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Quantum Computing API

QuantumStateEngine

Quantum Core

Core quantum state simulator with automatic backend selection based on qubit count. Supports exact statevector simulation (1-20 qubits), tensor networks (20-40 qubits), and MPS approximation (40-50 qubits).

__init__(num_qubits, backend=None)

Initialize quantum circuit with specified number of qubits.

Parameter Type Description
num_qubits int Number of qubits in the circuit (1-50)
backend str, optional Force specific backend ('statevector', 'tensor_network', 'mps')
Example: 
from aios.quantum_ml_algorithms import QuantumStateEngine

# Automatic backend selection
qc = QuantumStateEngine(num_qubits=10)

# Force specific backend
qc_large = QuantumStateEngine(num_qubits=30, backend='tensor_network')

hadamard(qubit)

Apply Hadamard gate to create superposition.

qc.hadamard(qubit: int) → None
Parameter Type Description
qubit int Target qubit index (0 to num_qubits-1)
Example: 
# Create superposition on all qubits
for i in range(5):
    qc.hadamard(i)

cnot(control, target)

Apply CNOT (controlled-NOT) gate for entanglement.

qc.cnot(control: int, target: int) → None
Parameter Type Description
control int Control qubit index
target int Target qubit index
Example: 
# Create entanglement chain
for i in range(4):
    qc.cnot(i, i + 1)

rx(qubit, angle), ry(qubit, angle), rz(qubit, angle)

Apply rotation gates around X, Y, or Z axis.

qc.rx(qubit: int, angle: float) → None
Parameter Type Description
qubit int Target qubit index
angle float Rotation angle in radians
Example: 
import numpy as np

# Rotate qubit 0 by π/4 around X-axis
qc.rx(0, np.pi / 4)

# Parameterized rotation
theta = np.random.uniform(0, 2 * np.pi)
qc.ry(1, theta)

measure(shots=1000)

Measure all qubits and return outcome distribution.

qc.measure(shots: int = 1000) → Dict[str, int]
Parameter Type Description
shots int Number of measurement repetitions
Returns: Dictionary mapping bitstrings to counts
Example: 
results = qc.measure(shots=1000)
# {'00': 245, '01': 253, '10': 247, '11': 255}

# Get most common outcome
most_common = max(results, key=results.get)
print(f"Most common: {most_common} ({results[most_common]} times)")

expectation_value(observable)

Compute expectation value of an observable.

qc.expectation_value(observable: str) → float
Parameter Type Description
observable str Observable string (e.g., 'Z0', 'Z0*Z1', 'X0*Y1')
Returns: Expectation value as float
Example: 
# Single-qubit observable
z0 = qc.expectation_value('Z0')

# Two-qubit correlation
z0z1 = qc.expectation_value('Z0*Z1')

# Complex observable
energy = qc.expectation_value('X0*X1') + 0.5 * qc.expectation_value('Z0')

QuantumVQE

Quantum Optimization

Variational Quantum Eigensolver for finding ground state energies. Uses hardware-efficient ansatz circuits with classical optimization loop.

__init__(num_qubits, depth=3, optimizer='adam')

Parameter Type Description
num_qubits int Number of qubits
depth int Circuit depth (more = more expressive)
optimizer str Optimizer ('adam', 'l-bfgs-b', 'cobyla')
Example: 
from aios.quantum_ml_algorithms import QuantumVQE

# Define Hamiltonian
def hamiltonian(qc):
    return qc.expectation_value('Z0*Z1') - 0.5 * qc.expectation_value('Z0')

# Initialize VQE
vqe = QuantumVQE(num_qubits=4, depth=3)

# Optimize
energy, params = vqe.optimize(hamiltonian, max_iter=100)

print(f"Ground state energy: {energy:.6f}")
print(f"Optimal parameters: {params}")

HHL Linear System Solver

Quantum Linear Algebra

Harrow-Hassidim-Lloyd algorithm for solving linear systems Ax = b with exponential speedup. Complexity: O(log(N)κ²) vs O(N³) classical.

hhl_linear_system_solver(A, b)

hhl_linear_system_solver(A: np.ndarray, b: np.ndarray) → Dict
Parameter Type Description
A np.ndarray Coefficient matrix (N × N)
b np.ndarray Right-hand side vector (N,)
Returns: Dictionary with solution expectation values, success probability, quantum advantage factor, and condition number
Example: 
from aios.quantum_hhl_algorithm import hhl_linear_system_solver
import numpy as np

