Performance Optimization Guide
This guide provides comprehensive strategies for optimizing quantum data embedding performance across different backends and use cases.
Circuit-Level Optimizations
Gate Count Reduction
from quantum_data_embedding_suite.embeddings import AngleEmbedding
from quantum_data_embedding_suite.utils import circuit_optimizer
import numpy as np
# Create embedding with optimization enabled
embedding = AngleEmbedding(
n_qubits=6,
optimize_circuits=True,
optimization_level=3
)
# Optimize existing circuit
def optimize_embedding_circuit(embedding, data):
"""Optimize embedding circuit for given data"""
# Create base circuit
circuit = embedding.create_circuit(data)
# Apply optimization passes
optimized = circuit_optimizer.optimize(
circuit,
passes=[
'remove_barriers',
'merge_rotations',
'eliminate_zero_gates',
'commute_through_cnots',
'optimize_1q_gates'
]
)
print(f"Original depth: {circuit.depth()}")
print(f"Optimized depth: {optimized.depth()}")
print(f"Gate count reduction: {circuit.count_ops()} -> {optimized.count_ops()}")
return optimized
# Example optimization
X = np.random.randn(10, 6)
for x in X[:3]:
optimized_circuit = optimize_embedding_circuit(embedding, x)
Parallel Circuit Execution
from concurrent.futures import ThreadPoolExecutor, ProcessPoolExecutor
import time
def parallel_embedding_execution(embedding, data_batch, backend, max_workers=4):
"""Execute multiple embeddings in parallel"""
def execute_single(data_point):
"""Execute single embedding"""
circuit = embedding.create_circuit(data_point)
result = backend.execute(circuit)
return result
start_time = time.time()
# Parallel execution
with ThreadPoolExecutor(max_workers=max_workers) as executor:
results = list(executor.map(execute_single, data_batch))
execution_time = time.time() - start_time
print(f"Parallel execution of {len(data_batch)} circuits: {execution_time:.2f}s")
print(f"Average time per circuit: {execution_time/len(data_batch):.3f}s")
return results
# Test parallel execution
X_batch = np.random.randn(20, 6)
parallel_results = parallel_embedding_execution(
embedding, X_batch, backend, max_workers=8
)
Backend-Specific Optimizations
Qiskit Optimization Strategies
from qiskit.compiler import transpile
from qiskit.transpiler import PassManager
from qiskit.transpiler.passes import *
def create_optimized_qiskit_backend():
"""Create highly optimized Qiskit backend"""
# Custom optimization pass manager
optimization_passes = PassManager([
# Layout optimization
TrivialLayout(),
FullAncillaAllocation(),
EnlargeWithAncilla(),
# Gate optimization
Unroller(['u1', 'u2', 'u3', 'cx']),
BasisTranslator(equivalence_library=qiskit.circuit.equivalence_library),
Optimize1qGates(),
CXCancellation(),
# Routing optimization
LookaheadSwap(coupling_map),
# Final cleanup
RemoveBarriers(),
Depth(),
FixedPoint('depth'),
RemoveFinalMeasurements()
])
backend = QiskitBackend(
device_name="aer_simulator",
shots=1024,
optimization_level=0, # We handle optimization manually
custom_passes=optimization_passes
)
return backend
optimized_qiskit = create_optimized_qiskit_backend()
PennyLane Performance Tuning
import pennylane as qml
from pennylane.optimize import AdamOptimizer, GradientDescentOptimizer
def create_optimized_pennylane_backend():
"""Create optimized PennyLane backend with performance tuning"""
# Use GPU if available
try:
device = qml.device('lightning.gpu', wires=8)
print("Using Lightning GPU backend")
except:
device = qml.device('lightning.qubit', wires=8)
print("Using Lightning CPU backend")
# Configure for performance
backend = PennyLaneBackend(
device=device,
interface='autograd', # Fastest interface for gradients
diff_method='best', # Automatic differentiation method selection
grad_on_execution=True # Compute gradients during execution
)
return backend
optimized_pennylane = create_optimized_pennylane_backend()
Memory and Computational Efficiency
Batch Processing Strategies
