Project 2: Quantum for Portfolio Optimization

📝 About This Repository

This repository is a remake of the original project, independently developed by me as part of my continuous learning and improvement efforts. While this version includes significant modifications, enhancements, and reanalysis, the original project was a collaborative team effort, with Aung Phone Kyaw contributing alongside me.

Credits:

• Remake Project: Developed by La Wun Nannda
• Original Project: Developed by the NaiveQuantum team
• Original Project Repository: click here

This remake represents my own work and contributions while honoring the collaborative foundation of the original project.

👥 Team

Name: NaiveQuantum

Members:

Name	WISER Enrollment ID
La Wun Nannda	gst-9Znx386rMl8rJMQ
Aung Phone Kyaw	gst-lXnHQNnvqFrUrS6

📋 Project Summary

This project implements a comprehensive comparative study of quantum computing techniques for portfolio optimization, specifically addressing the task of selecting optimal bond portfolios from a universe of 31 fixed income securities. We employ Variational Quantum Algorithms (VQAs) with the Variational Quantum Eigensolver (VQE) and Conditional Value-at-Risk (CVaR) optimization to solve this complex financial optimization problem.

The core challenge involves minimizing the difference between a portfolio's characteristics and target values while satisfying various constraints. Traditional classical optimization methods face computational challenges as problem size scales, making quantum computing an attractive alternative through its inherent ability to explore large solution spaces efficiently using quantum superposition and entanglement.

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🔬 PART A. Main Research Focus

Our comparative analysis aims to identify the best quantum optimization strategy based on the following research questions:

1. "Quantum vs. Hybrid": Does classical post-processing help reach target quality faster?
2. "Lightweight Deep vs. Heavyweight Shallow": Does parameter efficiency or circuit depth matter for solution quality?
3. Speed to Target Quality: Which configuration reaches the standardized solution quality fastest?
4. Other Factors: What additional factors are likely to affect the performance of each approach?
5. Computational Efficiency: Which approach minimizes computational cost while maintaining throughput?

⚡ Four Approaches

To answer these questions, we designed four distinct quantum configurations that systematically vary key algorithmic parameters:

1. Lightweight Quantum: BFCD ansatz with bilinear entanglement (high reps)
2. Lightweight Hybrid: BFCD ansatz with bilinear entanglement + Local Search (high reps)
3. Heavyweight Quantum: TwoLocal ansatz with full entanglement (low reps)
4. Heavyweight Hybrid: TwoLocal ansatz with full entanglement + Local Search (low reps)

🔍 Role of Local Search

Local Search is a post-processing technique that performs classical optimization on the quantum solution, potentially helping reach target quality faster by:

• Bit-flip optimization: Systematically testing single-bit changes
• Local neighborhood search: Exploring nearby solutions
• Classical refinement: Using classical methods to polish quantum results

⚙️ Technical Implementations

Our approach uses a QUBO (Quadratic Unconstrained Binary Optimization) formulation that transforms the original linear programming (LP) problem into a format suitable for VQAs. The conversion process involves constraint handling and objective function reformulation to ensure effective quantum algorithm exploration.

1. Lightweight Quantum

• Ansatz: BFCD ansatz with bilinear entanglement
• Rationale: BFCD ansatz uses specialized RZZ gates with optimized rotation patterns, making it inherently more parameter-efficient. Bilinear entanglement provides structured connectivity while minimizing gate count.
• Parameters: High reps (3) for deep circuit exploration

2. Lightweight Hybrid

• Ansatz: BFCD ansatz with bilinear entanglement + Local Search post-processing
• Rationale: Combines BFCD's parameter efficiency with classical local search refinement
• Parameters: High reps (3) + Local Search optimization

3. Heavyweight Quantum

• Ansatz: TwoLocal ansatz with full entanglement
• Rationale: TwoLocal ansatz uses standard rotation gates with more parameters but shallower circuits. Full entanglement captures maximum correlations between bonds.
• Parameters: Low reps (2) to balance resource usage

4. Heavyweight Hybrid

• Ansatz: TwoLocal ansatz with full entanglement + Local Search post-processing
• Rationale: Combines full entanglement's correlation capture with classical optimization
• Parameters: Low reps (2) + Local Search optimization

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⚛️🖥️ PART B. Extended Research Focus: Real Quantum Hardware

1. Real Hardware Performance: How does real quantum hardware performance compare to classical simulation in terms of execution time, computational resource requirements, and solution quality?
2. Feasibility: Based on the findings, is real quantum hardware currently feasible for portfolio optimization?

⚡ Two Approaches

To answer these questions, we designed two versions of the best approach found in Part A:

1. Best approach with AerSimulator (baseline simulation)
2. Best approach with real quantum hardware (IBM chosen as hardware provider)

⚠️ Limitations

The 31-bond portfolio optimization problem is too large and complex for IBM's free-tier real quantum hardware, as the 10-minute monthly limit cannot accommodate the full 31-qubit execution, requiring tradeoffs in implementation.

📌 Priority Ranking for Tradeoffs

1. More bonds (qubits)

   • More realistic problem representation and better portfolio diversity
   • Deeper circuits and longer runtime requirements
   • Problem size directly affects solution quality and practical applicability
   • Priority: high

2. More shots

   • Better CVaR estimate accuracy and statistical reliability
   • Longer per-iteration execution time
   • Critical for risk assessment but can be optimized through smart sampling
   • Priority: medium

3. More epochs/iterations

   • Better solution space exploration and convergence
   • Longer total runtime and higher computational costs
   • Classical local search can compensate for fewer quantum epochs
   • Priority: low

For portfolio optimization, bonds (problem size) matter most. The quantum-classical hybrid approach allows trading quantum epochs for classical local search optimization, but missing bonds cannot be recovered in post-processing. This means reducing the number of bonds significantly impacts the problem's realism and practical value.

