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Performance Optimization

This guide covers advanced techniques for optimizing the performance of the Probabilistic Quantum Reasoner across different hardware platforms and use cases.

Performance Analysis Framework

Profiling Tools

import time
import memory_profiler
import cProfile
import pstats
from contextlib import contextmanager
from probabilistic_quantum_reasoner import ProbabilisticQuantumReasoner

class PerformanceProfiler:
    """Comprehensive performance profiling for PQR."""

    def __init__(self):
        self.measurements = {}
        self.memory_usage = {}

    @contextmanager
    def profile_time(self, operation_name):
        """Profile execution time of an operation."""
        start_time = time.perf_counter()
        start_memory = memory_profiler.memory_usage()[0]

        try:
            yield
        finally:
            end_time = time.perf_counter()
            end_memory = memory_profiler.memory_usage()[0]

            self.measurements[operation_name] = {
                'execution_time': end_time - start_time,
                'memory_delta': end_memory - start_memory,
                'peak_memory': max(memory_profiler.memory_usage())
            }

    def profile_function(self, func, *args, **kwargs):
        """Profile a function with detailed statistics."""
        profiler = cProfile.Profile()

        start_time = time.perf_counter()
        profiler.enable()

        result = func(*args, **kwargs)

        profiler.disable()
        end_time = time.perf_counter()

        # Analyze profile data
        stats = pstats.Stats(profiler)
        stats.sort_stats('cumulative')

        return {
            'result': result,
            'total_time': end_time - start_time,
            'stats': stats,
            'top_functions': stats.get_stats_profile().func_profiles
        }

    def benchmark_inference(self, network, reasoner, num_trials=100):
        """Benchmark inference performance."""
        times = []
        memory_usage = []

        for _ in range(num_trials):
            with self.profile_time("inference_trial"):
                result = reasoner.infer(
                    network=network,
                    query=list(network.nodes.keys())[:3],  # First 3 nodes
                    evidence={}
                )

            times.append(self.measurements["inference_trial"]["execution_time"])
            memory_usage.append(self.measurements["inference_trial"]["memory_delta"])

        return {
            'mean_time': np.mean(times),
            'std_time': np.std(times),
            'min_time': np.min(times),
            'max_time': np.max(times),
            'mean_memory': np.mean(memory_usage),
            'total_memory': np.sum(memory_usage)
        }

# Usage example
profiler = PerformanceProfiler()

# Profile network creation
with profiler.profile_time("network_creation"):
    network = create_large_network(num_nodes=50)

# Profile inference
reasoner = ProbabilisticQuantumReasoner(backend="classical")
benchmark_results = profiler.benchmark_inference(network, reasoner)

print(f"Average inference time: {benchmark_results['mean_time']:.3f}s")
print(f"Memory usage: {benchmark_results['mean_memory']:.1f} MB")

Memory Optimization

import gc
import weakref
from typing import Dict, Any, Optional

class MemoryOptimizer:
    """Memory optimization utilities for PQR."""

    def __init__(self):
        self.cache_size_limit = 1000  # Maximum cached items
        self.weak_references = weakref.WeakSet()

    def optimize_network_memory(self, network):
        """Optimize memory usage of a Bayesian network."""

        # Convert dense arrays to sparse where appropriate
        for node_name, node in network.nodes.items():
            if hasattr(node, 'cpt'):
                node.cpt = self._sparsify_cpt(node.cpt)

            if hasattr(node, 'parents'):
                # Use weak references for parent relationships
                node._parent_refs = [weakref.ref(p) for p in node.parents]

        # Compact string representations
        self._intern_node_names(network)

        return network

    def _sparsify_cpt(self, cpt, threshold=1e-6):
        """Convert dense CPT to sparse representation if beneficial."""
        import scipy.sparse as sp

        if isinstance(cpt, np.ndarray):
            # Check sparsity
            zero_ratio = np.count_nonzero(cpt < threshold) / cpt.size

            if zero_ratio > 0.5:  # More than 50% zeros
                return sp.csr_matrix(cpt)

        return cpt

    def _intern_node_names(self, network):
        """Intern string names to save memory."""
        name_pool = {}

        for node in network.nodes.values():
            # Intern node name
            if node.name not in name_pool:
                name_pool[node.name] = sys.intern(node.name)
            node.name = name_pool[node.name]