class BatchProcessor:
"""Efficient batch processing for quantum embeddings"""
def __init__(self, embedding, backend, batch_size=32):
self.embedding = embedding
self.backend = backend
self.batch_size = batch_size
self.results_cache = {}
def process_dataset(self, X, use_cache=True, show_progress=True):
"""Process entire dataset efficiently"""
from tqdm import tqdm
n_samples = len(X)
n_batches = (n_samples + self.batch_size - 1) // self.batch_size
all_results = []
if show_progress:
pbar = tqdm(total=n_batches, desc="Processing batches")
for i in range(n_batches):
start_idx = i * self.batch_size
end_idx = min((i + 1) * self.batch_size, n_samples)
batch = X[start_idx:end_idx]
# Check cache first
batch_results = []
uncached_data = []
uncached_indices = []
for j, data_point in enumerate(batch):
data_hash = hash(data_point.tobytes())
if use_cache and data_hash in self.results_cache:
batch_results.append(self.results_cache[data_hash])
else:
uncached_data.append(data_point)
uncached_indices.append(j)
# Process uncached data
if uncached_data:
uncached_results = self._process_batch(uncached_data)
# Update cache and results
for idx, result in zip(uncached_indices, uncached_results):
data_hash = hash(batch[idx].tobytes())
if use_cache:
self.results_cache[data_hash] = result
batch_results.insert(idx, result)
all_results.extend(batch_results)
if show_progress:
pbar.update(1)
if show_progress:
pbar.close()
return all_results
def _process_batch(self, batch):
"""Process a single batch"""
# Create circuits for entire batch
circuits = [self.embedding.create_circuit(x) for x in batch]
# Execute batch
if hasattr(self.backend, 'execute_batch'):
results = self.backend.execute_batch(circuits)
else:
# Fallback to sequential execution
results = [self.backend.execute(circuit) for circuit in circuits]
return results
# Use batch processor
processor = BatchProcessor(embedding, optimized_qiskit, batch_size=64)
X_large = np.random.randn(1000, 6)
batch_results = processor.process_dataset(X_large, use_cache=True)
Memory-Efficient Kernel Computation
class MemoryEfficientKernel:
"""Memory-efficient kernel computation for large datasets"""
def __init__(self, embedding, chunk_size=100):
self.embedding = embedding
self.chunk_size = chunk_size
def compute_kernel_matrix_chunked(self, X, symmetric=True):
"""Compute kernel matrix in chunks to save memory"""
n_samples = len(X)
# Pre-allocate result matrix
K = np.zeros((n_samples, n_samples))
# Process in chunks
for i in range(0, n_samples, self.chunk_size):
i_end = min(i + self.chunk_size, n_samples)
for j in range(0, n_samples, self.chunk_size):
j_end = min(j + self.chunk_size, n_samples)
# Skip lower triangle if symmetric
if symmetric and j > i:
continue
# Compute chunk
X_i = X[i:i_end]
X_j = X[j:j_end]
K_chunk = self._compute_kernel_chunk(X_i, X_j)
K[i:i_end, j:j_end] = K_chunk
# Fill symmetric part
if symmetric and i != j:
K[j:j_end, i:i_end] = K_chunk.T
return K
def _compute_kernel_chunk(self, X_i, X_j):
"""Compute kernel for a chunk pair"""
n_i, n_j = len(X_i), len(X_j)
K_chunk = np.zeros((n_i, n_j))
for i, x_i in enumerate(X_i):
for j, x_j in enumerate(X_j):
K_chunk[i, j] = self._kernel_element(x_i, x_j)
return K_chunk
def _kernel_element(self, x_i, x_j):
"""Compute single kernel element"""
# Create circuits
circuit_i = self.embedding.create_circuit(x_i)
circuit_j = self.embedding.create_circuit(x_j)
# Compute fidelity
fidelity = self._compute_fidelity(circuit_i, circuit_j)
return fidelity
def _compute_fidelity(self, circuit_i, circuit_j):
"""Compute fidelity between two circuits"""
# This would use the actual fidelity computation
# For now, return a placeholder
return np.random.rand()
# Use memory-efficient kernel
efficient_kernel = MemoryEfficientKernel(embedding, chunk_size=50)
X_large = np.random.randn(500, 6)
K_large = efficient_kernel.compute_kernel_matrix_chunked(X_large)
GPU Acceleration
CUDA-Accelerated Backends
def setup_gpu_acceleration():