⚙️ Technical Implementations

Given these constraints, the approach focuses on strategic parameter adjustments to maximize performance within hardware limitations:

• Reduced bonds: 31 bonds to 10 bonds
• Reduced shots: 1024 shots to 512 shots
• Reduced quantum epochs: 5 epochs to 2 epochs
• Enhanced classical epochs: 5 epochs to 8 epochs to compensate for reduced quantum exploration

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📁 Project Structure

root/
├── 📊 data/                        # Problem datasets (Vanguard)
└── 📁 misc/                        # Miscellaneous files (Vanguard)
├── 📋 project/                     # Main project directory (NaiveQuantum)
├── 🔧 src/                         # Source code (Vanguard)
│   └── 🏗️ sbo/                     # Sampling-Based Optimization framework (Vanguard)

🛠️ Technologies Used

• Quantum Framework: Qiskit
• Optimization: VQE
• Risk Measure: CVaR
• Backend: AerSimulator, IBM real quantum hardware
  • GPU acceleration is not feasible for this project due to current Qiskit AerSimulator limitations. According to the official Qiskit documentation, the matrix_product_state method (required for 31-qubit problems) does not support GPU.
• Problem Formulation: QUBO transformation
• Post-processing: Local Search optimization

🚀 Setup

1. Clone the repository
2. Create virtual environment

conda env create -f conda_environment.yaml

or

python -m venv VQE_vanguard_womanium_wiser_2025
pip install -r requirements.txt

3. Activate the environment

conda activate VQE_vanguard_womanium_wiser_2025

or

.\VQE_vanguard_womanium_wiser_2025\Scripts\activate

4. Complete IBM Setup:
   1. Create IBM Cloud Account: Sign up for a free IBM Cloud account
   2. Log in to IBM Quantum: Access the IBM Quantum platform through your IBM Cloud account
   3. Create API Key: Generate an API key for programmatic access to IBM Quantum services
   4. Create New Instance: Set up a new quantum computing instance
   5. Configure Code: Use the necessary authentication and backend configuration code
   6. Execute: Run quantum circuits on real quantum hardware

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📊 Experimental Results

PART A. Main Research: AerSimulator vs. AerSimulator

• Solution Quality: All approaches achieved similar relative gaps (~56.5%) from the optimal classical solution
• Hybrid Approaches: Local search post-processing showed no improvement (0% hybrid improvement)
• Execution Time: Ranged from 24.7 minutes (Heavyweight Hybrid) to 195.1 minutes (Lightweight Quantum)
• Computational Cost: Function evaluations ranged from 1,862 (Heavyweight Hybrid) to 8,191 (Lightweight Quantum)

PART B. Extended Research: AerSimulator vs. Real Quantum Hardware

• Solution Quality: The solutions are quite similar (Hamming distance differs by one bit position; the relative difference is approximately 12.1%)
• Execution Time: QPU execution is approximately 53.61 times slower overall (AerSimulator CPU: 29.56 seconds; IBM QPU: 1584.84 seconds, or 26.41 minutes)
• Computational Cost: Both approaches use the same number of function evaluations (242)

🎯 Conclusions

PART A. Main Research: AerSimulator vs. AerSimulator

The heavyweight hybrid configuration emerged as the optimal choice.

1. Speed: Achieved target quality in 24.7 minutes (5.3× faster than lightweight quantum)
2. Cost: Best efficiency score (7.17×10⁻⁴) balancing quality and speed

Key Insight: While hybrid post-processing doesn't improve solution quality, the heavyweight configuration's shallow circuit design (reps=2) with full entanglement achieves optimal performance through reduced computational overhead.

PART B. Extended Research: AerSimulator vs. Real Quantum Hardware

The heavyweight hybrid configuration is adjusted to fit the 10-minute monthly limit of IBM's free-tier real quantum hardware. The execution time on real hardware exceeds that of the simulation by more than 50× and is therefore currently infeasible. However, we are optimistic about the future of quantum portfolio optimization, especially with recent advancements in quantum hardware, like tunable couplers in the Ankaa architecture (Mutus, 2025). These developments simplify the implementation of fully entangled circuits, such as the two-local full entanglement ansatz, making them more feasible on real quantum hardware.

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References

• Barkoutsos, P. K., Nannicini, G., Robert, A., Tavernelli, I., & Woerner, S. (2020, April 20). Improving variational quantum optimization using CVaR. Quantum, 4, 256. click here

• Chen, C. (2020, October 8). Portfolio optimization with Variational Quantum Eigensolver (VQE)-(2). Medium. click here

• Mehta, B. (2025, June 18). 2025 QUANTUM PROGRAM ❯ Day 7 ❯ Projects Orientation Part 2 [Video]. YouTube. click here

• Mutus, J. (2025, July 17). Quantum hardware demystified ❯ Dr. Josh Mutus ❯ 2025 QUANTUM PROGRAM [Video]. YouTube. click here

License

Some code and data in this repository are proprietary materials from Vanguard and remain their intellectual property. These materials are provided for educational purposes only and may not be redistributed, modified, or used for commercial purposes without explicit permission from Vanguard.