Add support for Cirq: library for writing, manipulating, and optimizing quantum circuits, and then running them on quantum computers and quantum simulators.

2026-03-27 07:09:27 +08:00 · 2025-11-30 08:02:58 -05:00
parent a077cee836
commit 16e47a1755
9 changed files with 3023 additions and 6 deletions
--- a/scientific-skills/cirq/references/noise.md
+++ b/scientific-skills/cirq/references/noise.md
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+# Noise Modeling and Mitigation
+
+This guide covers noise models, noisy simulation, characterization, and error mitigation in Cirq.
+
+## Noise Channels
+
+### Depolarizing Noise
+
+```python
+import cirq
+import numpy as np
+
+# Single-qubit depolarizing channel
+depol_channel = cirq.depolarize(p=0.01)
+
+# Apply to qubit
+q = cirq.LineQubit(0)
+noisy_op = depol_channel(q)
+
+# Add to circuit
+circuit = cirq.Circuit(
+    cirq.H(q),
+    depol_channel(q),
+    cirq.measure(q, key='m')
+)
+```
+
+### Amplitude Damping
+
+```python
+# Amplitude damping (T1 decay)
+gamma = 0.1
+amp_damp = cirq.amplitude_damp(gamma)
+
+# Apply after gate
+circuit = cirq.Circuit(
+    cirq.X(q),
+    amp_damp(q)
+)
+```
+
+### Phase Damping
+
+```python
+# Phase damping (T2 dephasing)
+gamma = 0.1
+phase_damp = cirq.phase_damp(gamma)
+
+circuit = cirq.Circuit(
+    cirq.H(q),
+    phase_damp(q)
+)
+```
+
+### Bit Flip Noise
+
+```python
+# Bit flip channel
+bit_flip_prob = 0.01
+bit_flip = cirq.bit_flip(bit_flip_prob)
+
+circuit = cirq.Circuit(
+    cirq.H(q),
+    bit_flip(q)
+)
+```
+
+### Phase Flip Noise
+
+```python
+# Phase flip channel
+phase_flip_prob = 0.01
+phase_flip = cirq.phase_flip(phase_flip_prob)
+
+circuit = cirq.Circuit(
+    cirq.H(q),
+    phase_flip(q)
+)
+```
+
+### Generalized Amplitude Damping
+
+```python
+# Generalized amplitude damping
+p = 0.1  # Damping probability
+gamma = 0.2  # Excitation probability
+gen_amp_damp = cirq.generalized_amplitude_damp(p=p, gamma=gamma)
+```
+
+### Reset Channel
+
+```python
+# Reset to |0⟩ or |1⟩
+reset_to_zero = cirq.reset(q)
+
+# Reset appears as measurement followed by conditional flip
+circuit = cirq.Circuit(
+    cirq.H(q),
+    reset_to_zero
+)
+```
+
+## Noise Models
+
+### Constant Noise Model
+
+```python
+# Apply same noise to all qubits
+noise = cirq.ConstantQubitNoiseModel(
+    qubit_noise_gate=cirq.depolarize(0.01)
+)
+
+# Simulate with noise
+simulator = cirq.DensityMatrixSimulator(noise=noise)
+result = simulator.run(circuit, repetitions=1000)
+```
+
+### Gate-Specific Noise
+
+```python
+class CustomNoiseModel(cirq.NoiseModel):
+    """Apply different noise to different gate types."""
+
+    def noisy_operation(self, op):
+        # Single-qubit gates: depolarizing noise
+        if len(op.qubits) == 1:
+            return [op, cirq.depolarize(0.001)(op.qubits[0])]
+
+        # Two-qubit gates: higher depolarizing noise
+        elif len(op.qubits) == 2:
+            return [
+                op,
+                cirq.depolarize(0.01)(op.qubits[0]),
+                cirq.depolarize(0.01)(op.qubits[1])
+            ]
+
+        return op
+
+# Use custom noise model
+noise_model = CustomNoiseModel()
+simulator = cirq.DensityMatrixSimulator(noise=noise_model)
+```
+
+### Qubit-Specific Noise
+
+```python
+class QubitSpecificNoise(cirq.NoiseModel):
+    """Different noise for different qubits."""
