Cirq - Quantum Computing with Python

Parameterized Circuit

import sympy

# Define symbolic parameter
theta = sympy.Symbol('theta')

# Create parameterized circuit
circuit = cirq.Circuit(
    cirq.ry(theta)(q0),
    cirq.measure(q0, key='m')
)

# Sweep over parameter values
sweep = cirq.Linspace('theta', start=0, stop=2*np.pi, length=20)
results = simulator.run_sweep(circuit, params=sweep, repetitions=1000)

# Process results
for params, result in zip(sweep, results):
    theta_val = params['theta']
    counts = result.histogram(key='m')
    print(f"θ={theta_val:.2f}: {counts}")

Core Capabilities

Circuit Building

For comprehensive information about building quantum circuits, including qubits, gates, operations, custom gates, and circuit patterns, see:

• references/building.md - Complete guide to circuit construction

Common topics:

• Qubit types (GridQubit, LineQubit, NamedQubit)
• Single and two-qubit gates
• Parameterized gates and operations
• Custom gate decomposition
• Circuit organization with moments
• Standard circuit patterns (Bell states, GHZ, QFT)
• Import/export (OpenQASM, JSON)
• Working with qudits and observables

Simulation

For detailed information about simulating quantum circuits, including exact simulation, noisy simulation, parameter sweeps, and the Quantum Virtual Machine, see:

• references/simulation.md - Complete guide to quantum simulation

Common topics:

• Exact simulation (state vector, density matrix)
• Sampling and measurements
• Parameter sweeps (single and multiple parameters)
• Noisy simulation
• State histograms and visualization
• Quantum Virtual Machine (QVM)
• Expectation values and observables
• Performance optimization

Circuit Transformation

For information about optimizing, compiling, and manipulating quantum circuits, see:

• references/transformation.md - Complete guide to circuit transformations

Common topics:

• Transformer framework
• Gate decomposition
• Circuit optimization (merge gates, eject Z gates, drop negligible operations)
• Circuit compilation for hardware
• Qubit routing and SWAP insertion
• Custom transformers
• Transformation pipelines

Hardware Integration

For information about running circuits on real quantum hardware from various providers, see:

• references/hardware.md - Complete guide to hardware integration

Supported providers:

• Google Quantum AI (cirq-google) - Sycamore, Weber processors
• IonQ (cirq-ionq) - Trapped ion quantum computers
• Azure Quantum (azure-quantum) - IonQ and Honeywell backends
• AQT (cirq-aqt) - Alpine Quantum Technologies
• Pasqal (cirq-pasqal) - Neutral atom quantum computers

Topics include device representation, qubit selection, authentication, job management, and circuit optimization for hardware.

Noise Modeling

For information about modeling noise, noisy simulation, characterization, and error mitigation, see:

• references/noise.md - Complete guide to noise modeling

Common topics:

• Noise channels (depolarizing, amplitude damping, phase damping)
• Noise models (constant, gate-specific, qubit-specific, thermal)
• Adding noise to circuits
• Readout noise
• Noise characterization (randomized benchmarking, XEB)
• Noise visualization (heatmaps)
• Error mitigation techniques

Quantum Experiments

For information about designing experiments, parameter sweeps, data collection, and using the ReCirq framework, see:

• references/experiments.md - Complete guide to quantum experiments

Common topics:

• Experiment design patterns
• Parameter sweeps and data collection
• ReCirq framework structure
• Common algorithms (VQE, QAOA, QPE)
• Data analysis and visualization
• Statistical analysis and fidelity estimation
• Parallel data collection

Common Patterns

Variational Algorithm Template

import scipy.optimize

def variational_algorithm(ansatz, cost_function, initial_params):
    """Template for variational quantum algorithms."""

    def objective(params):
        circuit = ansatz(params)
        simulator = cirq.Simulator()
        result = simulator.simulate(circuit)
        return cost_function(result)

    # Optimize
    result = scipy.optimize.minimize(
        objective,
        initial_params,
        method='COBYLA'
    )

    return result

# Define ansatz
def my_ansatz(params):
    q = cirq.LineQubit(0)
    return cirq.Circuit(
        cirq.ry(params[0])(q),
        cirq.rz(params[1])(q)
    )

