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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Slides

https://docs.google.com/presentation/d/1XIo6cwxRop6iZYg7M5266XKUhwO8SaDZ/edit?usp=sharing&ouid=100823284726496128305&rtpof=true&sd=true

Team

QuBots — YQuantum 2026