  --state "0.5,0.5,0.5,0.5" --lower -0.4 --upper 0.4 --tolerance 0.16
qsvt poisson-qsvt --n-points 4 --tolerance 0.4
qsvt hamiltonian-simulation --matrix "0,1;1,0" \
  --state "1,0" --time 0.5 --degree 8
qsvt research-sweep --config examples/accuracy_resource_frontier.json \
  --output-dir /tmp/qsvt-accuracy-resource-frontier
qsvt accuracy-resource-frontier --degrees 3,5,7 --tolerances 0.2 \
  --output-dir /tmp/qsvt-accuracy-resource-frontier
qsvt execute-spec --kind matrix --matrix "0.2,0;0,0.8" \
  --poly "0,0,1" --state "1,0"
qsvt benchmark cg-solve --matrix "4,1;1,3" --rhs "1,2" --qsvt-poly "0,1"
qsvt examples

Run copy-pasteable cookbook scripts from the repository root:

python examples/design_apply_report.py --output /tmp/qsvt-design-apply.json
python examples/linear_system_compare.py \
  --output /tmp/qsvt-linear-system.json \
  --rows-output /tmp/qsvt-linear-system.csv
python examples/problem_workflow.py --output /tmp/qsvt-problem-workflow.json
python examples/threshold_filter.py --output /tmp/qsvt-threshold-filter.json
python examples/block_encoded_workflow.py \
  --output /tmp/qsvt-block-encoded-workflow.json
python examples/circuit_execution.py --output /tmp/qsvt-circuit-execution.json
python examples/block_encoding_execution.py \
  --output /tmp/qsvt-block-encoding-execution.json
python examples/rectangular_execution.py \
  --output /tmp/qsvt-rectangular-execution.json
python examples/spectral_filter_qsvt.py \
  --output /tmp/qsvt-spectral-filter.json
python examples/poisson_qsvt.py --output /tmp/qsvt-poisson.json
python examples/hamiltonian_simulation.py \
  --output /tmp/qsvt-hamiltonian-simulation.json
python examples/accuracy_driven_plan.py \
  --output /tmp/qsvt-accuracy-driven-plan.json
python examples/custom_block_encoding.py \
  --output /tmp/qsvt-custom-block-encoding.json
python examples/finite_shot_qsvt.py \
  --output /tmp/qsvt-finite-shot.json --shots 2000 --seed 12345
python examples/encoding_aware_resources.py \
  --output /tmp/qsvt-encoding-aware-resources.json \
  --rows-output /tmp/qsvt-encoding-aware-resources.csv

See USAGE.md for full Python and CLI workflows.

Package Map

The public package lives under src/qsvt.

module	purpose
qsvt.polynomials	Chebyshev utilities, parity checks, boundedness checks
qsvt.approximation	polynomial fitting and approximation error helpers
qsvt.design	task-oriented and physics matrix-function polynomial builders
qsvt.algorithms	end-to-end simulator-scale algorithm workflows
qsvt.block_encoding	finite dense block-encoding construction and verification
qsvt.execution	single-sequence and coherent component-LCU QNode execution for block-encoding specifications
qsvt.hardware	experimental finite-shot execution on caller-supplied PennyLane devices with local preflight and decomposition reports
qsvt.synthesis	realizability classification, parity decomposition, and phase synthesis
qsvt.presets	ready-made named bounded polynomial families
qsvt.workflow	combined coefficient, diagnostic, compatibility, and high-level problem workflows
qsvt.planning, qsvt.degree	typed problem planning and target-error degree selection
qsvt.flagship	executable Pauli spectral-filter and Poisson workflows
qsvt.acceptance	versioned acceptance contracts for the three flagship workflows
qsvt.stable	frozen compact facade for the remainder of the 0.x series
qsvt.research	experimental repository tooling for deterministic and resumable research sweeps
qsvt.research_frontier	experimental repository accuracy/resource frontier tooling
qsvt.reports	JSON-safe reports, schema checks, and plot helpers
qsvt.resources	polynomial proxies and encoding-aware logical resource estimates
qsvt.benchmarks	classical baselines and QSVT-oriented benchmark summaries
qsvt.comparisons	experimental HHL and quantum-walk comparisons and tutorials
qsvt.matrices	small Hermitian test matrices
qsvt.spectral	classical spectral matrix-function references
qsvt.qsvt	PennyLane QSVT wrappers and comparisons
qsvt.hamiltonians, qsvt.pde, qsvt.rescaling	small helpers supporting QSVT examples and validation
qsvt.diagnostics	application-level validation metrics

For detailed function-level documentation, use docs/qsvt/api_reference.md.

