error_mitigation.py

from typing import List, Dict, Tuple, Optional, Callable
import numpy as np
from qiskit import QuantumCircuit
from qiskit.quantum_info import Operator
import scipy.optimize as optimize
from dataclasses import dataclass
import matplotlib.pyplot as plt

@dataclass
class NoiseModel:
    """Represents a quantum noise model"""
    single_qubit_error_rates: Dict[int, float]
    two_qubit_error_rates: Dict[Tuple[int, int], float]
    measurement_error_rates: Dict[int, float]
    coherence_times: Dict[int, Tuple[float, float]]  # T1, T2 times

@dataclass
class MitigationResult:
    """Results from error mitigation"""
    mitigated_counts: Dict[str, float]
    confidence_intervals: Dict[str, Tuple[float, float]]
    extrapolated_value: float
    mitigation_method: str
    fidelity_improvement: float

class QuantumErrorMitigator:
    def __init__(self, noise_model: NoiseModel):
        self.noise_model = noise_model
        self.measurement_calibration = None
        self.zne_scale_factors = [1.0, 1.5, 2.0, 2.5, 3.0]

    def zero_noise_extrapolation(self, 
                               circuit: QuantumCircuit,
                               results: Dict[str, float]) -> MitigationResult:
        """Perform zero-noise extrapolation"""
        # Generate scaled noise versions of the circuit
        scaled_circuits = self._generate_scaled_circuits(circuit)
        
        # Execute circuits and collect results
        scaled_results = []
        for scale in self.zne_scale_factors:
            scaled_circuit = self._apply_noise_scaling(circuit, scale)
            result = self._execute_circuit(scaled_circuit)
            scaled_results.append(result)
        
        # Perform Richardson extrapolation
        extrapolated_results = self._richardson_extrapolation(
            self.zne_scale_factors, scaled_results
        )
        
        # Calculate confidence intervals
        confidence = self._calculate_confidence_intervals(scaled_results)
        
        # Calculate fidelity improvement
        fidelity = self._estimate_fidelity_improvement(results, extrapolated_results)
        
        return MitigationResult(
            mitigated_counts=extrapolated_results,
            confidence_intervals=confidence,
            extrapolated_value=0.0,  # Set based on specific metric
            mitigation_method='zero_noise_extrapolation',
            fidelity_improvement=fidelity
        )

    def probabilistic_error_cancellation(self, 
                                      circuit: QuantumCircuit) -> MitigationResult:
        """Perform probabilistic error cancellation"""
        # Generate quasi-probability representation
        quasi_probs = self._generate_quasi_probabilities(circuit)
        
        # Sample from quasi-probability distribution
        sampled_circuits = self._sample_circuits(circuit, quasi_probs)
        
        # Execute sampled circuits
        results = []
        for sampled_circuit in sampled_circuits:
            result = self._execute_circuit(sampled_circuit)
            results.append(result)
        
        # Combine results with quasi-probability weights
        mitigated_results = self._combine_quasi_prob_results(results, quasi_probs)
        
        # Calculate confidence intervals
        confidence = self._calculate_confidence_intervals(results)
        
        # Calculate fidelity improvement
        fidelity = self._estimate_fidelity_improvement(
            self._execute_circuit(circuit), mitigated_results
        )
        
        return MitigationResult(
            mitigated_counts=mitigated_results,
            confidence_intervals=confidence,
            extrapolated_value=0.0,
            mitigation_method='probabilistic_error_cancellation',
            fidelity_improvement=fidelity
        )

    def measurement_error_mitigation(self, 
                                   results: Dict[str, float]) -> MitigationResult:
        """Perform measurement error mitigation"""
        if self.measurement_calibration is None:
            self._perform_measurement_calibration()
        
        # Apply calibration matrix
        mitigated_results = self._apply_calibration_matrix(results)
        
        # Calculate confidence intervals
        confidence = self._calculate_confidence_intervals([results, mitigated_results])
        
        # Calculate fidelity improvement
        fidelity = self._estimate_fidelity_improvement(results, mitigated_results)
        
        return MitigationResult(
            mitigated_counts=mitigated_results,
            confidence_intervals=confidence,
            extrapolated_value=0.0,
            mitigation_method='measurement_error_mitigation',
            fidelity_improvement=fidelity
        )

    def _generate_scaled_circuits(self, 
                                circuit: QuantumCircuit) -> List[QuantumCircuit]:
        """Generate circuits with scaled noise levels"""
        scaled_circuits = []
        
