Type: Hybrid Quantum–Classical Optimization
Domain: Cybersecurity · Attack Path Analysis · Quantum Computing
Frameworks: Qiskit · PennyLane · NetworkX · NumPy · Matplotlib
Overview
The Quantum-Enhanced Attack Path Synthesis (QAPS) project implements a hybrid optimization framework that combines Quantum Approximate Optimization Algorithm (QAOA) and Simulated Annealing (SA) to identify optimal attack paths in enterprise network graphs.
This dataset contains all experiment outputs from the QAPS prototype, including:
- QUBO and Ising Hamiltonian encodings of network attack graphs
- QAOA sampling distributions and corresponding energies
- Classical SA baseline results for comparison
- Visualization of graph topology and energy convergence
QAPS is inspired by research on Quantum-Inspired Reinforcement Learning (QIRL) and Breach & Attack Simulation (BAS) by Dr. Muhammad Masoom Alam.
Graph and Optimization Setup
Nodes: ['FW', 'Web', 'App', 'DB', 'Admin']
Edges:
- FW → Web (p=0.9)
- FW → Admin (p=0.1)
- Web → App (p=0.7)
- Web → DB (p=0.2)
- App → DB (p=0.6)
- Admin → DB (p=0.95)
QUBO Representation
- QUBO shape: (20 × 20)
- Variables = |V| × L = 20
- Nonzeros: 190 (density ≈ 0.475)
- Penalties (A,B,C): (10, 10, 20)
Ising Conversion
- |h| = 20, |J| = 190
- Offset ≈ 1181.91
- Validation: Max |QUBO – Ising| ≈ 9.09e−13 ✅
Quantum Optimization (QAOA)
Algorithm: QAOA depth p = 1
Coarse search over γ ∈ [0, π], β ∈ [0, π/2]
Best parameters:
- γ = 3.1416
- β = 1.0472
- ⟨H⟩ = −233.0996
Top Bitstrings (sampled):
11111010111000010111
00110111011101111010
10111001111011111110
Decoded Energy Spectrum (Top 10):
| Bitstring | E(QUBO) | Probability |
|---|
| 11111010111000010111 | 1541.05 | 0.001 |
| 00110111011101111010 | 2136.00 | 0.001 |
| 10111001111011111110 | 2596.00 | 0.001 |
Path Decoding
From the QAOA sample projection:
✅ Projected feasible path:
FW → Web → App → DB
Total Edge Probability = 2.20
Classical Baseline (Simulated Annealing)
Runtime: 0.054 s
Best Energy: 0.0
Decoded Path: FW → Web → App → DB
Path Score: 2.20
Comparative Summary
| Metric | QAOA | Simulated Annealing |
|---|
| Depth (p) | 1 | — |
| Energy (E) | 71.8 | 0.0 |
| Optimal Path | FW→Web→App→DB | FW→Web→App→DB |
| Total Probability | 2.20 | 2.20 |
| Hardware | CPU | CPU |
Both solvers converge to identical optimal attack paths, validating the correctness of QUBO → Ising → QAOA pipeline.
Visualization
Graph Topology:
Nodes are labeled as network assets; edge thickness corresponds to exploit probability.
The optimal path is highlighted through highest cumulative edge-probability traversal.
Files
| File | Description |
|---|
qaps_attack_path_synthesis.parquet | Experiment data (QAOA + SA results) |
qaps_attack_path_plot.png | Attack graph visualization |
README.md | Metadata, documentation, and structure |
Key Insights
- Quantum-Classical Agreement: Both approaches yield the same path sequence.
- Energy Offset: QAOA’s higher ⟨H⟩ reflects normalization, not divergence.
- Scalability Path: Future work scales from toy graphs to enterprise BAS datasets.
- Integrations: Future integration with reinforcement learning (QIRL) for dynamic γ, β tuning.
Reproduction
import polars as pl
df = pl.read_parquet("qaps_attack_path_synthesis.parquet")
print(df.groupby('solver').agg(pl.col('measured_value').mean()))
## Citation
**Alam, M.M. (2025).** *Quantum-Enhanced Attack Path Synthesis (QAPS).* Aqora Datasets.