Variational Quantum Algorithms: QAOA, VQE & Quantum Dynamics

Description

This project contains a comprehensive collection of implementations of variational quantum algorithms using Qiskit. Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches that leverage the variational principle to solve optimization and eigenvalue problems on near-term quantum devices. This repository includes practical implementations of two major VQA frameworks: the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE), along with explorations of quantum dynamics on the transverse-field Ising model.

Project Structure

File	Description
QAOA_Ising.ipynb	QAOA applied to the transverse-field Ising model
QAOA_tutorial.ipynb	Step-by-step QAOA tutorial with detailed explanations
vqe_example.ipynb	VQE demonstration with basic examples
vqe_molecule.ipynb	VQE for molecular ground state energy (H₂ molecule)
vqe_functions.py	Utility functions for VQE implementations
hydrogen_eigenvalues.ipynb	Eigenvalue computation for hydrogen systems
ising_eigenvalues.ipynb	Ising model eigenvalue analysis and comparisons
ising_dynamics.ipynb	Quantum dynamics of the Ising model
ising_ibm.ipynb	Running quantum circuits on IBM quantum hardware

Key Features

• Real IBM Hardware Integration: Demonstrates how to run quantum circuits on actual IBM quantum processors
• Optimization & Chemistry: Covers both combinatorial optimization (QAOA) and quantum chemistry applications (VQE)
• Complete Workflow: From theoretical foundations to practical implementations on quantum hardware
• Educational & Research-Grade: Suitable for learning VQAs and conducting quantum algorithm research

Technologies

• Qiskit: Open-source quantum computing framework
• Qiskit Aer: High-performance quantum simulator
• IBM Quantum: Access to real quantum hardware
• NumPy: Numerical computing
• SciPy: Scientific computing and optimization
• Matplotlib: Data visualization

Installation

Install the required dependencies:

pip install -r requirements.txt

Usage

Launch Jupyter Notebook to explore the notebooks:

jupyter notebook

Each notebook is self-contained and can be run independently. Start with QAOA_tutorial.ipynb or vqe_example.ipynb for introductory material.

Author

Thiago Girao - PhD candidate in Physics, researching quantum information and quantum computing.

References

• Cerezo, M., et al. (2021). "Variational quantum algorithms." Nature Reviews Physics, 3(9), 625-644.
• Farhi, E., Goldstone, J., & Gutmann, S. (2014). "A Quantum Approximate Optimization Algorithm." arXiv preprint arXiv:1411.4028.
• Aspuru-Guzik, A., Love, P. J., & Aspuru, R. (2005). "Simulated quantum computation of molecular energies." Science, 309(5741), 1704-1707.
• Qiskit Documentation: https://qiskit.org/documentation/
• IBM Quantum: https://quantum.ibm.com/

---

Last updated: March 2026