qsvt-pennylane documentation

qsvt-pennylane is a lightweight Python package for exploring Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP) using PennyLane.

The package provides small, explicit utilities for:

  • constructing bounded polynomials suitable for QSVT

  • approximating functions on bounded spectral intervals

  • building simple Hermitian test matrices

  • applying classical spectral matrix functions

  • extracting explicit QSVT transforms using qml.qsvt

  • comparing classical polynomial transforms with QSVT outputs

  • reporting QSVT-vs-classical transform error

  • building task-oriented polynomial designs

  • reusing ready-made polynomial templates

  • reporting fit error and boundedness for polynomial builders

  • saving, loading, and plotting diagnostics reports

The repository also includes a sequence of notebooks that introduce QSVT concepts step-by-step.

Documentation overview

Theory

Mathematical background and conceptual overview:

  • polynomial constraints for QSVT

  • block-encoding intuition

  • spectral transformations

  • inverse-like behaviour via bounded polynomials

  • projectors and sign functions

See: Theory

API reference

Detailed reference for the Python package:

  • module structure

  • function descriptions

  • input and output conventions

  • minimal usage examples

See: API reference

Package structure


qsvt
├── polynomials.py
├── approximation.py
├── matrices.py
├── spectral.py
├── design.py
├── templates.py
├── reports.py
├── qsvt.py
└── __main__.py

Each module is intentionally small and focused:

module

purpose

polynomials

Chebyshev utilities and polynomial helpers

approximation

bounded polynomial approximation tools

matrices

small Hermitian test matrices

spectral

classical spectral matrix functions

design

task-oriented bounded polynomial builders

templates

ready-made bounded polynomial families

reports

diagnostics serialization and plotting helpers

qsvt

PennyLane QSVT wrappers

__main__

command line interface

Relationship between notebooks and package

The notebooks provide conceptual explanations and worked examples.

The package extracts reusable components from these notebooks into a stable importable interface.

Typical workflow:

  1. read notebook explanation

  2. experiment interactively

  3. reuse helpers from qsvt

  4. build new examples or approximations

Minimal example

from qsvt.qsvt import qsvt_scalar_output
from qsvt.polynomials import chebyshev_t

# polynomial transform via QSVT
result = qsvt_scalar_output(
    0.5,
    [0, 0, 1],
    encoding_wires=[0],
)

print(result)

Command line interface

The package also provides a small CLI:

qsvt scalar --x 0.5 --poly "0,0,1"

qsvt diag \
  --values "1.0,0.7,0.3,0.1" \
  --poly "0,0,1" \
  --wires 3

qsvt cheb --degree 3 --x 0.5

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

qsvt compatibility-report --poly "0,0,1"

qsvt design-compatibility \
  --kind sign \
  --degree 13 \
  --gamma 0.2

qsvt compare-report \
  --values "1.0,0.7,0.3,0.1" \
  --poly "0,0,1" \
  --wires 3

qsvt matrix-report \
  --matrix "0.31351701,-0.23499807;-0.23499807,0.68648299" \
  --poly "0,0,1"

qsvt apply-design \
  --kind sign \
  --values="-0.8,-0.3,0.3,0.8" \
  --degree 13 \
  --gamma 0.2 \
  --wires 3

Scope

This project focuses on:

  • clarity of spectral intuition

  • explicit small-dimensional examples

  • polynomial mechanism understanding

  • reproducible notebook workflows

It does not aim to implement production-scale quantum linear solvers or hardware-optimised circuits.