# ML & Quantum Algorithms

State-of-the-art implementations powering intelligent security tools

## 🤖 Machine Learning Algorithms

### 1. AdaptiveStateSpace (Mamba Architecture)

Complexity: O(n) vs O(n²) for traditional attention

The Mamba architecture represents a breakthrough in sequence modeling. Unlike transformers which scale quadratically with sequence length, Mamba achieves linear complexity through selective state spaces. This makes it ideal for analyzing long network packet sequences, log files, and behavioral patterns in security assessments.

Use Cases:

- Real-time traffic pattern analysis
- Long-term behavioral anomaly detection
- Efficient processing of extended log sequences

`from red-team-tools.ml_algorithms import AdaptiveStateSpace # Initialize with state dimensions ssm = AdaptiveStateSpace(d_model=512, d_state=64) hidden_states = ssm.forward(input_sequence) # Process 10K+ tokens in linear time`

### 2. OptimalTransportFlowMatcher

Generation Speed: 10-20 steps vs 1000+ for diffusion models

Flow matching with optimal transport provides dramatically faster generative modeling. By learning direct velocity fields instead of iterative denoising, it achieves high-quality generation in a fraction of the steps. This is crucial for real-time payload generation and adaptive testing.

Use Cases:

- Fast adaptive payload generation
- Real-time fuzzing pattern creation
- Synthetic test data generation

### 3. NeuralGuidedMCTS (Monte Carlo Tree Search)

Inspired by: AlphaGo / MuZero

Combines the planning power of Monte Carlo Tree Search with neural network guidance. This hybrid approach excels at strategic decision-making in complex state spaces—perfect for planning attack chains, optimizing scan strategies, and adaptive testing.

Use Cases:

- Attack path planning and optimization
- Strategic scanning order determination
- Multi-stage penetration testing

### 4. AdaptiveParticleFilter (Sequential Monte Carlo)

Technique: Bayesian state estimation

Particle filters excel at tracking systems with uncertainty. By maintaining multiple hypotheses (particles) about the system state, they handle noisy observations and non-linear dynamics. Essential for real-time threat tracking and anomaly detection.

Use Cases:

- Real-time intrusion detection
- Tracking evolving threat patterns
- Sensor fusion from multiple security tools

### 5. NoUTurnSampler (NUTS / HMC)

Used in: Stan, PyMC3

The No-U-Turn Sampler represents the gold standard for Bayesian posterior sampling. It automatically tunes trajectory length using Hamiltonian dynamics, providing efficient exploration of complex probability distributions without manual tuning.

Use Cases:

- Risk assessment with uncertainty quantification
- Bayesian vulnerability scoring
- Probabilistic threat modeling

### 6. SparseGaussianProcess

Complexity: O(m²n) vs O(n³) for standard GP

Sparse GPs with inducing points make Gaussian processes scalable to millions of data points. This enables regression with calibrated uncertainty—critical for understanding confidence in security predictions.

Use Cases:

- Vulnerability score prediction with uncertainty
- Resource usage forecasting
- Anomaly detection with confidence bounds

### 7. AutonomousLLMAgent (Level 4 Autonomy)

Framework: AWS 2025 Autonomy Standards

The autonomous LLM agent achieves Level 4 autonomy—fully self-directed goal setting and learning. It can autonomously research threat vectors, learn attack techniques, and synthesize security knowledge without human guidance.

Use Cases:

- Autonomous threat intelligence gathering
- Self-directed security research
- Continuous learning from new vulnerabilities

## ⚛️ Quantum Computing Algorithms

Simulation Capabilities:

- 1-20 qubits: Exact statevector simulation (100% accurate)
- 20-40 qubits: Tensor network approximation
- 40-50 qubits: Matrix Product State (MPS) compression
- GPU acceleration: Automatic when CUDA available

### 1. QuantumStateEngine

Core Capability: 1-50 qubit universal quantum simulator

The quantum state engine provides a full-featured quantum circuit simulator with automatic backend selection. It seamlessly scales from exact simulation for small circuits to approximate methods for larger systems.

`from red-team-tools.quantum_ml_algorithms import QuantumStateEngine qc = QuantumStateEngine(num_qubits=10) for i in range(10): qc.hadamard(i) # Create superposition if i < 9: qc.cnot(i, i+1) # Entangle # Measure expectation value energy = qc.expectation_value('Z0')`

### 2. QuantumVQE (Variational Quantum Eigensolver)

Application: Ground state finding, optimization

VQE is a hybrid quantum-classical algorithm that uses quantum circuits to evaluate energies and classical optimization to find minimal states. It's one of the most promising near-term quantum algorithms for chemistry and optimization.

Use Cases:

- Cryptographic key strength analysis
- Optimization of scan strategies
- Pattern recognition in security data

### 3. HHLQuantumLinearSolver

Speedup: O(log(N)κ²) vs O(N³) classical

The Harrow-Hassidim-Lloyd algorithm provides exponential speedup for solving linear systems Ax = b when the condition number κ is low. This has profound implications for machine learning, optimization, and differential equations.

`from red-team-tools.quantum_hhl_algorithm import hhl_linear_system_solver # Solve Ax = b with quantum advantage A = np.array([[2.0, -0.5], [-0.5, 2.0]]) b = np.array([1.0, 0.0]) result = hhl_linear_system_solver(A, b) print(f"Quantum advantage: {result['quantum_advantage']:.1f}x") print(f"Success probability: {result['success_probability']:.2%}")`

Use Cases:

- Fast network flow analysis
- Accelerated machine learning training
- Rapid differential equation solving

### 4. SchrodingerTimeEvolution

Method: Quantum dynamics via Schrödinger equation

Simulates quantum time evolution: iℏ d/dt |Ψ⟩ = Ĥ|Ψ⟩. This enables probabilistic forecasting by encoding system states as quantum amplitudes and evolving them forward in time.

`from red-team-tools.quantum_schrodinger_dynamics import quantum_dynamics_forecasting # Two-state system: secure/compromised H = np.array([[1.0, 0.3], [0.3, -1.0]]) # Hamiltonian psi0 = np.array([1.0, 0.0]) # Currently secure # Forecast 1 time unit ahead forecast = quantum_dynamics_forecasting(H, psi0, forecast_time=1.0) print(f"Secure: {forecast['probabilities'][0]:.1%}") print(f"Compromised: {forecast['probabilities'][1]:.1%}")`

Use Cases:

- Probabilistic threat forecasting
- System state prediction
- Risk evolution modeling

### Ready to Experiment?

All algorithms are fully documented and ready to use. Check the getting started guide to begin exploring.

Get Started