Add Quantum Haar Wavelet Transform as a PennyLane template

[deepakg-2511]

I would like to contribute a Quantum Haar Wavelet Transform as a reusable PennyLane template. The template implements the Haar wavelet transform as a unitary quantum circuit acting on n qubits, enabling multiresolution analysis of quantum states in the computational basis.

Wavelet transforms are a fundamental tool in multiscale signal processing and numerical analysis. A quantum Haar wavelet circuit can be useful for:

• Quantum signal processing
• Quantum PDE solvers
• Multiscale quantum machine learning
• Compression and sparsity-aware quantum algorithms

Currently, PennyLane does not provide a wavelet-based circuit template.

Theoretical Reference

A. Fijany and C. P. Williams,
Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits,
Lecture Notes in Computer Science, vol. 1509, 1998.
DOI: 10.1007/3-540-49208-9_2

The proposed template follows the explicit circuit constructions for the quantum Haar wavelet transform presented in this work.

Prototype Implementation

A working prototype implemented in PennyLane is available at: https://github.com/deepakg-2511/quantum-wavelet-transforms

The prototype includes:

• Quantum Haar wavelet circuits
• Validation against classical Haar wavelets
• Numerical checks for norm preservation and unitarity

Tests

• Circuit execution within PennyLane QNodes
• Norm preservation (‖ψ‖₂ invariance)
• Comparison with classical Haar wavelet coefficients for small systems

[CatalinaAlbornoz]

Hi @deepakg-2511 ,

Thanks for proposing this contribution! This looks like it would be really useful indeed. Our team has some core tasks they need to prioritize at the moment so they may take some time to review your suggestion and come back with next steps. Note that this is in our queue though so we'll get to it as soon as we can 🙏 .

[deepakg-2511]

Hi @CatalinaAlbornoz ,

Thanks for the update!
I appreciate it, and I’m happy to wait. Please let me know if you need anything from my side.