PFTM - Python

Projection Friendly Tree Mapping - improvement on the quantum fermionic boundary operator circuit. Quantum paper for PhD in progress.

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Projection-Friendly Tree Mapping (PFTM)

Short-depth fermionic mappings for quantum topological algorithms.

This repository accompanies the paper:

Projection-Friendly Tree Mapping: A Log-Depth Fermionic Operator Mapping for Quantum Circuits
(K. Naidoo, 2025, draft in preparation)

It provides:

• Python code (with optional pytket) to construct and measure circuit depths for the Projection-Friendly Tree Mapping (PFTM) and compare against the Jordan–Wigner (JW) mapping. This code is an improvement on the quantum circuit first announced in the paper - Representation of the fermionic boundary operator - Akhalwaya et al. - publish in 2022 in Physical Review A - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.106.022407
• Reproducible evidence that PFTM reduces worst-case depth from O(n) (JW) to O(log n), while preserving bitwise projectors required for topological quantum algorithms (QTDA).

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Background

Many quantum algorithms in Topological Data Analysis (TDA) and quantum chemistry require fermionic operator mappings.

• Jordan–Wigner (JW)

  • Simple, local definition.
  • Circuit depth grows linearly with n because parity strings are computed serially.

• Bravyi–Kitaev (BK)

  • Logarithmic depth.
  • But complicates projector structure: weight-(k) projections (P_k) become expensive.

• Projection-Friendly Tree Mapping (PFTM)

  • Achieves O(log n) depth using a binary-tree parity network.
  • Preserves bitwise projector semantics: (P_k = \sum_{|x|=k} |x\rangle\langle x|) remains trivial.
  • Supports restricted boundary operators for chain complexes in QTDA.

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Repository Structure

├── code/
│   ├── pftm_vs_jw_depth.py # Python driver: builds JW/PFTM depth models
│   ├── requirements.txt    # Dependencies (numpy, pandas, matplotlib, optional pytket)
│   └── examples/           # Example outputs, plots, circuit screenshots
├── README.md               # This file
└── LICENSE