# Define linear system
A = np.array([[2.0, -0.5], [-0.5, 2.0]])
b = np.array([1.0, 0.0])

# Solve with quantum advantage
result = hhl_linear_system_solver(A, b)

print(f"Success probability: {result['success_probability']:.4f}")
print(f"Quantum advantage: {result['quantum_advantage']:.1f}x")
print(f"Condition number κ: {result['condition_number']:.2f}")

# Note: HHL outputs expectation values, not full solution vector
print(f"Solution expectation: {result['solution_expectation']}")

Important: HHL algorithm outputs expectation values ⟨x|M|x⟩, not the full solution vector x. This is sufficient for many applications (e.g., expectation values in quantum chemistry, optimization objectives).

When to use: Best for sparse, well-conditioned matrices (low κ). For dense or ill-conditioned systems, classical methods may be more efficient.

ML Algorithms API

Mamba (Adaptive State Space)

ML Sequence Modeling

Mamba architecture with O(N) complexity vs O(N²) for attention. Input-dependent parameters enable content-based reasoning.

AdaptiveStateSpace(input_dim, state_dim, output_dim)

Parameter Type Description
input_dim int Input feature dimension
state_dim int Hidden state dimension
output_dim int Output feature dimension
Example: 
from aios.ml_algorithms import AdaptiveStateSpace
import torch

# Initialize Mamba layer
mamba = AdaptiveStateSpace(
    input_dim=512,
    state_dim=128,
    output_dim=512
)

# Process long sequence efficiently
x = torch.randn(32, 10000, 512)  # (batch, length, features)
output, final_state = mamba(x)

print(f"Output shape: {output.shape}")  # (32, 10000, 512)
print(f"Final state: {final_state.shape}")  # (32, 128)

# Complexity: O(N) vs O(N²) for attention!

Optimal Transport Flow Matching

ML Generative

Fast generative modeling with 10-20 sampling steps vs 1000 for diffusion models. Direct velocity field learning with straight sampling paths.

OptimalTransportFlowMatcher(data_dim, time_dim)

Parameter Type Description
data_dim int Data dimension (e.g., 784 for 28×28 images)
time_dim int Time embedding dimension
Example: 
from aios.ml_algorithms import OptimalTransportFlowMatcher
import torch

# Initialize flow matcher
flow = OptimalTransportFlowMatcher(
    data_dim=784,  # 28×28 images
    time_dim=32
)

# Fast sampling: only 20 steps!
samples = flow.sample(
    num_samples=16,
    num_steps=20  # vs 1000 for diffusion
)

print(f"Generated samples: {samples.shape}")  # (16, 784)

# 50x faster sampling than diffusion models!

Neural-Guided MCTS

ML Planning

Monte Carlo Tree Search with neural policy/value guidance (AlphaGo-style). PUCT algorithm balances exploration and exploitation.

NeuralGuidedMCTS(policy_fn, value_fn, num_simulations, c_puct)

Example: 
from aios.ml_algorithms import NeuralGuidedMCTS

# Define neural network functions
def policy_fn(state):
    """Neural network policy: returns [(action, prob), ...]"""
    # Your neural network here
    return [(action, prob) for action, prob in action_probs]

def value_fn(state):
    """Neural network value estimate"""
    # Your neural network here
    return estimated_value

# Initialize MCTS
mcts = NeuralGuidedMCTS(
    policy_fn=policy_fn,
    value_fn=value_fn,
    num_simulations=800,  # AlphaGo uses 800-1600
    c_puct=1.0  # Exploration constant
)

# Search for best move
best_action = mcts.search(current_state)
print(f"Best action: {best_action}")

Adaptive Particle Filter

ML Bayesian

Sequential Monte Carlo for real-time state estimation and sensor fusion. Adaptive resampling based on effective sample size.

