QuBots - Quantum Portfolio Optimisation

YQuantum 2026 | The Hartford & Capgemini Quantum Lab | QuEra

A quantum-classical hybrid approach to insurance portfolio optimisation using QUBO/Ising formulations and QAOA executed on Bloqade's neutral atom simulator.

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Problem

Insurance companies must invest large premium volumes under strict solvency and liquidity constraints. Constructing a portfolio that maximises return while minimising correlated risk across asset classes is a highly non-trivial combinatorial problem. We model it as a Markowitz mean-variance optimisation, reformulate it as a QUBO, and solve it using quantum approaches.

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Approach

1. Data

• 8 assets selected from 50 (one per sector): Gov Bonds, IG Credit, HY Credit, Equities US, Equities Intl, Infrastructure, Real Estate, Cash
• Expected returns mu and covariance matrix cov extracted from investment_dataset_covariance.csv

2. QUBO Formulation

The Markowitz objective with budget constraint becomes: min x^T Q x

where the Q matrix encodes:

• Return reward: -mu[i] on the diagonal
• Risk penalty: q_risk * cov[i,j] on off-diagonals
• Budget penalty: lambda * (sum(x_i) - B)^2 expanded into the matrix

Parameters: q_risk = 1, lambda = 5, B = 4 (pick 4 of 8 assets)

3. Ising Mapping

QUBO binary variables x_i ∈ {0,1} are mapped to Ising spins s_i ∈ {-1,+1} via x_i = (1 + s_i) / 2, giving: H = sum_i h_i * Z_i + sum_{i<j} J_ij * Z_i * Z_j

4. Quantum Circuit (Bloqade)

• 8 qubits in a 2×4 neutral atom grid, spacing 5μm, Rydberg blockade radius 15μm
• Fully connected graph — matches the dense QUBO structure of the portfolio problem
• QAOA circuit with p=1 and p=2 layers built using @qasm2.main
• Angles optimised via grid search + refinement
• Executed via Bloqade's PyQrack simulator (state_vector + multi_run)

5. Classical Baselines

• Simulated Annealing (01_simulated_annealing.py) — classical combinatorial solver
• Markowitz MVO (03_bloqade_circuit.py) — continuous mean-variance optimisation via scipy SLSQP
• Quantum Annealing — adiabatic interpolation H(s) = (1-s)H_M + s*H_C for D-Wave comparison

6. Noise Analysis

Depolarising noise swept from 0% to 5% per-qubit per-layer using a proper density matrix channel: rho_noisy = (1 - p) * U rho U† + p * I/dim Results show energy remains stable up to ~1% gate error, consistent with current Rydberg hardware capabilities.

7. Stress Testing (Hartford-specific)

Portfolio performance evaluated under real market stress scenarios from investment_dataset_scenarios.csv. CVaR (worst-5 average) computed for QAOA and brute-force portfolios to assess insurance solvency risk.

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Files

File	Description
01_simulated_annealing.py	Classical SA baseline — QUBO/Ising build + simulated annealing solver
02_qaoa_numpy_simulation.py	Exact state-vector QAOA simulation (numpy/scipy), noise sweep, 9-panel plots
03_bloqade_circuit.py	Real Bloqade @qasm2.main circuit, PyQrack execution, shot sampling, MVO baseline, stress test
investment_dataset_full.xlsx	Full 50-asset return history
investment_dataset_covariance.csv	Full 50×50 covariance matrix
investment_dataset_correlation.csv	Full 50×50 correlation matrix
investment_dataset_assets.csv	Asset metadata (sector, expected return, etc.)
investment_dataset_scenarios.csv	Stress scenario data (used for CVaR analysis)

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Setup

Requirements

• Python 3.10 or 3.11 (recommended — PyQrack wheels are not available for all platforms on 3.12+)
• All dependencies in requirements.txt

Install

pip install -r requirements.txt

⚠️ Bloqade note: bloqade-pyqrack[pyqrack-cpu] is the simulator backend required by 03_bloqade_circuit.py. If installation fails (e.g. no wheel for your platform/Python version), scripts 01 and 02 still run fully. Script 03 will automatically fall back to an exact numpy simulation producing identical results — you will see a clear message at startup.

Verify Bloqade works (optional but recommended before running script 03)

python -c "from bloqade import qasm2; from bloqade.pyqrack import PyQrack; print('Bloqade OK')"

Run Order

Run scripts in sequence — each builds on the previous:

# 1. Classical baseline (no quantum dependencies)
python 01_simulated_annealing.py

# 2. Exact QAOA simulation + plots (no Bloqade needed)
python 02_qaoa_numpy_simulation.py
# → saves outputs/qaoa_numpy_results.png

# 3. Full Bloqade circuit + four-way comparison + stress test
python 03_bloqade_circuit.py
# → saves bloqade_qaoa_results.png

Key Parameters

Parameter	Value	Meaning
N	8	Number of qubits / assets
B	4	Portfolio size (assets to select)
q_risk	1	Risk aversion
λ	5	Budget penalty strength
p	2	QAOA circuit depth

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Results

(Run python 03_bloqade_circuit.py to generate final numbers — outputs saved to bloqade_qaoa_results.png)

• Noise tolerance: stable up to ~1% gate error
• Connectivity: fully connected via Rydberg blockade — ideal for dense QUBO graphs

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Team

QuBots - YQuantum 2026

YQuantum 2026

Contribution Note

Core quantum circuit architecture, QUBO formulation, and Bloqade integration developed collaboratively by the QuBots team at YQuantum 2026. See commit history for individual contributions including noise analysis, CVaR stress testing, and dataset pipeline.