Quantum-Accelerated SCF-DFT Simulation Using QSVT and QCBM

🌍 Vision and Social Impact

This project was developed as part of the [Hackathon Initiative – Team 6], aiming to explore how cutting-edge quantum computing tools can be harnessed to create technologies for the public good.

Our simulation platform is a technical proof-of-concept that connects quantum machine learning and computational chemistry to potential real-world use cases such as:

• Designing new sustainable materials
• Modeling electronic behavior for next-gen electronics
• Accelerating scientific discovery with fewer resources

By democratizing access to quantum-accelerated simulation tools and integrating intuitive quantum–classical workflows, we contribute to building a more inclusive and future-ready computational science toolkit.

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📘 Overview

This project implements and extends the methodology described in:

"Quantum-Accelerated Self-Consistent Field Method for Real-Space DFT Using QSVT"
Mohamed Lamane et al., arXiv:2307.07067
https://arxiv.org/abs/2307.07067

We reproduce the core framework of the paper and expand it by:

• Integrating generative quantum circuits (QCBMs),
• Estimating conductivity via DOS,
• Structuring it into a Colab-friendly, educational platform.

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🎯 Objective

Our primary technical goals are:

• Simulate a real-space self-consistent field (SCF) loop for DFT,
• Approximate the Fermi–Dirac function ( f(H) ) using Chebyshev polynomials (QSVT-inspired),
• Compute electron densities iteratively until convergence,
• Estimate material conductivity via the density of states (DOS),
• Generate and benchmark candidate densities using a Quantum Circuit Born Machine (QCBM).

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🧪 Methods Implemented

1. Molecular Hamiltonian Construction

• Built using pennylane.qchem.Molecule
• Basis set: STO-3G
• Supports both test cases (e.g., LiH) and complex systems (e.g., Cu₂–C₆)

2. QSVT-Inspired Fermi–Dirac Filtering

• Approximates: [ f(H) = \frac{1}{1 + e^{\beta(H - \mu)}} \approx \sum_k c_k T_k(H) ]
• Chebyshev polynomials are used to simulate QSVT filtering in a classical setting

3. Self-Consistent Field (SCF) Loop

• Uses filtered density to update the Hamiltonian iteratively
• Simple local potential ( V[n] = \alpha \cdot \text{diag}(n) ) is used for updating ( H[n] )
• Loop terminates when density change falls below a threshold

4. Quantum Circuit Born Machine (QCBM)

• 4-qubit variational quantum circuit (VQC) with entanglement and rotation layers
• Produces synthetic densities for benchmarking or future inverse-design tasks

5. Density of States (DOS) and Conductivity

• Eigenvalue histogram of ( H[n] ) used to estimate DOS
• Conductivity is approximated by evaluating: [ \sigma \propto g(E_F) ] where ( g(E_F) ) is the DOS at the Fermi level

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🔁 Workflow Summary

[Input Geometry]
      ↓
[Build Hamiltonian H₀]
      ↓
[Apply Chebyshev Filter f(H)]
      ↓
[Extract Density n(rⱼ)]
      ↓
[Update H[n]] → repeat until convergence
      ↓
[Estimate DOS & Conductivity] + [QCBM Sampling for Comparison]

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📊 Results

• Visual and numerical comparison of QSVT-SCF-derived density vs QCBM-generated samples
• Density of States (DOS) plots for conductivity inference
• Demonstrated convergence of SCF loop in 5–20 iterations for various systems

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📂 File Structure

├── main_notebook.ipynb        # Full simulation pipeline (Colab-compatible)
├── README.md                  # Project documentation
└── data/
    └── cached_H.npy           # Optional: saved Hamiltonians for faster reruns

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🎥 Presentation

You can view the full presentation here:
https://www.canva.com/design/DAGs1gttXeY/EdGxj6zRi65g-7BG9pG0Aw/edit?utm_content=DAGs1gttXeY&utm_campaign=designshare&utm_medium=link2&utm_source=sharebutton

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📚 References and Related Work

1. Lamane et al. (2023) – Quantum-Accelerated SCF for DFT via QSVT.
   arXiv:2008.06449

2. Pix2Pix–YOLOv7 with mmWave Radar for Object Detection – RSC Advances (2023).
   Link

3. QML-Accelerated Real-Space DFT – Applied Sciences, 14(20), 9273 (2024).
   MDPI

4. Quantum-Enhanced Electronic Structure Modelling – Magnetic Resonance in Chemistry (2024).
   Wiley Online Library

5. Ko et al. (2023) – DFT on Quantum Computers with Linear Scaling w.r.t. Number of Atoms.
   arXiv:2307.07067

6. Gorsse et al. (2023) – Mechanical Properties and Electrical Conductivity of Copper-Based Alloys.
   Scientific Data, 10, Article 504.
   Nature

7. World Bank (2025) – Electric power transmission and distribution losses (% of output).
   World Bank Indicator EG.ELC.LOSS.ZS

8. United Nations (2015) – Sustainable Development Goals (SDGs).
   UN SDGs

🧠 Credits

This work was developed as part of a hackathon initiative (Team 6), with the broader goal of empowering researchers, educators, and developers to integrate quantum acceleration into real-world scientific simulations — from materials discovery to energy systems.

We are committed to accessible, interpretable, and ethically-aligned quantum computing.