        for scale in self.zne_scale_factors:
            # Create scaled version of the circuit
            scaled = QuantumCircuit(circuit.num_qubits)
            
            for instruction in circuit.data:
                # Add noise scaling through gate decomposition
                if len(instruction.qubits) == 1:
                    # Scale single-qubit gates
                    self._scale_single_qubit_gate(
                        scaled, instruction, scale
                    )
                else:
                    # Scale two-qubit gates
                    self._scale_two_qubit_gate(
                        scaled, instruction, scale
                    )
            
            scaled_circuits.append(scaled)
            
        return scaled_circuits

    def _scale_single_qubit_gate(self, circuit: QuantumCircuit, 
                                instruction, scale: float):
        """Scale noise in single-qubit gates"""
        # Implement gate stretching
        if instruction.operation.name in ['rx', 'ry', 'rz']:
            angle = instruction.operation.params[0]
            stretched_angle = angle * scale
            getattr(circuit, instruction.operation.name)(
                stretched_angle, instruction.qubits[0]
            )
        else:
            # For non-rotation gates, use identity decomposition
            circuit.append(instruction.operation, instruction.qubits)

    def _scale_two_qubit_gate(self, circuit: QuantumCircuit, 
                             instruction, scale: float):
        """Scale noise in two-qubit gates"""
        if instruction.operation.name == 'cx':
            # Decompose CNOT into rotations and scale
            q1, q2 = instruction.qubits
            circuit.h(q2)
            circuit.cx(q1, q2)
            circuit.h(q2)
        else:
            # Direct scaling for other two-qubit gates
            circuit.append(instruction.operation, instruction.qubits)

    def _richardson_extrapolation(self, 
                                scale_factors: List[float],
                                results: List[Dict[str, float]]) -> Dict[str, float]:
        """Perform Richardson extrapolation to zero noise"""
        # Combine results for each basis state
        extrapolated_results = {}
        
        # Get all possible basis states
        basis_states = set()
        for result in results:
            basis_states.update(result.keys())
        
        for state in basis_states:
            # Get probabilities for this state at different noise scales
            probs = [result.get(state, 0.0) for result in results]
            
            # Perform polynomial fit
            coeffs = np.polyfit(scale_factors, probs, len(scale_factors) - 1)
            
            # Extrapolate to zero noise
            extrapolated_results[state] = np.polyval(coeffs, 0.0)
        
        return extrapolated_results

    def _generate_quasi_probabilities(self, 
                                    circuit: QuantumCircuit) -> Dict[str, float]:
        """Generate quasi-probability representation of the circuit"""
        quasi_probs = {}
        
        # Analyze circuit gates
        for instruction in circuit.data:
            # Generate quasi-probabilities for each gate
            if len(instruction.qubits) == 1:
                quasi_probs.update(
                    self._single_qubit_quasi_probs(instruction)
                )
            else:
                quasi_probs.update(
                    self._two_qubit_quasi_probs(instruction)
                )
        
        return quasi_probs

    def _single_qubit_quasi_probs(self, instruction) -> Dict[str, float]:
        """Generate quasi-probabilities for single-qubit gates"""
        qubit = instruction.qubits[0].index
        error_rate = self.noise_model.single_qubit_error_rates.get(qubit, 0.01)
        
        # Basic quasi-probability decomposition
        return {
            f"ideal_{instruction.operation.name}_{qubit}": 1.0 + error_rate,
            f"error_{instruction.operation.name}_{qubit}": -error_rate
        }

    def _two_qubit_quasi_probs(self, instruction) -> Dict[str, float]:
        """Generate quasi-probabilities for two-qubit gates"""
        q1, q2 = [q.index for q in instruction.qubits]
        error_rate = self.noise_model.two_qubit_error_rates.get((q1, q2), 0.05)
        
        return {
            f"ideal_{instruction.operation.name}_{q1}_{q2}": 1.0 + error_rate,
            f"error_{instruction.operation.name}_{q1}_{q2}": -error_rate
        }

    def _perform_measurement_calibration(self):
        """Perform measurement calibration"""
        num_qubits = len(self.noise_model.measurement_error_rates)
        calibration_matrix = np.zeros((2**num_qubits, 2**num_qubits))
        