            # Intern state names
            if hasattr(node, 'states'):
                for i, state in enumerate(node.states):
                    if state not in name_pool:
                        name_pool[state] = sys.intern(state)
                    node.states[i] = name_pool[state]

    def cleanup_unused_objects(self):
        """Force cleanup of unused objects."""
        # Clear weak references to deleted objects
        self.weak_references = weakref.WeakSet([
            obj for obj in self.weak_references if obj is not None
        ])

        # Force garbage collection
        collected = gc.collect()
        print(f"Garbage collected {collected} objects")

        return collected

    def monitor_memory_usage(self, func, *args, **kwargs):
        """Monitor memory usage during function execution."""
        import psutil
        import os

        process = psutil.Process(os.getpid())

        # Initial memory
        initial_memory = process.memory_info().rss / 1024 / 1024  # MB

        # Execute function
        result = func(*args, **kwargs)

        # Final memory
        final_memory = process.memory_info().rss / 1024 / 1024  # MB

        return {
            'result': result,
            'memory_delta': final_memory - initial_memory,
            'peak_memory': final_memory
        }

# Memory optimization example
optimizer = MemoryOptimizer()

# Optimize existing network
optimized_network = optimizer.optimize_network_memory(large_network)

# Monitor memory during inference
memory_result = optimizer.monitor_memory_usage(
    reasoner.infer,
    network=optimized_network,
    query=["target_node"],
    evidence={}
)

print(f"Memory delta: {memory_result['memory_delta']:.1f} MB")

Quantum Circuit Optimization

Circuit Depth Reduction

from probabilistic_quantum_reasoner.optimization import CircuitOptimizer

class QuantumCircuitOptimizer:
    """Optimize quantum circuits for better performance."""

    def __init__(self):
        self.optimization_passes = [
            'single_qubit_merge',
            'commutative_cancellation', 
            'redundant_gate_removal',
            'circuit_depth_reduction'
        ]

    def optimize_circuit(self, circuit, optimization_level=3):
        """Optimize quantum circuit based on optimization level."""

        optimized_circuit = circuit.copy()

        if optimization_level >= 1:
            optimized_circuit = self._merge_single_qubit_gates(optimized_circuit)

        if optimization_level >= 2:
            optimized_circuit = self._cancel_commutative_gates(optimized_circuit)
            optimized_circuit = self._remove_redundant_gates(optimized_circuit)

        if optimization_level >= 3:
            optimized_circuit = self._reduce_circuit_depth(optimized_circuit)
            optimized_circuit = self._optimize_two_qubit_gates(optimized_circuit)

        return optimized_circuit

    def _merge_single_qubit_gates(self, circuit):
        """Merge consecutive single-qubit gates."""
        new_gates = []
        gate_buffer = {}  # qubit -> list of gates

        for gate_info in circuit.gates:
            gate_name, qubits, params = gate_info

            if len(qubits) == 1:  # Single-qubit gate
                qubit = qubits[0]
                if qubit not in gate_buffer:
                    gate_buffer[qubit] = []
                gate_buffer[qubit].append(gate_info)
            else:
                # Flush single-qubit gate buffer
                for q, gates in gate_buffer.items():
                    if gates:
                        merged_gate = self._merge_single_qubit_sequence(gates)
                        if merged_gate:
                            new_gates.append(merged_gate)
                gate_buffer.clear()

                # Add two-qubit gate
                new_gates.append(gate_info)

        # Flush remaining gates
        for q, gates in gate_buffer.items():
            if gates:
                merged_gate = self._merge_single_qubit_sequence(gates)
                if merged_gate:
                    new_gates.append(merged_gate)

        circuit.gates = new_gates
        return circuit

    def _merge_single_qubit_sequence(self, gate_sequence):
        """Merge a sequence of single-qubit gates into one."""
        if not gate_sequence:
            return None

        # Compute combined rotation matrix
        combined_matrix = np.eye(2, dtype=complex)
        qubit = gate_sequence[0][1][0]

        for gate_name, qubits, params in gate_sequence:
            gate_matrix = self._get_gate_matrix(gate_name, params)
            combined_matrix = gate_matrix @ combined_matrix

        # Convert back to rotation parameters
        if np.allclose(combined_matrix, np.eye(2)):
            return None  # Identity operation, can be removed

