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Quantum Computing with Python\n\nCirq is Google Quantum AI's open-source framework for designing, simulating, and running quantum circuits on quantum computers and simulators.\n\n## Installation\n\n```bash\nuv pip install cirq\n```\n\nFor hardware integration:\n```bash\n# Google Quantum Engine\nuv pip install cirq-google\n\n# IonQ\nuv pip install cirq-ionq\n\n# AQT (Alpine Quantum Technologies)\nuv pip install cirq-aqt\n\n# Pasqal\nuv pip install cirq-pasqal\n\n# Azure Quantum\nuv pip install azure-quantum cirq\n```\n\n## Quick Start\n\n### Basic Circuit\n\n```python\nimport cirq\nimport numpy as np\n\n# Create qubits\nq0, q1 = cirq.LineQubit.range(2)\n\n# Build circuit\ncircuit = cirq.Circuit(\n    cirq.H(q0),              # Hadamard on q0\n    cirq.CNOT(q0, q1),       # CNOT with q0 control, q1 target\n    cirq.measure(q0, q1, key='result')\n)\n\nprint(circuit)\n\n# Simulate\nsimulator = cirq.Simulator()\nresult = simulator.run(circuit, repetitions=1000)\n\n# Display results\nprint(result.histogram(key='result'))\n```\n\n### Parameterized Circuit\n\n```python\nimport sympy\n\n# Define symbolic parameter\ntheta = sympy.Symbol('theta')\n\n# Create parameterized circuit\ncircuit = cirq.Circuit(\n    cirq.ry(theta)(q0),\n    cirq.measure(q0, key='m')\n)\n\n# Sweep over parameter values\nsweep = cirq.Linspace('theta', start=0, stop=2*np.pi, length=20)\nresults = simulator.run_sweep(circuit, params=sweep, repetitions=1000)\n\n# Process results\nfor params, result in zip(sweep, results):\n    theta_val = params['theta']\n    counts = result.histogram(key='m')\n    print(f\"θ={theta_val:.2f}: {counts}\")\n```\n\n## Core Capabilities\n\n### Circuit Building\nFor comprehensive information about building quantum circuits, including qubits, gates, operations, custom gates, and circuit patterns, see:\n- **[references\u002Fbuilding.md](references\u002Fbuilding.md)** - Complete guide to circuit construction\n\nCommon topics:\n- Qubit types (GridQubit, LineQubit, NamedQubit)\n- Single and two-qubit gates\n- Parameterized gates and operations\n- Custom gate decomposition\n- Circuit organization with moments\n- Standard circuit patterns (Bell states, GHZ, QFT)\n- Import\u002Fexport (OpenQASM, JSON)\n- Working with qudits and observables\n\n### Simulation\nFor detailed information about simulating quantum circuits, including exact simulation, noisy simulation, parameter sweeps, and the Quantum Virtual Machine, see:\n- **[references\u002Fsimulation.md](references\u002Fsimulation.md)** - Complete guide to quantum simulation\n\nCommon topics:\n- Exact simulation (state vector, density matrix)\n- Sampling and measurements\n- Parameter sweeps (single and multiple parameters)\n- Noisy simulation\n- State histograms and visualization\n- Quantum Virtual Machine (QVM)\n- Expectation values and observables\n- Performance optimization\n\n### Circuit Transformation\nFor information about optimizing, compiling, and manipulating quantum circuits, see:\n- **[references\u002Ftransformation.md](references\u002Ftransformation.md)** - Complete guide to circuit transformations\n\nCommon topics:\n- Transformer framework\n- Gate decomposition\n- Circuit optimization (merge gates, eject Z gates, drop negligible operations)\n- Circuit compilation for hardware\n- Qubit routing and SWAP insertion\n- Custom transformers\n- Transformation pipelines\n\n### Hardware Integration\nFor information about running circuits on real quantum hardware from various providers, see:\n- **[references\u002Fhardware.md](references\u002Fhardware.md)** - Complete guide to hardware integration\n\nSupported providers:\n- **Google Quantum AI** (cirq-google) - Sycamore, Weber processors\n- **IonQ** (cirq-ionq) - Trapped ion quantum computers\n- **Azure Quantum** (azure-quantum) - IonQ and Honeywell backends\n- **AQT** (cirq-aqt) - Alpine Quantum Technologies\n- **Pasqal** (cirq-pasqal) - Neutral atom quantum computers\n\nTopics include device representation, qubit selection, authentication, job management, and circuit optimization for hardware.\n\n### Noise Modeling\nFor information about modeling noise, noisy simulation, characterization, and error mitigation, see:\n- **[references\u002Fnoise.md](references\u002Fnoise.md)** - Complete guide to noise modeling\n\nCommon topics:\n- Noise channels (depolarizing, amplitude damping, phase damping)\n- Noise models (constant, gate-specific, qubit-specific, thermal)\n- Adding noise to circuits\n- Readout noise\n- Noise characterization (randomized benchmarking, XEB)\n- Noise visualization (heatmaps)\n- Error mitigation techniques\n\n### Quantum Experiments\nFor information about designing experiments, parameter sweeps, data collection, and using the ReCirq framework, see:\n- **[references\u002Fexperiments.md](references\u002Fexperiments.md)** - Complete guide to quantum experiments\n\nCommon topics:\n- Experiment design patterns\n- Parameter sweeps and data collection\n- ReCirq framework structure\n- Common algorithms (VQE, QAOA, QPE)\n- Data analysis and visualization\n- Statistical analysis and fidelity estimation\n- Parallel data collection\n\n## Common Patterns\n\n### Variational Algorithm Template\n\n```python\nimport scipy.optimize\n\ndef variational_algorithm(ansatz, cost_function, initial_params):\n    \"\"\"Template for variational quantum algorithms.