        # Prepare and measure all basis states
        for i in range(2**num_qubits):
            # Create calibration circuit for basis state |i⟩
            circuit = QuantumCircuit(num_qubits)
            binary = format(i, f'0{num_qubits}b')
            
            # Prepare basis state
            for j, bit in enumerate(binary):
                if bit == '1':
                    circuit.x(j)
            
            # Add measurements
            circuit.measure_all()
            
            # Execute and store results
            results = self._execute_circuit(circuit)
            for j, count in results.items():
                calibration_matrix[i][int(j, 2)] = count
        
        # Normalize calibration matrix
        self.measurement_calibration = calibration_matrix / np.sum(
            calibration_matrix, axis=1, keepdims=True
        )

    def _apply_calibration_matrix(self, 
                                results: Dict[str, float]) -> Dict[str, float]:
        """Apply measurement calibration matrix to results"""
        if self.measurement_calibration is None:
            return results
            
        # Convert results to vector form
        num_qubits = len(self.noise_model.measurement_error_rates)
        result_vector = np.zeros(2**num_qubits)
        
        for bitstring, count in results.items():
            result_vector[int(bitstring, 2)] = count
            
        # Apply inverse calibration matrix
        mitigated_vector = np.linalg.solve(
            self.measurement_calibration, result_vector
        )
        
        # Convert back to dictionary form
        mitigated_results = {}
        for i, value in enumerate(mitigated_vector):
            if value > 0:  # Filter out negative values
                bitstring = format(i, f'0{num_qubits}b')
                mitigated_results[bitstring] = value
                
        return mitigated_results

    def _calculate_confidence_intervals(self, 
                                     results: List[Dict[str, float]],
                                     confidence_level: float = 0.95) -> Dict[str, Tuple[float, float]]:
        """Calculate confidence intervals for results"""
        confidence_intervals = {}
        
        # Get all possible states
        states = set()
        for result in results:
            states.update(result.keys())
        
        for state in states:
            # Get values for this state
            values = [result.get(state, 0.0) for result in results]
            
            # Calculate mean and standard error
            mean = np.mean(values)
            std_error = np.std(values) / np.sqrt(len(values))
            
            # Calculate confidence interval
            z_score = 1.96  # 95% confidence level
            margin = z_score * std_error
            
            confidence_intervals[state] = (mean - margin, mean + margin)
            
        return confidence_intervals

    def _estimate_fidelity_improvement(self, 
                                     original_results: Dict[str, float],
                                     mitigated_results: Dict[str, float]) -> float:
        """Estimate the improvement in fidelity after mitigation"""
        # Calculate state overlap
        overlap = 0.0
        states = set(original_results.keys()).union(mitigated_results.keys())
        
        for state in states:
            orig_prob = original_results.get(state, 0.0)
            mitig_prob = mitigated_results.get(state, 0.0)
            overlap += np.sqrt(orig_prob * mitig_prob)
            
        return overlap

    def visualize_mitigation_results(self, 
                                   original_results: Dict[str, float],
                                   mitigated_results: MitigationResult):
        """Visualize the effects of error mitigation"""
        plt.figure(figsize=(15, 5))
        
        # Plot original results
        plt.subplot(131)
        self._plot_results(original_results, "Original Results")
        
        # Plot mitigated results
        plt.subplot(132)
        self._plot_results(
            mitigated_results.mitigated_counts,
            f"Mitigated Results\n({mitigated_results.mitigation_method})"
        )
        
        # Plot improvement metrics
        plt.subplot(133)
        self._plot_improvement_metrics(mitigated_results)
        
        plt.tight_layout()
        plt.savefig('error_mitigation_results.png')
        plt.close()

    def _plot_results(self, results: Dict[str, float], title: str):
        """Helper function to plot measurement results"""
        plt.bar(range(len(results)), list(results.values()))
        plt.xticks(range(len(results)), list(results.keys()), rotation=45)
        plt.title(title)
        plt.ylabel('Probability')

    def _plot_improvement_metrics(self, results: MitigationResult):
        """Plot improvement metrics"""
        metrics = {
            'Fidelity\nImprovement': results.fidelity_improvement,
            'Confidence\nLevel': 0.95,
            'Error\nReduction': 1.0 - (1.0 / results.fidelity_improvement)
        }
        
        plt.bar(range(len(metrics)), list(metrics.values()))
        plt.xticks(range(len(metrics)), list(metrics.keys()))
        plt.title('Improvement Metrics')
        plt.ylabel('Value')