        # Decompose into rotation gates (simplified)
        return self._matrix_to_rotation_gates(combined_matrix, qubit)

    def _cancel_commutative_gates(self, circuit):
        """Cancel commuting gates that result in identity."""
        new_gates = []
        i = 0

        while i < len(circuit.gates):
            gate = circuit.gates[i]

            # Look for canceling pair
            if i + 1 < len(circuit.gates):
                next_gate = circuit.gates[i + 1]

                if self._gates_cancel(gate, next_gate):
                    i += 2  # Skip both gates
                    continue

            new_gates.append(gate)
            i += 1

        circuit.gates = new_gates
        return circuit

    def _gates_cancel(self, gate1, gate2):
        """Check if two gates cancel each other."""
        gate1_name, qubits1, params1 = gate1
        gate2_name, qubits2, params2 = gate2

        # Same gate on same qubits
        if gate1_name == gate2_name and qubits1 == qubits2:
            # Check if they're inverses
            if gate1_name in ['X', 'Y', 'Z', 'H']:
                return True  # Self-inverse gates
            elif gate1_name.startswith('R') and params1 and params2:
                return abs(params1[0] + params2[0]) < 1e-10  # Opposite rotations

        return False

    def _reduce_circuit_depth(self, circuit):
        """Reduce circuit depth by parallelizing commuting gates."""
        # Group gates by dependency
        dependency_graph = self._build_dependency_graph(circuit)

        # Topological sort to find parallelizable operations
        parallel_layers = self._extract_parallel_layers(dependency_graph)

        # Reconstruct circuit with optimized ordering
        new_gates = []
        for layer in parallel_layers:
            new_gates.extend(layer)

        circuit.gates = new_gates
        return circuit

    def _build_dependency_graph(self, circuit):
        """Build dependency graph for circuit gates."""
        dependencies = {}
        qubit_last_gate = {}  # qubit -> last gate index

        for i, (gate_name, qubits, params) in enumerate(circuit.gates):
            dependencies[i] = []

            # Add dependencies on previous gates affecting same qubits
            for qubit in qubits:
                if qubit in qubit_last_gate:
                    dependencies[i].append(qubit_last_gate[qubit])
                qubit_last_gate[qubit] = i

        return dependencies

    def _extract_parallel_layers(self, dependency_graph):
        """Extract layers of parallelizable gates."""
        layers = []
        remaining_gates = set(dependency_graph.keys())

        while remaining_gates:
            # Find gates with no remaining dependencies
            ready_gates = []
            for gate_idx in remaining_gates:
                if all(dep not in remaining_gates for dep in dependency_graph[gate_idx]):
                    ready_gates.append(gate_idx)

            if not ready_gates:
                # Circular dependency or error
                ready_gates = list(remaining_gates)

            layers.append(ready_gates)
            remaining_gates -= set(ready_gates)

        return layers

# Circuit optimization example
circuit_optimizer = QuantumCircuitOptimizer()

# Create test circuit
circuit = backend.create_circuit(num_qubits=4)
circuit.add_hadamard(0)
circuit.add_hadamard(0)  # Redundant - will be removed
circuit.add_cnot(0, 1)
circuit.add_rotation("RY", 2, np.pi/4)
circuit.add_rotation("RY", 2, -np.pi/4)  # Cancels previous rotation

print(f"Original circuit depth: {circuit.depth()}")

# Optimize circuit
optimized_circuit = circuit_optimizer.optimize_circuit(circuit, optimization_level=3)

print(f"Optimized circuit depth: {optimized_circuit.depth()}")

Noise-Aware Optimization

class NoiseAwareOptimizer:
    """Optimize circuits considering quantum noise."""

    def __init__(self, noise_model):
        self.noise_model = noise_model
        self.gate_fidelities = self._compute_gate_fidelities()

    def _compute_gate_fidelities(self):
        """Compute fidelities for different gates under noise."""
        fidelities = {}

        # Single-qubit gate fidelities
        fidelities['H'] = 0.999
        fidelities['X'] = 0.999
        fidelities['Y'] = 0.999
        fidelities['Z'] = 0.9995  # Virtual Z-gate, higher fidelity
        fidelities['RX'] = 0.998
        fidelities['RY'] = 0.998
        fidelities['RZ'] = 0.9995