+
+    def __init__(self, qubit_noise_map):
+        self.qubit_noise_map = qubit_noise_map
+
+    def noisy_operation(self, op):
+        noise_ops = [op]
+        for qubit in op.qubits:
+            if qubit in self.qubit_noise_map:
+                noise = self.qubit_noise_map[qubit]
+                noise_ops.append(noise(qubit))
+        return noise_ops
+
+# Define per-qubit noise
+q0, q1, q2 = cirq.LineQubit.range(3)
+noise_map = {
+    q0: cirq.depolarize(0.001),
+    q1: cirq.depolarize(0.005),
+    q2: cirq.depolarize(0.002)
+}
+
+noise_model = QubitSpecificNoise(noise_map)
+```
+
+### Thermal Noise
+
+```python
+class ThermalNoise(cirq.NoiseModel):
+    """Thermal relaxation noise."""
+
+    def __init__(self, T1, T2, gate_time):
+        self.T1 = T1  # Amplitude damping time
+        self.T2 = T2  # Dephasing time
+        self.gate_time = gate_time
+
+    def noisy_operation(self, op):
+        # Calculate probabilities
+        p_amp = 1 - np.exp(-self.gate_time / self.T1)
+        p_phase = 1 - np.exp(-self.gate_time / self.T2)
+
+        noise_ops = [op]
+        for qubit in op.qubits:
+            noise_ops.append(cirq.amplitude_damp(p_amp)(qubit))
+            noise_ops.append(cirq.phase_damp(p_phase)(qubit))
+
+        return noise_ops
+
+# Typical superconducting qubit parameters
+T1 = 50e-6  # 50 μs
+T2 = 30e-6  # 30 μs
+gate_time = 25e-9  # 25 ns
+
+noise_model = ThermalNoise(T1, T2, gate_time)
+```
+
+## Adding Noise to Circuits
+
+### with_noise Method
+
+```python
+# Add noise to all operations
+noisy_circuit = circuit.with_noise(cirq.depolarize(p=0.01))
+
+# Simulate noisy circuit
+simulator = cirq.DensityMatrixSimulator()
+result = simulator.run(noisy_circuit, repetitions=1000)
+```
+
+### insert_into_circuit Method
+
+```python
+# Manual noise insertion
+def add_noise_to_circuit(circuit, noise_model):
+    noisy_moments = []
+    for moment in circuit:
+        ops = []
+        for op in moment:
+            ops.extend(noise_model.noisy_operation(op))
+        noisy_moments.append(cirq.Moment(ops))
+    return cirq.Circuit(noisy_moments)
+```
+
+## Readout Noise
+
+### Measurement Error Model
+
+```python
+class ReadoutNoiseModel(cirq.NoiseModel):
+    """Model readout/measurement errors."""
+
+    def __init__(self, p0_given_1, p1_given_0):
+        # p0_given_1: Probability of measuring 0 when state is 1
+        # p1_given_0: Probability of measuring 1 when state is 0
+        self.p0_given_1 = p0_given_1
+        self.p1_given_0 = p1_given_0
+
+    def noisy_operation(self, op):
+        if isinstance(op.gate, cirq.MeasurementGate):
+            # Apply bit flip before measurement
+            noise_ops = []
+            for qubit in op.qubits:
+                # Average readout error
+                p_error = (self.p0_given_1 + self.p1_given_0) / 2
+                noise_ops.append(cirq.bit_flip(p_error)(qubit))
+            noise_ops.append(op)
+            return noise_ops
+        return op
+
+# Typical readout errors
+readout_noise = ReadoutNoiseModel(p0_given_1=0.02, p1_given_0=0.01)
+```
+
+## Noise Characterization
+
+### Randomized Benchmarking
+
+```python
+import cirq
+
+def generate_rb_circuit(qubits, depth):
+    """Generate randomized benchmarking circuit."""
