GSoC2026: An Alternative Approach to Spin Hamiltonians

[RichRick1]

📚 Package Description and Impact

This project aims to enhance the Model Hamiltonian package by implementing a new spin representation system. The current implementation's limitations in handling certain spin operators will be addressed through a more flexible and comprehensive approach, enabling support for general XYZ Heisenberg models.

👷 What will you do?

You will implement a direct spin modeling system using creation and annihilation operators. The key components include:

• Implementation of spin operators ($S_k^+$, $S_k^-$, $S^Z_k$)
• Handling of maximum seniority states
• Support for different $N_\alpha$ and $N_{\beta}$ electron configurations
• Verification of spin algebra commutation relations

🏁 Expected Outcomes

1. Implement new spin operator representations

$$ \begin{align*} S_k^+ &= a_{k\alpha}^\dagger a_{k\beta} \\ S_k^- &= a_{k\beta}^\dagger a_{k\alpha} \\ S^Z_k &= \tfrac{1}{2}\left(a_{k\alpha}^\dagger a_{k\alpha}-a_{k\beta}^\dagger a_{k\beta} \right) \end{align*} $$

2. Develop support for general XYZ Heisenberg models
3. Write comprehensive documentation for the new spin representation system

Required skills	Python, Linear Algebra, Quantum Mechanics
Preferred skills	Experience with quantum chemistry, familiarity with spin operators
Project size	90 hours, Small
Difficulty	Medium 🤓

🙋 Mentors

Valerii Chuiko	valerachuiko_at_gmail_dot_com	@RichRick1
Paul Ayers	ayers_at_mcmaster_dot_ca	@PaulWAyers

[iamkagwe]

Sounds cool ⚛️! Would love to work on this, I've sent an email.

[Sanjana1-Shiva]

Hello,

I’ve been reading through the ModelHamiltonian repository and the GSoC 2026 project idea about an alternative approach to spin Hamiltonians.

Previously I worked on a small quantum simulation project using Qiskit where we modeled reaction pathways using Hamiltonian operators, so this topic is particularly interesting to me.

While going through the repository I started exploring how spin Hamiltonians are currently represented in the codebase and exploring how an alternative representation might improve flexibility or computational efficiency.

Before digging deeper into the implementation, I wanted to ask if there are particular parts of the codebase you would recommend studying first for contributors interested in this project.

I’m currently setting up the environment and exploring the existing tests and examples.

Thank you for your time.