        # Two-qubit gate fidelities
        fidelities['CNOT'] = 0.99
        fidelities['CZ'] = 0.992

        return fidelities

    def optimize_for_noise(self, circuit):
        """Optimize circuit considering noise characteristics."""
        optimized_circuit = circuit.copy()

        # Replace gates with higher-fidelity equivalents
        optimized_circuit = self._replace_low_fidelity_gates(optimized_circuit)

        # Minimize two-qubit gates
        optimized_circuit = self._minimize_two_qubit_gates(optimized_circuit)

        # Add error correction if beneficial
        optimized_circuit = self._add_error_correction(optimized_circuit)

        return optimized_circuit

    def _replace_low_fidelity_gates(self, circuit):
        """Replace gates with higher-fidelity alternatives."""
        new_gates = []

        for gate_name, qubits, params in circuit.gates:
            if gate_name == 'Y':
                # Replace Y with Z-RX-Z sequence (higher fidelity)
                new_gates.extend([
                    ('Z', qubits, []),
                    ('RX', qubits, [np.pi]),
                    ('Z', qubits, [])
                ])
            elif gate_name == 'CNOT' and len(qubits) == 2:
                # Check if CZ is available and has higher fidelity
                if self.gate_fidelities.get('CZ', 0) > self.gate_fidelities.get('CNOT', 0):
                    # Convert CNOT to CZ + single-qubit gates
                    control, target = qubits
                    new_gates.extend([
                        ('H', [target], []),
                        ('CZ', qubits, []),
                        ('H', [target], [])
                    ])
                else:
                    new_gates.append((gate_name, qubits, params))
            else:
                new_gates.append((gate_name, qubits, params))

        circuit.gates = new_gates
        return circuit

    def _minimize_two_qubit_gates(self, circuit):
        """Minimize the number of two-qubit gates."""
        # Count current two-qubit gates
        two_qubit_count = sum(1 for gate_name, qubits, _ in circuit.gates 
                             if len(qubits) == 2)

        if two_qubit_count <= 5:  # Already minimal
            return circuit

        # Apply more aggressive single-qubit optimizations
        optimized = circuit.copy()

        # Try to decompose multi-qubit gates differently
        optimized = self._decompose_for_minimal_cnots(optimized)

        return optimized

    def _add_error_correction(self, circuit):
        """Add error correction if circuit is long enough to benefit."""
        circuit_depth = circuit.depth()

        if circuit_depth > 100:  # Only for deep circuits
            # Add simple repetition code
            return self._add_repetition_code(circuit)

        return circuit

    def estimate_circuit_fidelity(self, circuit):
        """Estimate overall circuit fidelity under noise."""
        total_fidelity = 1.0

        for gate_name, qubits, params in circuit.gates:
            gate_fidelity = self.gate_fidelities.get(gate_name, 0.95)
            total_fidelity *= gate_fidelity

        # Account for decoherence time
        circuit_time = self._estimate_circuit_time(circuit)
        decoherence_factor = np.exp(-circuit_time / self.noise_model.t1_time)

        return total_fidelity * decoherence_factor

# Noise-aware optimization example
from probabilistic_quantum_reasoner.noise import DepolarizingNoise

noise_model = DepolarizingNoise(probability=0.01)
noise_optimizer = NoiseAwareOptimizer(noise_model)

# Optimize for noise
noisy_circuit = create_test_circuit()
optimized_for_noise = noise_optimizer.optimize_for_noise(noisy_circuit)

original_fidelity = noise_optimizer.estimate_circuit_fidelity(noisy_circuit)
optimized_fidelity = noise_optimizer.estimate_circuit_fidelity(optimized_for_noise)

print(f"Original fidelity: {original_fidelity:.4f}")
print(f"Optimized fidelity: {optimized_fidelity:.4f}")
print(f"Improvement: {(optimized_fidelity/original_fidelity - 1)*100:.1f}%")

Classical Inference Optimization

Sparse Matrix Operations

import scipy.sparse as sp
from scipy.sparse.linalg import spsolve

class SparseInferenceEngine:
    """Inference engine optimized for sparse networks."""

    def __init__(self, sparsity_threshold=0.1):
        self.sparsity_threshold = sparsity_threshold
        self.sparse_cache = {}

    def optimize_network_for_sparsity(self, network):
        """Convert network to sparse representation."""

        for node_name, node in network.nodes.items():
            if hasattr(node, 'cpt'):
                # Convert CPT to sparse if beneficial
                cpt = node.cpt
                sparsity = np.count_nonzero(cpt) / cpt.size

                if sparsity < self.sparsity_threshold:
                    node.cpt = sp.csr_matrix(cpt)
                    print(f"Converted {node_name} CPT to sparse (sparsity: {sparsity:.3f})")

        return network

    def sparse_variable_elimination(self, network, query_vars, evidence):
        """Perform variable elimination using sparse operations."""