"""Setup GPU acceleration for quantum simulations"""
# Check GPU availability
import torch
if torch.cuda.is_available():
print(f"CUDA available: {torch.cuda.get_device_name()}")
print(f"Memory: {torch.cuda.get_device_properties(0).total_memory / 1e9:.1f} GB")
# Qiskit GPU backend
try:
from qiskit_aer import AerSimulator
gpu_backend = AerSimulator(method='statevector', device='GPU')
print("Qiskit GPU backend available")
return gpu_backend
except ImportError:
print("Qiskit Aer GPU not available")
# PennyLane GPU backend
try:
import pennylane as qml
gpu_device = qml.device('lightning.gpu', wires=10)
print("PennyLane GPU backend available")
return gpu_device
except:
print("PennyLane GPU not available")
# Fallback to CPU
print("Using CPU backend")
return None
gpu_backend = setup_gpu_acceleration()
Multi-GPU Scaling
import multiprocessing as mp
from functools import partial
def multi_gpu_kernel_computation(X, embedding, n_gpus=2):
"""Distribute kernel computation across multiple GPUs"""
n_samples = len(X)
chunk_size = n_samples // n_gpus
# Split data across GPUs
data_chunks = []
for i in range(n_gpus):
start_idx = i * chunk_size
end_idx = min((i + 1) * chunk_size, n_samples)
data_chunks.append(X[start_idx:end_idx])
# Define worker function
def compute_chunk_kernel(chunk_data, gpu_id):
"""Compute kernel for data chunk on specific GPU"""
import torch
torch.cuda.set_device(gpu_id)
# Setup GPU backend for this process
gpu_embedding = embedding.clone()
gpu_embedding.set_backend(setup_gpu_backend(gpu_id))
# Compute kernel matrix for chunk
kernel = MemoryEfficientKernel(gpu_embedding)
K_chunk = kernel.compute_kernel_matrix_chunked(chunk_data)
return K_chunk
# Execute in parallel
with mp.Pool(processes=n_gpus) as pool:
chunk_kernels = pool.starmap(
compute_chunk_kernel,
[(chunk, i) for i, chunk in enumerate(data_chunks)]
)
# Combine results
K_combined = np.block([[chunk_kernels[i] for i in range(n_gpus)]])
return K_combined
# Use multi-GPU computation
if torch.cuda.device_count() > 1:
K_multi_gpu = multi_gpu_kernel_computation(X_large, embedding, n_gpus=2)
Algorithm-Level Optimizations
Adaptive Sampling Strategies
class AdaptiveSampler:
"""Adaptive sampling for efficient quantum embedding evaluation"""
def __init__(self, embedding, initial_samples=10, max_samples=1000):
self.embedding = embedding
self.initial_samples = initial_samples
self.max_samples = max_samples
self.sample_history = []
self.variance_history = []
def adaptive_metric_computation(self, X, metric_func, tolerance=1e-3):
"""Compute metric with adaptive sampling"""
current_samples = self.initial_samples
previous_estimate = None
converged = False
while current_samples <= self.max_samples and not converged:
# Sample subset
indices = np.random.choice(len(X), size=current_samples, replace=False)
X_sample = X[indices]
# Compute metric
current_estimate = metric_func(self.embedding, X_sample)
# Check convergence
if previous_estimate is not None:
change = abs(current_estimate - previous_estimate)
if change < tolerance:
converged = True
print(f"Converged after {current_samples} samples")
self.sample_history.append(current_samples)
self.variance_history.append(current_estimate)
previous_estimate = current_estimate
current_samples = min(int(current_samples * 1.5), self.max_samples)
return current_estimate
def plot_convergence(self):
"""Plot convergence behavior"""
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 6))
plt.subplot(1, 2, 1)
plt.plot(self.sample_history, self.variance_history, 'o-')
plt.xlabel('Number of Samples')
plt.ylabel('Metric Value')
plt.title('Metric Convergence')
plt.grid(True)
plt.subplot(1, 2, 2)
if len(self.variance_history) > 1:
changes = np.abs(np.diff(self.variance_history))
plt.plot(self.sample_history[1:], changes, 'o-')
plt.xlabel('Number of Samples')
plt.ylabel('Absolute Change')
plt.title('Convergence Rate')
plt.yscale('log')
plt.grid(True)
plt.tight_layout()