The package includes a py.typed marker so type checkers can consume the inline type annotations shipped with the public modules.

During the 0.x series, new applications should import from qsvt.stable. That module contains the frozen 20-name facade. qsvt.api_status(name) labels other root exports as compatibility or experimental; compatibility names remain importable and receive at least two minor releases of deprecation warning before removal. See API stability for the exact list and policy.

Roadmap

Finite coherent mixed-parity execution and all three flagship acceptance paths are now implemented. The immediate priorities are phase-synthesis robustness, block-encoding verification across access models, and hardening the coherent execution/report contracts. Hardware execution, noise-aware planning, and broader applications remain experimental or later work.

Physics and mathematics applications are thin clients of domain-general QSVT interfaces, not domain libraries maintained by the core package. HHL and quantum-walk implementations remain adjacent experimental comparisons. Research sweeps and aggregate plotting support repository benchmarks and are not part of qsvt.stable.

See ROADMAP.md for the current development direction.

Documentation

• USAGE.md: practical package and CLI workflows
• examples/: short cookbook scripts for common package workflows
• THEORY.md: QSVT, QSP, polynomial constraints, and spectral interpretation
• RESULTS.md: result-producing notebooks and reproducible artefact conventions
• docs/qsvt/tutorial_results.md: generated tutorial notebook outputs
• docs/qsvt/real_example_results.md: generated real-example notebook outputs
• docs/qsvt/benchmark_results.md: generated benchmark notebook outputs
• docs/qsvt/classical_baselines.md: classical benchmark assumptions and baseline details
• docs/qsvt/qsvt_resource_model.md: QSVT proxy-resource interpretation and omitted costs
• docs/qsvt/design.md: polynomial design helpers
• docs/qsvt/algorithms.md: workflow-level algorithm notes, diagnostics, and limitations
• docs/qsvt/planning.md: typed accuracy-driven planning, degree selection, and finite execution
• docs/qsvt/flagship_workflows.md: executable Pauli spectral-filter and Poisson workflows plus the three-workflow acceptance matrix
• docs/qsvt/stability.md: compact stable facade, compatibility tier, and deprecation policy
• docs/qsvt/research.md: experimental repository sweep tooling, deterministic artifacts, and the accuracy-resource frontier
• docs/qsvt/block_encoding.md: finite dense block encodings, normalization, verification, and omitted oracle costs
• docs/qsvt/compatibility.md: QSVT boundedness, parity, synthesis checks, and common failure modes
• docs/qsvt/presets.md: named polynomial preset families
• docs/qsvt/physics.md: Hamiltonian, PDE, rescaling, and matrix-function workflows
• docs/qsvt/implementation.md: implementation conventions, report serialization, and API status
• docs/qsvt/notebooks.md: tutorial, benchmark, and real-example notebook index

Current release: 0.2.21

Notebooks

Tutorial notebooks live in notebooks/tutorials/ and introduce QSVT as polynomial functional calculus, from scalar transforms through sign functions, projectors, matrix functions, reusable design workflows, end-to-end algorithm workflows, reproducible reports, degree/error tradeoff studies, and resource-proxy limitations. The accuracy-driven planning tutorial connects a requested error to degree search, phase synthesis, access-model selection, logical resources, and finite circuit execution. The workflow tutorial and three corresponding real examples also show the versioned flagship acceptance checks and distinguish stated-scope acceptance from full-QSVT acceptance.

Real physics examples live in notebooks/real_examples/. The curated eight-notebook gallery covers Poisson inversion, Hamiltonian simulation, Green's functions, Ising filtering, electronic occupations, topological band projectors, singular-value deblurring, and matrix-log graph entropy. Each notebook identifies the physical system, QSVT implementation strategy, and classical validation boundary.

Benchmark notebooks live in notebooks/benchmarks/ and compare classical linear-system, spectral, and polynomial matrix-function baselines against QSVT-oriented resource proxies and their underlying assumptions. The encoding-aware resource benchmark compares embedding, FABLE, PrepSelPrep, and qubitization for the same logical operator.

See docs/qsvt/notebooks.md for the full notebook map.

Notebook Result Workflow

Committed notebook outputs and generated result artefacts are the source of truth for the published documentation. GitHub Pages builds from committed docs/qsvt/*_results.md, results/plots/, and results/tables/ files; it does not execute notebooks during deployment.