        # Convert factors to sparse matrices
        sparse_factors = self._convert_factors_to_sparse(network, evidence)

        # Determine elimination order
        elimination_order = self._compute_elimination_order(network, query_vars)

        # Eliminate variables one by one
        for var in elimination_order:
            if var not in query_vars:
                sparse_factors = self._eliminate_variable_sparse(sparse_factors, var)

        # Compute final marginals
        return self._compute_marginals_sparse(sparse_factors, query_vars)

    def _convert_factors_to_sparse(self, network, evidence):
        """Convert network factors to sparse representation."""
        factors = []

        for node_name, node in network.nodes.items():
            if hasattr(node, 'cpt'):
                factor = node.cpt

                # Apply evidence
                if node_name in evidence:
                    factor = self._apply_evidence_to_factor(factor, evidence[node_name])

                # Convert to sparse if not already
                if not sp.issparse(factor):
                    factor = sp.csr_matrix(factor)

                factors.append({
                    'factor': factor,
                    'variables': [node_name] + [p.name for p in node.parents],
                    'name': node_name
                })

        return factors

    def _eliminate_variable_sparse(self, factors, var):
        """Eliminate a variable using sparse operations."""
        # Find factors involving the variable
        relevant_factors = [f for f in factors if var in f['variables']]
        other_factors = [f for f in factors if var not in f['variables']]

        if not relevant_factors:
            return factors

        # Multiply relevant factors
        product_factor = relevant_factors[0]['factor']
        product_variables = relevant_factors[0]['variables']

        for factor_info in relevant_factors[1:]:
            product_factor = self._multiply_sparse_factors(
                product_factor, factor_info['factor']
            )
            product_variables = list(set(product_variables + factor_info['variables']))

        # Sum out the variable
        marginalized_factor = self._marginalize_sparse(product_factor, var, product_variables)
        marginalized_variables = [v for v in product_variables if v != var]

        # Add marginalized factor to other factors
        other_factors.append({
            'factor': marginalized_factor,
            'variables': marginalized_variables,
            'name': f'marginalized_{var}'
        })

        return other_factors

    def _multiply_sparse_factors(self, factor1, factor2):
        """Multiply two sparse factors."""
        # This is a simplified implementation
        # Real implementation would handle arbitrary tensor operations

        if factor1.shape == factor2.shape:
            return factor1.multiply(factor2)
        else:
            # Handle different shapes through broadcasting
            return sp.kron(factor1, factor2)

    def _marginalize_sparse(self, factor, var, variables):
        """Marginalize out a variable from sparse factor."""
        # Simplified marginalization for sparse matrices
        # Real implementation would handle arbitrary tensor marginalization

        var_index = variables.index(var)

        if factor.ndim == 2 and var_index == 0:
            return sp.csr_matrix(factor.sum(axis=0))
        elif factor.ndim == 2 and var_index == 1:
            return sp.csr_matrix(factor.sum(axis=1))
        else:
            # For higher dimensions, convert to dense temporarily
            dense_factor = factor.toarray()
            marginalized = np.sum(dense_factor, axis=var_index)
            return sp.csr_matrix(marginalized)

# Sparse optimization example
sparse_engine = SparseInferenceEngine(sparsity_threshold=0.15)

# Optimize network for sparsity
sparse_network = sparse_engine.optimize_network_for_sparsity(large_network)

# Perform sparse inference
start_time = time.time()
sparse_result = sparse_engine.sparse_variable_elimination(
    sparse_network, 
    query_vars=["target"],
    evidence={"obs1": "value1"}
)
sparse_time = time.time() - start_time

print(f"Sparse inference time: {sparse_time:.3f}s")

Parallel Classical Inference

import concurrent.futures
import multiprocessing as mp
from functools import partial

class ParallelInferenceEngine:
    """Parallel inference engine for classical networks."""

    def __init__(self, num_workers=None):
        self.num_workers = num_workers or mp.cpu_count()
        self.chunk_size = 1000  # For batch operations

    def parallel_variable_elimination(self, network, queries, evidences):
        """Perform variable elimination in parallel for multiple queries."""

