PennyLane

import pennylane as qml
from pennylane import numpy as np

# Create device
dev = qml.device('default.qubit', wires=2)

# Define quantum circuit
@qml.qnode(dev)
def circuit(params):
    qml.RX(params[0], wires=0)
    qml.RY(params[1], wires=1)
    qml.CNOT(wires=[0, 1])
    return qml.expval(qml.PauliZ(0))

# Optimize parameters
opt = qml.GradientDescentOptimizer(stepsize=0.1)
params = np.array([0.1, 0.2], requires_grad=True)

for i in range(100):
    params = opt.step(circuit, params)

Core Capabilities

1. Quantum Circuit Construction

Build circuits with gates, measurements, and state preparation. See references/quantum_circuits.md for:

• Single and multi-qubit gates
• Controlled operations and conditional logic
• Mid-circuit measurements and adaptive circuits
• Various measurement types (expectation, probability, samples)
• Circuit inspection and debugging

2. Quantum Machine Learning

Create hybrid quantum-classical models. See references/quantum_ml.md for:

• Integration with PyTorch, JAX, TensorFlow
• Quantum neural networks and variational classifiers
• Data encoding strategies (angle, amplitude, basis, IQP)
• Training hybrid models with backpropagation
• Transfer learning with quantum circuits

3. Quantum Chemistry

Simulate molecules and compute ground state energies. See references/quantum_chemistry.md for:

• Molecular Hamiltonian generation
• Variational Quantum Eigensolver (VQE)
• UCCSD ansatz for chemistry
• Geometry optimization and dissociation curves
• Molecular property calculations

4. Device Management

Execute on simulators or quantum hardware. See references/devices_backends.md for:

• Built-in simulators (default.qubit, lightning.qubit, default.mixed)
• Hardware plugins (IBM, Amazon Braket, Google, Rigetti, IonQ)
• Device selection and configuration
• Performance optimization and caching
• GPU acceleration and JIT compilation

5. Optimization

Train quantum circuits with various optimizers. See references/optimization.md for:

• Built-in optimizers (Adam, gradient descent, momentum, RMSProp)
• Gradient computation methods (backprop, parameter-shift, adjoint)
• Variational algorithms (VQE, QAOA)
• Training strategies (learning rate schedules, mini-batches)
• Handling barren plateaus and local minima

6. Advanced Features

Leverage templates, transforms, and compilation. See references/advanced_features.md for:

• Circuit templates and layers
• Transforms and circuit optimization
• Pulse-level programming
• Catalyst JIT compilation
• Noise models and error mitigation
• Resource estimation

Common Workflows

Train a Variational Classifier

# 1. Define ansatz
@qml.qnode(dev)
def classifier(x, weights):
    # Encode data
    qml.AngleEmbedding(x, wires=range(4))

    # Variational layers
    qml.StronglyEntanglingLayers(weights, wires=range(4))

    return qml.expval(qml.PauliZ(0))

# 2. Train
opt = qml.AdamOptimizer(stepsize=0.01)
weights = np.random.random((3, 4, 3))  # 3 layers, 4 wires

for epoch in range(100):
    for x, y in zip(X_train, y_train):
        weights = opt.step(lambda w: (classifier(x, w) - y)**2, weights)

Run VQE for Molecular Ground State

from pennylane import qchem

# 1. Build Hamiltonian
symbols = ['H', 'H']
coords = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.74])
H, n_qubits = qchem.molecular_hamiltonian(symbols, coords)

# 2. Define ansatz
@qml.qnode(dev)
def vqe_circuit(params):
    qml.BasisState(qchem.hf_state(2, n_qubits), wires=range(n_qubits))
    qml.UCCSD(params, wires=range(n_qubits))
    return qml.expval(H)

# 3. Optimize
opt = qml.AdamOptimizer(stepsize=0.1)
params = np.zeros(10, requires_grad=True)

for i in range(100):
    params, energy = opt.step_and_cost(vqe_circuit, params)
    print(f"Step {i}: Energy = {energy:.6f} Ha")

Switch Between Devices

# Same circuit, different backends
circuit_def = lambda dev: qml.qnode(dev)(circuit_function)

# Test on simulator
dev_sim = qml.device('default.qubit', wires=4)
result_sim = circuit_def(dev_sim)(params)

# Run on quantum hardware
dev_hw = qml.device('qiskit.ibmq', wires=4, backend='ibmq_manila')
result_hw = circuit_def(dev_hw)(params)

Detailed Documentation

For comprehensive coverage of specific topics, consult the reference files:

• Getting started: references/getting_started.md - Installation, basic concepts, first steps
• Quantum circuits: references/quantum_circuits.md - Gates, measurements, circuit patterns
• Quantum ML: references/quantum_ml.md - Hybrid models, framework integration, QNNs
• Quantum chemistry: references/quantum_chemistry.md - VQE, molecular Hamiltonians, chemistry workflows
• Devices: references/devices_backends.md - Simulators, hardware plugins, device configuration
• Optimization: references/optimization.md - Optimizers, gradients, variational algorithms
• Advanced: references/advanced_features.md - Templates, transforms, JIT compilation, noise

Best Practices

1. Start with simulators - Test on default.qubit before deploying to hardware
2. Use parameter-shift for hardware - Backpropagation only works on simulators
3. Choose appropriate encodings - Match data encoding to problem structure
4. Initialize carefully - Use small random values to avoid barren plateaus
5. Monitor gradients - Check for vanishing gradients in deep circuits
6. Cache devices - Reuse device objects to reduce initialization overhead
7. Profile circuits - Use qml.specs() to analyze circuit complexity
8. Test locally - Validate on simulators before submitting to hardware
9. Use templates - Leverage built-in templates for common circuit patterns
10. Compile when possible - Use Catalyst JIT for performance-critical code

Resources

• Official documentation: https://docs.pennylane.ai
• Codebook (tutorials): https://pennylane.ai/codebook
• QML demonstrations: https://pennylane.ai/qml/demonstrations
• Community forum: https://discuss.pennylane.ai
• GitHub: https://github.com/PennyLaneAI/pennylane