plt.show()
# Use adaptive sampling
sampler = AdaptiveSampler(embedding)
adaptive_expressibility = sampler.adaptive_metric_computation(
X_large, expressibility, tolerance=1e-4
)
sampler.plot_convergence()
Efficient Hyperparameter Optimization
from sklearn.model_selection import GridSearchCV
from skopt import gp_minimize
from skopt.space import Real, Integer
class EmbeddingOptimizer:
"""Efficient hyperparameter optimization for embeddings"""
def __init__(self, embedding_class, X_train, y_train=None):
self.embedding_class = embedding_class
self.X_train = X_train
self.y_train = y_train
self.best_params = None
self.optimization_history = []
def bayesian_optimization(self, param_space, n_calls=20, objective='expressibility'):
"""Bayesian optimization of embedding hyperparameters"""
def objective_function(params):
"""Objective function for optimization"""
try:
# Create embedding with current parameters
param_dict = dict(zip(param_space.keys(), params))
embedding = self.embedding_class(**param_dict)
# Compute objective metric
if objective == 'expressibility':
score = expressibility(embedding, n_samples=200)
elif objective == 'trainability':
score = trainability(embedding, self.X_train[:50])
else:
raise ValueError(f"Unknown objective: {objective}")
# We minimize, so negate for maximization objectives
result = -score
# Record history
self.optimization_history.append({
'params': param_dict,
'score': score,
'objective_value': result
})
return result
except Exception as e:
print(f"Error in objective function: {e}")
return 1.0 # Large penalty for failed evaluations
# Convert parameter space
space = [param_space[key] for key in param_space.keys()]
# Run optimization
result = gp_minimize(
func=objective_function,
dimensions=space,
n_calls=n_calls,
random_state=42,
acq_func='EI' # Expected Improvement
)
# Extract best parameters
best_param_values = result.x
self.best_params = dict(zip(param_space.keys(), best_param_values))
print(f"Best parameters: {self.best_params}")
print(f"Best score: {-result.fun:.6f}")
return self.best_params
def plot_optimization_history(self):
"""Plot optimization history"""
import matplotlib.pyplot as plt
scores = [entry['score'] for entry in self.optimization_history]
iterations = range(1, len(scores) + 1)
plt.figure(figsize=(12, 4))
plt.subplot(1, 2, 1)
plt.plot(iterations, scores, 'o-')
plt.xlabel('Iteration')
plt.ylabel('Objective Score')
plt.title('Optimization Progress')
plt.grid(True)
# Running best
running_best = []
current_best = -np.inf
for score in scores:
current_best = max(current_best, score)
running_best.append(current_best)
plt.subplot(1, 2, 2)
plt.plot(iterations, running_best, 'o-', color='red')
plt.xlabel('Iteration')
plt.ylabel('Best Score So Far')
plt.title('Best Score Evolution')
plt.grid(True)
plt.tight_layout()
plt.show()
# Example usage
param_space = {
'n_qubits': Integer(3, 8),
'depth': Integer(1, 5),
'rotation_gates': ['rx', 'ry', 'rz']
}
optimizer = EmbeddingOptimizer(IQPEmbedding, X_large[:100])
best_params = optimizer.bayesian_optimization(param_space, n_calls=15)
optimizer.plot_optimization_history()
Performance Monitoring and Profiling
Comprehensive Performance Profiler
import cProfile
import pstats
from memory_profiler import profile
import psutil
import time
class QuantumEmbeddingProfiler:
"""Comprehensive profiling for quantum embeddings"""
def __init__(self):
self.profile_results = {}
self.memory_usage = []
self.timing_data = {}
def profile_execution(self, func, *args, **kwargs):
"""Profile function execution"""
# CPU profiling
profiler = cProfile.Profile()
profiler.enable()
# Memory monitoring
process = psutil.Process()
initial_memory = process.memory_info().rss / 1024 / 1024 # MB
start_time = time.time()
# Execute function
result = func(*args, **kwargs)
end_time = time.time()
execution_time = end_time - start_time
# Stop profiling
profiler.disable()
# Get memory usage
final_memory = process.memory_info().rss / 1024 / 1024 # MB