+    # Random Clifford gates
+    clifford_gates = [cirq.X, cirq.Y, cirq.Z, cirq.H, cirq.S]
+
+    circuit = cirq.Circuit()
+    for _ in range(depth):
+        for qubit in qubits:
+            gate = np.random.choice(clifford_gates)
+            circuit.append(gate(qubit))
+
+    # Add inverse to return to initial state (ideally)
+    # (simplified - proper RB requires tracking full sequence)
+
+    circuit.append(cirq.measure(*qubits, key='result'))
+    return circuit
+
+# Run RB experiment
+def run_rb_experiment(qubits, depths, repetitions=1000):
+    """Run randomized benchmarking at various depths."""
+    simulator = cirq.DensityMatrixSimulator(
+        noise=cirq.ConstantQubitNoiseModel(cirq.depolarize(0.01))
+    )
+
+    survival_probs = []
+    for depth in depths:
+        circuits = [generate_rb_circuit(qubits, depth) for _ in range(20)]
+
+        total_survival = 0
+        for circuit in circuits:
+            result = simulator.run(circuit, repetitions=repetitions)
+            # Calculate survival probability (returned to |0⟩)
+            counts = result.histogram(key='result')
+            survival = counts.get(0, 0) / repetitions
+            total_survival += survival
+
+        avg_survival = total_survival / len(circuits)
+        survival_probs.append(avg_survival)
+
+    return survival_probs
+
+# Fit to extract error rate
+# p_survival = A * p^depth + B
+# Error per gate ≈ (1 - p) / 2
+```
+
+### Cross-Entropy Benchmarking (XEB)
+
+```python
+def xeb_fidelity(circuit, simulator, ideal_probs, repetitions=10000):
+    """Calculate XEB fidelity."""
+
+    # Run noisy simulation
+    result = simulator.run(circuit, repetitions=repetitions)
+    measured_probs = result.histogram(key='result')
+
+    # Normalize
+    for key in measured_probs:
+        measured_probs[key] /= repetitions
+
+    # Calculate cross-entropy
+    cross_entropy = 0
+    for bitstring, prob in measured_probs.items():
+        if bitstring in ideal_probs:
+            cross_entropy += prob * np.log2(ideal_probs[bitstring])
+
+    # Convert to fidelity
+    n_qubits = len(circuit.all_qubits())
+    fidelity = (2**n_qubits * cross_entropy + 1) / (2**n_qubits - 1)
+
+    return fidelity
+```
+
+## Noise Visualization
+
+### Heatmap Visualization
+
+```python
+import matplotlib.pyplot as plt
+
+def plot_noise_heatmap(device, noise_metric):
+    """Plot noise characteristics across 2D grid device."""
+
+    # Get device qubits (assuming GridQubit)
+    qubits = sorted(device.metadata.qubit_set)
+    rows = max(q.row for q in qubits) + 1
+    cols = max(q.col for q in qubits) + 1
+
+    # Create heatmap data
+    heatmap = np.full((rows, cols), np.nan)
+
+    for qubit in qubits:
+        if isinstance(qubit, cirq.GridQubit):
+            value = noise_metric.get(qubit, 0)
+            heatmap[qubit.row, qubit.col] = value
+
+    # Plot
+    plt.figure(figsize=(10, 8))
+    plt.imshow(heatmap, cmap='RdYlGn_r', interpolation='nearest')
+    plt.colorbar(label='Error Rate')
+    plt.title('Qubit Error Rates')
+    plt.xlabel('Column')
+    plt.ylabel('Row')
+    plt.show()
+
+# Example usage
+noise_metric = {q: np.random.random() * 0.01 for q in device.metadata.qubit_set}
+plot_noise_heatmap(device, noise_metric)
+```
+
+### Gate Fidelity Visualization
+
+```python
+def plot_gate_fidelities(calibration_data):
+    """Plot single- and two-qubit gate fidelities."""