# Define cost function
def my_cost(result):
    state = result.final_state_vector
    # Calculate cost based on state
    return np.real(state[0])

# Run optimization
result = variational_algorithm(my_ansatz, my_cost, [0.0, 0.0])

Hardware Execution Template

def run_on_hardware(circuit, provider='google', device_name='weber', repetitions=1000):
    """Template for running on quantum hardware."""

    if provider == 'google':
        import cirq_google
        engine = cirq_google.get_engine()
        processor = engine.get_processor(device_name)
        job = processor.run(circuit, repetitions=repetitions)
        return job.results()[0]

    elif provider == 'ionq':
        import cirq_ionq
        service = cirq_ionq.Service()
        result = service.run(circuit, repetitions=repetitions, target='qpu')
        return result

    elif provider == 'azure':
        from azure.quantum.cirq import AzureQuantumService
        # Setup workspace...
        service = AzureQuantumService(workspace)
        result = service.run(circuit, repetitions=repetitions, target='ionq.qpu')
        return result

    else:
        raise ValueError(f"Unknown provider: {provider}")

Noise Study Template

def noise_comparison_study(circuit, noise_levels):
    """Compare circuit performance at different noise levels."""

    results = {}

    for noise_level in noise_levels:
        # Create noisy circuit
        noisy_circuit = circuit.with_noise(cirq.depolarize(p=noise_level))

        # Simulate
        simulator = cirq.DensityMatrixSimulator()
        result = simulator.run(noisy_circuit, repetitions=1000)

        # Analyze
        results[noise_level] = {
            'histogram': result.histogram(key='result'),
            'dominant_state': max(
                result.histogram(key='result').items(),
                key=lambda x: x[1]
            )
        }

    return results

# Run study
noise_levels = [0.0, 0.001, 0.01, 0.05, 0.1]
results = noise_comparison_study(circuit, noise_levels)

Best Practices

1. Circuit Design

   • Use appropriate qubit types for your topology
   • Keep circuits modular and reusable
   • Label measurements with descriptive keys
   • Validate circuits against device constraints before execution

2. Simulation

   • Use state vector simulation for pure states (more efficient)
   • Use density matrix simulation only when needed (mixed states, noise)
   • Leverage parameter sweeps instead of individual runs
   • Monitor memory usage for large systems (2^n grows quickly)

3. Hardware Execution

   • Always test on simulators first
   • Select best qubits using calibration data
   • Optimize circuits for target hardware gateset
   • Implement error mitigation for production runs
   • Store expensive hardware results immediately

4. Circuit Optimization

   • Start with high-level built-in transformers
   • Chain multiple optimizations in sequence
   • Track depth and gate count reduction
   • Validate correctness after transformation

5. Noise Modeling

   • Use realistic noise models from calibration data
   • Include all error sources (gate, decoherence, readout)
   • Characterize before mitigating
   • Keep circuits shallow to minimize noise accumulation

6. Experiments

   • Structure experiments with clear separation (data generation, collection, analysis)
   • Use ReCirq patterns for reproducibility
   • Save intermediate results frequently
   • Parallelize independent tasks
   • Document thoroughly with metadata

Additional Resources

• Official Documentation: https://quantumai.google/cirq
• API Reference: https://quantumai.google/reference/python/cirq
• Tutorials: https://quantumai.google/cirq/tutorials
• Examples: https://github.com/quantumlib/Cirq/tree/master/examples
• ReCirq: https://github.com/quantumlib/ReCirq

Common Issues

Circuit too deep for hardware:

• Use circuit optimization transformers to reduce depth
• See transformation.md for optimization techniques

Memory issues with simulation:

• Switch from density matrix to state vector simulator
• Reduce number of qubits or use stabilizer simulator for Clifford circuits

Device validation errors:

• Check qubit connectivity with device.metadata.nx_graph
• Decompose gates to device-native gateset
• See hardware.md for device-specific compilation

Noisy simulation too slow:

• Density matrix simulation is O(2^2n) - consider reducing qubits
• Use noise models selectively on critical operations only
• See simulation.md for performance optimization

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