        # Create worker function
        worker_func = partial(self._single_inference_worker, network)

        # Execute in parallel
        with concurrent.futures.ProcessPoolExecutor(max_workers=self.num_workers) as executor:
            futures = [
                executor.submit(worker_func, query, evidence)
                for query, evidence in zip(queries, evidences)
            ]

            results = []
            for future in concurrent.futures.as_completed(futures):
                results.append(future.result())

        return results

    def _single_inference_worker(self, network, query, evidence):
        """Worker function for single inference task."""
        from probabilistic_quantum_reasoner.inference import BeliefPropagation

        bp = BeliefPropagation()
        return bp.infer(network, query, evidence)

    def parallel_factor_multiplication(self, factors_list):
        """Multiply factors in parallel."""

        if len(factors_list) <= 2:
            return self._multiply_factors_sequential(factors_list)

        # Divide factors into chunks
        chunk_size = max(2, len(factors_list) // self.num_workers)
        chunks = [factors_list[i:i+chunk_size] 
                 for i in range(0, len(factors_list), chunk_size)]

        # Multiply within chunks in parallel
        with concurrent.futures.ThreadPoolExecutor(max_workers=self.num_workers) as executor:
            futures = [
                executor.submit(self._multiply_factors_sequential, chunk)
                for chunk in chunks
            ]

            chunk_results = [future.result() for future in futures]

        # Multiply chunk results sequentially
        return self._multiply_factors_sequential(chunk_results)

    def _multiply_factors_sequential(self, factors):
        """Multiply a list of factors sequentially."""
        if not factors:
            return None

        result = factors[0]
        for factor in factors[1:]:
            result = np.multiply(result, factor)

        return result

    def parallel_sampling(self, network, num_samples, batch_size=None):
        """Generate samples in parallel."""

        if batch_size is None:
            batch_size = max(1, num_samples // self.num_workers)

        # Create batches
        batches = []
        remaining = num_samples
        while remaining > 0:
            current_batch = min(batch_size, remaining)
            batches.append(current_batch)
            remaining -= current_batch

        # Generate samples in parallel
        with concurrent.futures.ProcessPoolExecutor(max_workers=self.num_workers) as executor:
            futures = [
                executor.submit(self._generate_samples_batch, network, batch_size)
                for batch_size in batches
            ]

            all_samples = []
            for future in futures:
                all_samples.extend(future.result())

        return all_samples

    def _generate_samples_batch(self, network, num_samples):
        """Generate a batch of samples."""
        samples = []

        for _ in range(num_samples):
            sample = {}

            # Topological sampling
            for node_name in self._topological_sort(network):
                node = network.nodes[node_name]

                if hasattr(node, 'sample'):
                    # Sample from node distribution
                    value = node.sample(evidence=sample)
                    sample[node_name] = value
                else:
                    # Default sampling
                    if hasattr(node, 'states'):
                        value = np.random.choice(node.states)
                        sample[node_name] = value

            samples.append(sample)

        return samples

    def _topological_sort(self, network):
        """Topological sort of network nodes."""
        # Simplified topological sort
        sorted_nodes = []
        in_degree = {name: 0 for name in network.nodes}

        # Compute in-degrees
        for node_name, node in network.nodes.items():
            if hasattr(node, 'parents'):
                in_degree[node_name] = len(node.parents)

        # Find nodes with no incoming edges
        queue = [name for name, degree in in_degree.items() if degree == 0]

        while queue:
            current = queue.pop(0)
            sorted_nodes.append(current)

            # Update in-degrees
            current_node = network.nodes[current]
            if hasattr(current_node, 'children'):
                for child in current_node.children:
                    in_degree[child.name] -= 1
                    if in_degree[child.name] == 0:
                        queue.append(child.name)

        return sorted_nodes

# Parallel inference example
parallel_engine = ParallelInferenceEngine(num_workers=4)

# Multiple queries in parallel
queries = [["node1"], ["node2"], ["node3"]]
evidences = [{}, {"obs": "val1"}, {"obs": "val2"}]

parallel_results = parallel_engine.parallel_variable_elimination(
    network, queries, evidences
)

print(f"Processed {len(queries)} queries in parallel")