+
+    sq_fidelities = []
+    tq_fidelities = []
+
+    for qubit, metrics in calibration_data.items():
+        if 'single_qubit_rb_fidelity' in metrics:
+            sq_fidelities.append(metrics['single_qubit_rb_fidelity'])
+        if 'two_qubit_rb_fidelity' in metrics:
+            tq_fidelities.append(metrics['two_qubit_rb_fidelity'])
+
+    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
+
+    ax1.hist(sq_fidelities, bins=20)
+    ax1.set_xlabel('Single-Qubit Gate Fidelity')
+    ax1.set_ylabel('Count')
+    ax1.set_title('Single-Qubit Gate Fidelities')
+
+    ax2.hist(tq_fidelities, bins=20)
+    ax2.set_xlabel('Two-Qubit Gate Fidelity')
+    ax2.set_ylabel('Count')
+    ax2.set_title('Two-Qubit Gate Fidelities')
+
+    plt.tight_layout()
+    plt.show()
+```
+
+## Error Mitigation Techniques
+
+### Zero-Noise Extrapolation
+
+```python
+def zero_noise_extrapolation(circuit, noise_levels, simulator):
+    """Extrapolate to zero noise limit."""
+
+    expectation_values = []
+
+    for noise_level in noise_levels:
+        # Scale noise
+        noisy_circuit = circuit.with_noise(
+            cirq.depolarize(p=noise_level)
+        )
+
+        # Measure expectation
+        result = simulator.simulate(noisy_circuit)
+        # ... calculate expectation value
+        exp_val = calculate_expectation(result)
+        expectation_values.append(exp_val)
+
+    # Extrapolate to zero noise
+    from scipy.optimize import curve_fit
+
+    def exponential_fit(x, a, b, c):
+        return a * np.exp(-b * x) + c
+
+    popt, _ = curve_fit(exponential_fit, noise_levels, expectation_values)
+    zero_noise_value = popt[2]
+
+    return zero_noise_value
+```
+
+### Probabilistic Error Cancellation
+
+```python
+def quasi_probability_decomposition(noisy_gate, ideal_gate, noise_model):
+    """Decompose noisy gate into quasi-probability distribution."""
+
+    # Decompose noisy gate as: N = ideal + error
+    # Invert: ideal = (N - error) / (1 - error_rate)
+
+    # This creates a quasi-probability distribution
+    # (some probabilities may be negative)
+
+    # Implementation depends on specific noise model
+    pass
+```
+
+### Readout Error Mitigation
+
+```python
+def mitigate_readout_errors(results, confusion_matrix):
+    """Apply readout error mitigation using confusion matrix."""
+
+    # Invert confusion matrix
+    inv_confusion = np.linalg.inv(confusion_matrix)
+
+    # Get measured counts
+    counts = results.histogram(key='result')
+
+    # Convert to probability vector
+    total_counts = sum(counts.values())
+    measured_probs = np.array([counts.get(i, 0) / total_counts
+                               for i in range(len(confusion_matrix))])
+
+    # Apply inverse
+    corrected_probs = inv_confusion @ measured_probs
+
+    # Convert back to counts
+    corrected_counts = {i: int(p * total_counts)
+                       for i, p in enumerate(corrected_probs) if p > 0}
+
+    return corrected_counts
+```
+
+## Hardware-Based Noise Models
+
+### From Google Calibration
+
+```python
+import cirq_google
+
+# Get calibration data
+processor = cirq_google.get_engine().get_processor('weber')
+noise_props = processor.get_device_specification()
+
+# Create noise model from calibration
+noise_model = cirq_google.NoiseModelFromGoogleNoiseProperties(noise_props)
+
+# Simulate with realistic noise
+simulator = cirq.DensityMatrixSimulator(noise=noise_model)
+result = simulator.run(circuit, repetitions=1000)
+```
+
+## Best Practices
+
+1. **Use density matrix simulator for noisy simulations**: State vector simulators cannot model mixed states
+2. **Match noise model to hardware**: Use calibration data when available
+3. **Include all error sources**: Gate errors, decoherence, readout errors
+4. **Characterize before mitigating**: Understand noise before applying mitigation
+5. **Consider error propagation**: Noise compounds through circuit depth
+6. **Use appropriate benchmarking**: RB for gate errors, XEB for full circuit fidelity
+7. **Visualize noise patterns**: Identify problematic qubits and gates
+8. **Apply targeted mitigation**: Focus on dominant error sources
+9. **Validate mitigation**: Verify that mitigation improves results
+10. **Keep circuits shallow**: Minimize noise accumulation