memory_usage = final_memory - initial_memory
# Store results
func_name = func.__name__
self.profile_results[func_name] = {
'execution_time': execution_time,
'memory_usage': memory_usage,
'profiler': profiler
}
print(f"{func_name} - Time: {execution_time:.3f}s, Memory: +{memory_usage:.1f}MB")
return result
def generate_detailed_report(self, func_name):
"""Generate detailed profiling report"""
if func_name not in self.profile_results:
print(f"No profile data for {func_name}")
return
profiler = self.profile_results[func_name]['profiler']
# Create stats object
stats = pstats.Stats(profiler)
stats.sort_stats('cumulative')
print(f"\nDetailed Profile Report for {func_name}:")
print("=" * 50)
stats.print_stats(20) # Top 20 functions
# Memory report
print(f"\nMemory Usage: +{self.profile_results[func_name]['memory_usage']:.1f}MB")
print(f"Execution Time: {self.profile_results[func_name]['execution_time']:.3f}s")
@profile
def memory_intensive_operation(self, embedding, X):
"""Example memory-profiled operation"""
# This decorator will show line-by-line memory usage
kernel_matrices = []
for i in range(len(X)):
if i % 10 == 0:
kernel = FidelityKernel(embedding)
K = kernel.compute_kernel_matrix(X[i:i+10])
kernel_matrices.append(K)
return kernel_matrices
# Use profiler
profiler = QuantumEmbeddingProfiler()
# Profile embedding creation
embedding = profiler.profile_execution(
lambda: AngleEmbedding(n_qubits=6),
)
# Profile kernel computation
X_small = X_large[:50]
kernel_result = profiler.profile_execution(
lambda: FidelityKernel(embedding).compute_kernel_matrix(X_small)
)
# Generate detailed reports
profiler.generate_detailed_report('<lambda>')
Best Practices Summary
1. Circuit Optimization
- Use circuit optimization passes
- Minimize gate count and depth
- Leverage hardware-specific optimizations
2. Computational Efficiency
- Implement batch processing
- Use memory-efficient algorithms
- Cache intermediate results
3. Hardware Utilization
- Utilize GPU acceleration when available
- Implement parallel processing
- Monitor resource usage
4. Algorithm Design
- Use adaptive sampling strategies
- Implement efficient hyperparameter optimization
- Profile and monitor performance
5. Scalability
- Design for large datasets
- Implement chunked processing
- Use distributed computing when needed
Performance Benchmarks
def run_performance_benchmarks():
"""Run comprehensive performance benchmarks"""
benchmarks = {
'small_dataset': np.random.randn(100, 4),
'medium_dataset': np.random.randn(500, 6),
'large_dataset': np.random.randn(1000, 8)
}
embeddings = {
'angle': AngleEmbedding,
'iqp': IQPEmbedding,
'amplitude': AmplitudeEmbedding
}
results = {}
for emb_name, emb_class in embeddings.items():
results[emb_name] = {}
for data_name, data in benchmarks.items():
n_features = data.shape[1]
embedding = emb_class(n_qubits=n_features)
# Time various operations
start_time = time.time()
# Circuit creation
circuits = [embedding.create_circuit(x) for x in data[:10]]
circuit_time = time.time() - start_time
# Expressibility computation
start_time = time.time()
expr_score = expressibility(embedding, n_samples=100)
expr_time = time.time() - start_time
results[emb_name][data_name] = {
'circuit_creation_time': circuit_time,
'expressibility_time': expr_time,
'total_time': circuit_time + expr_time
}
# Display results
import pandas as pd
for metric in ['circuit_creation_time', 'expressibility_time', 'total_time']:
print(f"\n{metric.replace('_', ' ').title()}:")
data_for_df = {}
for emb_name in results:
data_for_df[emb_name] = [results[emb_name][data_name][metric]
for data_name in benchmarks]
df = pd.DataFrame(data_for_df, index=benchmarks.keys())
print(df.round(4))
# Run benchmarks
run_performance_benchmarks()
This comprehensive optimization guide provides strategies for maximizing the performance of quantum data embeddings across different scales and use cases.