# Parallel sampling
samples = parallel_engine.parallel_sampling(network, num_samples=10000)
print(f"Generated {len(samples)} samples in parallel")

Hardware-Specific Optimizations

GPU Acceleration

import cupy as cp
import numpy as np

class GPUOptimizedReasoner:
    """GPU-optimized quantum reasoner."""

    def __init__(self, device_id=0):
        cp.cuda.Device(device_id).use()
        self.device_id = device_id
        self.stream = cp.cuda.Stream()

    def gpu_accelerated_inference(self, network, query, evidence):
        """Perform inference using GPU acceleration."""

        with self.stream:
            # Convert network to GPU arrays
            gpu_factors = self._network_to_gpu(network)

            # Apply evidence on GPU
            gpu_factors = self._apply_evidence_gpu(gpu_factors, evidence)

            # Perform inference on GPU
            result = self._infer_on_gpu(gpu_factors, query)

            # Transfer result back to CPU
            cpu_result = cp.asnumpy(result)

        return cpu_result

    def _network_to_gpu(self, network):
        """Transfer network to GPU memory."""
        gpu_factors = []

        for node_name, node in network.nodes.items():
            if hasattr(node, 'cpt'):
                gpu_cpt = cp.asarray(node.cpt)
                gpu_factors.append({
                    'name': node_name,
                    'cpt': gpu_cpt,
                    'variables': [node_name] + [p.name for p in node.parents]
                })

        return gpu_factors

    def batch_quantum_simulation(self, circuits, shots_per_circuit):
        """Simulate multiple quantum circuits in parallel on GPU."""

        # Batch state vector computations
        batch_states = []

        for circuit in circuits:
            state = self._compute_state_vector_gpu(circuit)
            batch_states.append(state)

        # Stack states for batch processing
        batch_tensor = cp.stack(batch_states)

        # Batch measurement simulation
        results = self._batch_measure_gpu(batch_tensor, shots_per_circuit)

        return results

    def _compute_state_vector_gpu(self, circuit):
        """Compute state vector on GPU."""
        num_qubits = circuit.num_qubits
        state = cp.zeros(2**num_qubits, dtype=cp.complex128)
        state[0] = 1.0  # |00...0⟩

        # Apply gates using GPU operations
        for gate_name, qubits, params in circuit.gates:
            gate_matrix = self._get_gate_matrix_gpu(gate_name, params)
            state = self._apply_gate_gpu(state, gate_matrix, qubits, num_qubits)

        return state

    def _apply_gate_gpu(self, state, gate_matrix, qubits, num_qubits):
        """Apply quantum gate on GPU."""
        # This is a simplified implementation
        # Real implementation would use tensor contractions

        if len(qubits) == 1:
            # Single-qubit gate
            full_matrix = self._construct_full_matrix_gpu(gate_matrix, qubits[0], num_qubits)
            return full_matrix @ state
        else:
            # Multi-qubit gate (simplified)
            return gate_matrix @ state  # Placeholder

    def _batch_measure_gpu(self, batch_states, shots_per_circuit):
        """Perform batch measurements on GPU."""
        batch_results = []

        for i, state in enumerate(batch_states):
            # Compute probabilities
            probabilities = cp.abs(state) ** 2

            # Sample on GPU
            samples = cp.random.choice(
                len(probabilities), 
                size=shots_per_circuit[i],
                p=probabilities
            )

            # Convert to measurement outcomes
            outcomes = {}
            for sample in samples:
                bitstring = format(int(sample), f'0{int(cp.log2(len(state)))}b')
                outcomes[bitstring] = outcomes.get(bitstring, 0) + 1

            batch_results.append(outcomes)

        return batch_results

# GPU optimization example
gpu_reasoner = GPUOptimizedReasoner(device_id=0)

# Batch circuit simulation
test_circuits = [create_test_circuit(i) for i in range(10)]
shots_list = [1000] * 10

gpu_results = gpu_reasoner.batch_quantum_simulation(test_circuits, shots_list)
print(f"Simulated {len(test_circuits)} circuits on GPU")

FPGA Acceleration

class FPGAAcceleratedBackend:
    """FPGA-accelerated backend for specific operations."""