AdaptiveParticleFilter(num_particles, state_dim, obs_dim)

Example: 
from aios.ml_algorithms import AdaptiveParticleFilter
import numpy as np

# Initialize filter
pf = AdaptiveParticleFilter(
    num_particles=1000,
    state_dim=4,  # [x, y, vx, vy]
    obs_dim=2     # [x, y] measurements
)

# Time update (prediction)
def transition_fn(x):
    """State transition model"""
    x_new = x.copy()
    x_new[:2] += x_new[2:] * 0.1  # Position update
    return x_new

pf.predict(transition_fn=transition_fn, process_noise=0.05)

# Measurement update
def likelihood_fn(x, obs):
    """Measurement likelihood"""
    diff = x[:2] - obs
    return np.exp(-0.5 * np.sum(diff**2))

observation = np.array([1.0, 2.0])
pf.update(observation=observation, likelihood_fn=likelihood_fn)

# Get state estimate
estimate = pf.estimate()
print(f"State estimate: {estimate}")

Autonomous Discovery API

AutonomousLLMAgent

ML Level 4

Level 4 autonomous agent with self-directed learning capabilities. Synthesizes goals, builds knowledge graphs, and pursues learning independently.

__init__(model_name, autonomy_level)

Parameter Type Description
model_name str LLM model name (e.g., "deepseek-r1")
autonomy_level AgentAutonomy Level 0-4 (use AgentAutonomy.LEVEL_4)
Example: 
from aios.autonomous_discovery import AutonomousLLMAgent, AgentAutonomy

# Create Level 4 autonomous agent
agent = AutonomousLLMAgent(
    model_name="deepseek-r1",
    autonomy_level=AgentAutonomy.LEVEL_4
)

# Give it a mission
agent.set_mission(
    "quantum computing machine learning applications",
    duration_hours=1.0
)

# Agent autonomously:
# - Decomposes mission into learning objectives
# - Balances exploration vs exploitation
# - Builds knowledge graph
# - Self-evaluates and adapts
await agent.pursue_autonomous_learning()

# Export discovered knowledge
knowledge = agent.export_knowledge_graph()

print(f"Discovered {knowledge['stats']['total_concepts']} concepts")
print(f"Average confidence: {knowledge['stats']['average_confidence']:.2f}")
print(f"High confidence count: {knowledge['stats']['high_confidence_count']}")

export_knowledge_graph()

agent.export_knowledge_graph() → Dict
Returns: Dictionary with 'nodes' (concepts with confidence scores), 'edges' (relationships), and 'stats' (summary statistics)
Example: 
knowledge = agent.export_knowledge_graph()

# Structure:
{
    "nodes": {
        "quantum_entanglement": {
            "confidence": 0.95,
            "timestamp": "2025-10-13T10:30:00Z",
            "parent": "quantum_mechanics"
        },
        ...
    },
    "edges": [
        {"source": "quantum_computing", "target": "quantum_entanglement", "type": "requires"},
        ...
    ],
    "stats": {
        "total_concepts": 247,
        "average_confidence": 0.87,
        "high_confidence_count": 189
    }
}

Utilities

Algorithm Catalog

get_algorithm_catalog()

Get comprehensive catalog of all available algorithms with metadata.

Example: 
from aios.ml_algorithms import get_algorithm_catalog

catalog = get_algorithm_catalog()

for name, info in catalog.items():
    print(f"{name}:")
    print(f"  Category: {info['category']}")
    print(f"  Complexity: {info['complexity']}")
    print(f"  Available: {info['available']}")
    print(f"  Requires: {info['requires']}")
    print()

Dependency Checking

check_dependencies()

Example: 
# Check quantum algorithms
from aios.quantum_ml_algorithms import check_dependencies as check_quantum
status = check_quantum()
print(f"Quantum algorithms available: {status['available']}")

# Check autonomous discovery
from aios.autonomous_discovery import check_autonomous_discovery_dependencies
status = check_autonomous_discovery_dependencies()
print(f"Autonomous discovery ready: {status['ready']}")

Quick Reference

Import Cheatsheet

# Quantum Computing
from aios.quantum_ml_algorithms import (
    QuantumStateEngine,
    QuantumVQE,
    QuantumQAOA,
    QuantumNeuralNetwork
)
from aios.quantum_hhl_algorithm import hhl_linear_system_solver

# ML Algorithms
from aios.ml_algorithms import (
    AdaptiveStateSpace,           # Mamba
    OptimalTransportFlowMatcher,  # Flow Matching
    NeuralGuidedMCTS,             # AlphaGo-style
    AdaptiveParticleFilter,       # Bayesian tracking
    NoUTurnSampler,               # NUTS HMC
    SparseGaussianProcess,        # Scalable GP
    get_algorithm_catalog         # List all
)

# Autonomous Discovery
from aios.autonomous_discovery import (
    AutonomousLLMAgent,
    AgentAutonomy,
    create_autonomous_discovery_action
)