This project demonstrates how Quantum Computing can be applied to real-world financial problems. Specifically, it uses the Quantum Approximate Optimization Algorithm (QAOA) to solve a Portfolio Optimization problem, comparing the quantum results against a Classical Exact Eigensolver.

The Business Problem: Given a basket of 4 tech stocks (AAPL, MSFT, GOOGL, AMZN), historical market data, and a specific risk/return appetite, what is the mathematically optimal combination of exactly 2 stocks to hold?

The Quantum Solution: We formulate this as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solve it using IBM's Qiskit framework.

Because QAOA is a probabilistic algorithm, running the quantum circuit yields a distribution of probabilities for all possible portfolio combinations.

(Note: Binary strings represent asset selection. e.g., 0110 means buy GOOGL and AMZN)

1. Classical Benchmark: The classical exact solver identified the absolute optimal portfolio based on our risk/return parameters.
2. Quantum Alignment: The QAOA quantum simulation successfully identified high-probability states that align perfectly with the classical solution.
3. Constraint Penalties: The visualization shows how the algorithm navigates "penalties" (picking too many or too few stocks), demonstrating the behavior of quantum heuristic optimization.

• Language: Python
• Quantum Framework: Qiskit, Qiskit-Finance, Qiskit-Optimization
• Classical Math/Data: NumPy, Pandas, Yahoo Finance (yfinance)
• Visualization: Matplotlib

1. Clone the repository

git clone https://github.com/rupajietishere/Quantum-Portfolio-Optimization.git
cd quantum-portfolio-optimization

2. Install dependencies

pip install -r requirements.txt

3. Run the Jupyter Notebook

jupyter notebook portfolio_qaoa.ipynb

The problem utilizes Markowitz's Mean-Variance Portfolio Theory. We aim to minimize the objective function:

$$ \min_{x} \left( q \cdot x^T \Sigma x - (1-q) \cdot \mu^T x \right) $$

Where:

• $x \in {0, 1}^n$: Binary decision variables (Buy / Don't Buy)
• $\mu$: Expected returns of the assets
• $\Sigma$: Covariance matrix (Risk)
• $q$: Risk factor tolerance

We apply a penalty to enforce a hard budget constraint (exactly 2 assets must be chosen).