    def __init__(self, fpga_device="/dev/fpga0"):
        self.fpga_device = fpga_device
        self.fpga_available = self._check_fpga_availability()

    def _check_fpga_availability(self):
        """Check if FPGA device is available."""
        try:
            import os
            return os.path.exists(self.fpga_device)
        except:
            return False

    def fpga_accelerated_matrix_multiplication(self, matrices):
        """Perform matrix multiplication on FPGA."""

        if not self.fpga_available:
            # Fallback to CPU
            return self._cpu_matrix_multiplication(matrices)

        # FPGA-specific implementation
        return self._fpga_multiply_matrices(matrices)

    def _fpga_multiply_matrices(self, matrices):
        """FPGA matrix multiplication implementation."""
        # This would interface with actual FPGA hardware
        # Using placeholder implementation

        result = matrices[0]
        for matrix in matrices[1:]:
            # Simulate FPGA operation with optimized CPU code
            result = np.dot(result, matrix)

        return result

    def fpga_quantum_simulation(self, circuit):
        """Simulate quantum circuit on FPGA."""

        if not self.fpga_available:
            return None

        # FPGA-specific quantum simulation
        # This would use dedicated quantum simulation cores on FPGA
        return self._fpga_simulate_circuit(circuit)

# FPGA example
fpga_backend = FPGAAcceleratedBackend()

if fpga_backend.fpga_available:
    print("FPGA acceleration available")
else:
    print("FPGA not available, using CPU fallback")

Benchmark Results

Performance Comparison

def comprehensive_benchmark():
    """Comprehensive performance benchmark."""

    # Test configurations
    configurations = [
        {"backend": "classical", "optimization": "none"},
        {"backend": "classical", "optimization": "sparse"},
        {"backend": "classical", "optimization": "parallel"},
        {"backend": "qiskit", "optimization": "none"},
        {"backend": "qiskit", "optimization": "circuit_opt"},
        {"backend": "gpu_classical", "optimization": "gpu"},
    ]

    # Test networks of different sizes
    network_sizes = [10, 25, 50, 100]

    results = {}

    for config in configurations:
        config_name = f"{config['backend']}_{config['optimization']}"
        results[config_name] = {}

        for size in network_sizes:
            print(f"Benchmarking {config_name} with {size} nodes...")

            # Create test network
            network = create_test_network(size)

            # Setup reasoner with configuration
            reasoner = setup_reasoner(config)

            # Benchmark inference
            times = []
            for _ in range(10):  # 10 trials
                start_time = time.time()
                result = reasoner.infer(
                    network=network,
                    query=list(network.nodes.keys())[:3],
                    evidence={}
                )
                end_time = time.time()
                times.append(end_time - start_time)

            results[config_name][size] = {
                'mean_time': np.mean(times),
                'std_time': np.std(times),
                'min_time': np.min(times)
            }

    return results

# Run comprehensive benchmark
benchmark_results = comprehensive_benchmark()

# Display results
print("\nBenchmark Results:")
print("="*50)

for config, size_results in benchmark_results.items():
    print(f"\n{config}:")
    for size, metrics in size_results.items():
        print(f"  {size} nodes: {metrics['mean_time']:.3f}s ± {metrics['std_time']:.3f}s")

Best Practices Summary

Performance Optimization Guidelines

  1. Profile First: Always profile before optimizing
  2. Start with Algorithms: Algorithmic improvements usually beat micro-optimizations
  3. Use Appropriate Data Structures: Sparse vs dense, GPU vs CPU arrays
  4. Cache Wisely: Cache expensive computations but manage memory
  5. Parallelize When Possible: Use all available cores and accelerators
  6. Optimize for Your Use Case: Different applications need different optimizations

Memory Management

  1. Monitor Memory Usage: Track memory consumption during inference
  2. Use Weak References: Prevent memory leaks in large networks
  3. Clear Caches Regularly: Implement cache eviction policies
  4. Optimize Data Types: Use appropriate precision (float32 vs float64)

Hardware Utilization

  1. Match Backend to Hardware: Use GPU backends for GPU systems
  2. Batch Operations: Process multiple items together when possible
  3. Minimize Data Transfer: Keep data on accelerators when possible
  4. Use Vendor Optimizations: Leverage hardware-specific libraries

This comprehensive guide provides the foundation for optimizing PQR performance across different hardware platforms and use cases.