\"\"\"\n\n    def objective(params):\n        circuit = ansatz(params)\n        simulator = cirq.Simulator()\n        result = simulator.simulate(circuit)\n        return cost_function(result)\n\n    # Optimize\n    result = scipy.optimize.minimize(\n        objective,\n        initial_params,\n        method='COBYLA'\n    )\n\n    return result\n\n# Define ansatz\ndef my_ansatz(params):\n    q = cirq.LineQubit(0)\n    return cirq.Circuit(\n        cirq.ry(params[0])(q),\n        cirq.rz(params[1])(q)\n    )\n\n# Define cost function\ndef my_cost(result):\n    state = result.final_state_vector\n    # Calculate cost based on state\n    return np.real(state[0])\n\n# Run optimization\nresult = variational_algorithm(my_ansatz, my_cost, [0.0, 0.0])\n```\n\n### Hardware Execution Template\n\n```python\ndef run_on_hardware(circuit, provider='google', device_name='weber', repetitions=1000):\n    \"\"\"Template for running on quantum hardware.\"\"\"\n\n    if provider == 'google':\n        import cirq_google\n        engine = cirq_google.get_engine()\n        processor = engine.get_processor(device_name)\n        job = processor.run(circuit, repetitions=repetitions)\n        return job.results()[0]\n\n    elif provider == 'ionq':\n        import cirq_ionq\n        service = cirq_ionq.Service()\n        result = service.run(circuit, repetitions=repetitions, target='qpu')\n        return result\n\n    elif provider == 'azure':\n        from azure.quantum.cirq import AzureQuantumService\n        # Setup workspace...\n        service = AzureQuantumService(workspace)\n        result = service.run(circuit, repetitions=repetitions, target='ionq.qpu')\n        return result\n\n    else:\n        raise ValueError(f\"Unknown provider: {provider}\")\n```\n\n### Noise Study Template\n\n```python\ndef noise_comparison_study(circuit, noise_levels):\n    \"\"\"Compare circuit performance at different noise levels.\"\"\"\n\n    results = {}\n\n    for noise_level in noise_levels:\n        # Create noisy circuit\n        noisy_circuit = circuit.with_noise(cirq.depolarize(p=noise_level))\n\n        # Simulate\n        simulator = cirq.DensityMatrixSimulator()\n        result = simulator.run(noisy_circuit, repetitions=1000)\n\n        # Analyze\n        results[noise_level] = {\n            'histogram': result.histogram(key='result'),\n            'dominant_state': max(\n                result.histogram(key='result').items(),\n                key=lambda x: x[1]\n            )\n        }\n\n    return results\n\n# Run study\nnoise_levels = [0.0, 0.001, 0.01, 0.05, 0.1]\nresults = noise_comparison_study(circuit, noise_levels)\n```\n\n## Best Practices\n\n1. **Circuit Design**\n   - Use appropriate qubit types for your topology\n   - Keep circuits modular and reusable\n   - Label measurements with descriptive keys\n   - Validate circuits against device constraints before execution\n\n2. **Simulation**\n   - Use state vector simulation for pure states (more efficient)\n   - Use density matrix simulation only when needed (mixed states, noise)\n   - Leverage parameter sweeps instead of individual runs\n   - Monitor memory usage for large systems (2^n grows quickly)\n\n3. **Hardware Execution**\n   - Always test on simulators first\n   - Select best qubits using calibration data\n   - Optimize circuits for target hardware gateset\n   - Implement error mitigation for production runs\n   - Store expensive hardware results immediately\n\n4. **Circuit Optimization**\n   - Start with high-level built-in transformers\n   - Chain multiple optimizations in sequence\n   - Track depth and gate count reduction\n   - Validate correctness after transformation\n\n5. **Noise Modeling**\n   - Use realistic noise models from calibration data\n   - Include all error sources (gate, decoherence, readout)\n   - Characterize before mitigating\n   - Keep circuits shallow to minimize noise accumulation\n\n6. **Experiments**\n   - Structure experiments with clear separation (data generation, collection, analysis)\n   - Use ReCirq patterns for reproducibility\n   - Save intermediate results frequently\n   - Parallelize independent tasks\n   - Document thoroughly with metadata\n\n## Additional Resources\n\n- **Official Documentation**: https:\u002F\u002Fquantumai.google\u002Fcirq\n- **API Reference**: https:\u002F\u002Fquantumai.google\u002Freference\u002Fpython\u002Fcirq\n- **Tutorials**: https:\u002F\u002Fquantumai.google\u002Fcirq\u002Ftutorials\n- **Examples**: https:\u002F\u002Fgithub.com\u002Fquantumlib\u002FCirq\u002Ftree\u002Fmaster\u002Fexamples\n- **ReCirq**: https:\u002F\u002Fgithub.com\u002Fquantumlib\u002FReCirq\n\n## Common Issues\n\n**Circuit too deep for hardware:**\n- Use circuit optimization transformers to reduce depth\n- See `transformation.md` for optimization techniques\n\n**Memory issues with simulation:**\n- Switch from density matrix to state vector simulator\n- Reduce number of qubits or use stabilizer simulator for Clifford circuits\n\n**Device validation errors:**\n- Check qubit connectivity with device.metadata.nx_graph\n- Decompose gates to device-native gateset\n- See `hardware.md` for device-specific compilation\n\n**Noisy simulation too slow:**\n- Density matrix simulation is O(2^2n) - 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