Before committing notebook or result changes, run:

scripts/update_notebook_results.sh

Commit the updated notebooks, extracted plots, manifests, and generated result pages together. CI checks that the committed result pages and manifests can be regenerated from the committed notebook outputs without re-executing notebooks.

Packaging

PyPI distributions are package-focused: they include the importable qsvt package plus essential project metadata and root documentation. Full notebooks, rendered documentation, committed result snapshots, and regression tests remain in the GitHub repository and project website, where they can be audited and regenerated without making installs or source distributions unnecessarily large.

Truth Contract

The package is designed to be useful for education, research prototyping, and small real physics/math case studies, but its claims are deliberately scoped.

Implemented and tested:

• dense spectral polynomial references for finite matrices,
• bounded polynomial design and sampled diagnostics,
• simulator-scale workflows for linear systems, filters, matrix functions, resolvents, Gibbs weights, spectral density, and projectors,
• tolerance-driven planning from matrices, PennyLane operators, and block-encoding specifications,
• executable Pauli-LCU spectral filtering and finite-difference Poisson direct/CG/QSVT comparisons with component error ledgers,
• PennyLane QSVT block checks for supported small compatible polynomials,
• PennyLane QNode execution for finite QSVT circuits with state preparation, queued qml.qsvt, statevector/probability measurement, and circuit resource metadata,
• lower-level QSVT execution from dense, rectangular, PennyLane-operator, and custom-circuit block-encoding specifications, including caller-supplied signal projectors and structured backend failures,
• coherent even/odd and complex component-LCU execution using forward and adjoint QSVT sequences, selector ancillas, measured postselection probabilities, and component circuit-resource ledgers,
• finite coherent-QSVT Hamiltonian simulation with cosine/sine sequence combination and full stated-scope flagship acceptance,
• finite-shot QSVT execution on caller-supplied PennyLane devices with caller-supplied preparation circuits, local preflight checks, probability measurements, shot-noise uncertainty fields, logical resource summaries, and credential-free provider/fake-backend metadata capture,
• non-executing hardware circuit audit reports that expose logical and decomposed operation sequences plus unsupported-operation checks before spending shots,
• classical benchmark baselines plus QSVT-oriented proxy metadata.

Reported as assumptions or proxies:

• scalable block-encoding availability beyond the reported finite or logical access model,
• input-state preparation and data loading,
• measurement/readout and amplitude amplification,
• fault-tolerant synthesis, error correction, provider-native hardware compilation, and provider job management,
• end-to-end runtime or quantum advantage claims.

Hardware-oriented execution is now an experimental package layer for small finite-shot circuits on caller-created PennyLane devices. It performs local preflight checks before execution, records provider/fake-backend metadata when devices expose it, checks advertised native operations and shot limits, and records compilation fields explicitly. Provider credential management, paid submission, native compilation, job persistence, calibration capture, and mitigation remain outside the portable report schema.

Every high-level algorithm, direct QSVT comparison, resource, and benchmark report includes a truth_contract field. Circuit execution reports separately state when a QNode was actually executed. The fields state the implemented dense-polynomial, small-backend check, or QNode path, the conditional QSVT interpretation, and the omitted quantum components. Resource reports are proxy summaries, not hardware estimates; benchmark reports time only the classical baseline path and include benchmark_environment metadata for interpreting timing snapshots.

Stable algorithm reports derive an execution_tier and per-polynomial polynomial_evidence from the artifacts returned by that run. The evidence records the design and QSVT certification domains, output prefactor, extrema-based boundedness certificate, parity, single-sequence realizability, and any parity-decomposition requirement. A successful backend call alone does not promote a polynomial to the qsvt_circuit tier when the polynomial lacks a QSVT realizability certificate.

New algorithm reports emit qsvt-algorithm-workflow schema 1.1. Legacy schema 1.0 reports remain loadable and can be migrated when their saved polynomial coefficients are sufficient to derive the 1.1 evidence.

Scope

This project is intentionally educational, explicit, research-oriented, and polynomial-focused. Its hardware-oriented execution layer is for small auditable finite-shot experiments, not production hardware optimization.

It does not aim to provide production-scale circuit optimization, fault-tolerant constructions, amplitude amplification, or problem-specific scalable state preparation methods. The emphasis is understanding how polynomial transforms act on spectra and how finite QSVT circuits behave under explicit simulator or caller-supplied device execution.

Support

If this repository is useful for research, learning, or experimentation, you can support continued development through GitHub Sponsors.

Author

Sid Richards

• GitHub: SidRichardsQuantum
• LinkedIn: Sid Richards

License

MIT License. See LICENSE.