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 >= 0.36
• NumPy >= 1.23
• Matplotlib >= 3.7

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.workflow import design_workflow

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

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

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 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

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 polynomial builders
qsvt.algorithms	end-to-end simulator-scale algorithm workflows
qsvt.block_encoding	finite dense block-encoding construction and verification
qsvt.execution	QNode execution for matrices and block-encoding specifications
qsvt.hardware	finite-shot execution on caller-supplied PennyLane devices with preflight and provider/fake-backend metadata reports
qsvt.synthesis	realizability classification, parity decomposition, and phase synthesis
qsvt.templates	ready-made bounded polynomial families
qsvt.workflow	combined coefficient, diagnostic, compatibility, and high-level problem workflows
qsvt.reports	JSON-safe reports, schema checks, and plot helpers
qsvt.resources	degree, phase-count, width, and compatibility proxy reports
qsvt.benchmarks	classical baselines and QSVT-oriented benchmark summaries
qsvt.notebook	experimental notebook presentation and path helpers used by committed notebooks
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	reusable physics and PDE helpers
qsvt.matrix_functions, qsvt.diagnostics	matrix-function designs and 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, qsvt.api_status(name) labels exported names as stable or experimental. Workflow-level helpers and report/export utilities are the most stable user-facing surface; lower-level circuit execution and backend-adapter helpers remain experimental while the package approaches a 1.0 API.

Roadmap

The project is moving toward general package workflows that users can apply to specific physics and mathematics problems from thin client notebooks. Core helpers should stay reusable across domains; notebooks should focus on problem setup, parameter choices, and interpretation.

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/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/templates.md: template polynomial 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: 0.2.15

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.

Real physics examples live in notebooks/real_examples/ and cover Hamiltonian simulation, ground-state filtering, quantum chemistry, Green's functions, spectral density estimation, Gibbs states, PDE systems, transport physics, spin-chain diagnostics, electronic occupations, singular-value inverse problems, matrix-log graph entropy, photonic band gaps, graphene density of states, topological band projectors, and tensor-network hybrid filtering. Each real-example notebook includes a near-top orientation block for the system, QSVT implementation strategy, and quantum relevance.

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.

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,
• 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,
• 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:

• block-encoding availability and query cost,
• 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.

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.