Struct QuantumMLErrorMitigator 

pub struct QuantumMLErrorMitigator {
    pub mitigation_strategy: MitigationStrategy,
    pub noise_model: NoiseModel,
    pub calibration_data: CalibrationData,
    pub adaptive_config: AdaptiveConfig,
    pub performance_metrics: PerformanceMetrics,
}

Advanced error mitigation framework for quantum ML

Fields

mitigation_strategy: MitigationStrategy

noise_model: NoiseModel

calibration_data: CalibrationData

adaptive_config: AdaptiveConfig

performance_metrics: PerformanceMetrics

Implementations

impl QuantumMLErrorMitigator

pub fn new( mitigation_strategy: MitigationStrategy, noise_model: NoiseModel, ) -> Result<Self>

Create a new error mitigation framework

Examples found in repository

examples/advanced_error_mitigation_demo.rs (line 100)

fn main() -> Result<()> {
    println!("=== Advanced Quantum ML Error Mitigation Demo ===\n");

    // Step 1: Initialize noise model and calibration data
    println!("1. Setting up noise model and calibration data...");

    let noise_model = create_realistic_noise_model()?;
    println!(
        "   - Noise model configured with {} gate types",
        noise_model.gate_errors.len()
    );
    println!(
        "   - Average gate error rate: {:.4}",
        calculate_average_error_rate(&noise_model)
    );
    println!(
        "   - Measurement fidelity: {:.3}",
        noise_model.measurement_errors.readout_fidelity
    );

    // Step 2: Create different mitigation strategies
    println!("\n2. Creating error mitigation strategies...");

    let strategies = create_mitigation_strategies()?;
    println!(
        "   - Created {} different mitigation strategies",
        strategies.len()
    );

    for (i, strategy) in strategies.iter().enumerate() {
        println!("   {}. {}", i + 1, get_strategy_name(strategy));
    }

    // Step 3: Initialize quantum ML circuit for testing
    println!("\n3. Initializing quantum ML circuit...");

    let test_circuit = create_test_qml_circuit(4, 3)?; // 4 qubits, 3 layers
    let initial_parameters = Array1::from_vec(vec![0.1, 0.2, 0.3, 0.4, 0.5, 0.6]);

    println!(
        "   - Circuit: {} qubits, {} parameters",
        test_circuit.num_qubits(),
        initial_parameters.len()
    );
    println!(
        "   - Circuit depth: approximately {} gates",
        estimate_circuit_depth(&test_circuit)
    );

    // Step 4: Simulate noisy measurements
    println!("\n4. Simulating noisy quantum measurements...");

    let noisy_measurements = simulate_noisy_measurements(&test_circuit, &noise_model, 1000)?;
    let noisy_gradients =
        simulate_noisy_gradients(&test_circuit, &initial_parameters, &noise_model)?;

    println!(
        "   - Generated {} measurement shots",
        noisy_measurements.nrows()
    );
    println!(
        "   - Noise level in measurements: {:.3}",
        assess_noise_level(&noisy_measurements)
    );
    println!(
        "   - Gradient noise standard deviation: {:.4}",
        noisy_gradients.std(0.0)
    );

    // Step 5: Apply different mitigation strategies
    println!("\n5. Applying different error mitigation strategies...");

    let mut mitigation_results = Vec::new();

    for (strategy_idx, strategy) in strategies.iter().enumerate() {
        println!(
            "   Testing strategy {}: {}",
            strategy_idx + 1,
            get_strategy_name(strategy)
        );

        let mut mitigator = QuantumMLErrorMitigator::new(strategy.clone(), noise_model.clone())?;

        let mitigated_data = mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &noisy_measurements,
            &noisy_gradients,
        )?;

        let improvement = calculate_improvement(&noisy_measurements, &mitigated_data.measurements)?;
        println!(
            "     - Measurement improvement: {:.1}%",
            improvement * 100.0
        );
        println!(
            "     - Confidence score: {:.3}",
            mitigated_data.confidence_scores.mean().unwrap()
        );
        println!(
            "     - Mitigation overhead: {:.1}%",
            mitigated_data.mitigation_overhead * 100.0
        );

        mitigation_results.push((strategy_idx, improvement, mitigated_data));
    }

    // Step 6: Compare mitigation effectiveness
    println!("\n6. Comparing mitigation effectiveness...");

    let mut sorted_results = mitigation_results.clone();
    sorted_results.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());

    println!("   Ranking by improvement:");
    for (rank, (strategy_idx, improvement, _)) in sorted_results.iter().enumerate() {
        println!(
            "   {}. {}: {:.1}% improvement",
            rank + 1,
            get_strategy_name(&strategies[*strategy_idx]),
            improvement * 100.0
        );
    }

    // Step 7: Demonstrate adaptive mitigation
    println!("\n7. Demonstrating adaptive error mitigation...");

    let adaptive_strategy = MitigationStrategy::AdaptiveMultiStrategy {
        strategies: strategies.clone(),
        selection_policy: create_smart_selection_policy()?,
        performance_tracker: create_performance_tracker()?,
    };

    let mut adaptive_mitigator =
        QuantumMLErrorMitigator::new(adaptive_strategy, noise_model.clone())?;

    // Simulate training loop with adaptive mitigation
    println!("   Simulating training with adaptive mitigation:");
    let num_training_steps = 10;
    let mut training_history = Vec::new();

    for step in 0..num_training_steps {
        // Simulate changing noise conditions
        let dynamic_noise = simulate_dynamic_noise(&noise_model, step)?;
        adaptive_mitigator.noise_model = dynamic_noise;

        let step_measurements = simulate_training_step_measurements(&test_circuit, step)?;
        let step_gradients = simulate_training_step_gradients(&test_circuit, step)?;

        let mitigated_step = adaptive_mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &step_measurements,
            &step_gradients,
        )?;

        let step_improvement =
            calculate_improvement(&step_measurements, &mitigated_step.measurements)?;
        training_history.push(step_improvement);

        if step % 3 == 0 {
            println!(
                "     Step {}: {:.1}% improvement, confidence: {:.3}",
                step + 1,
                step_improvement * 100.0,
                mitigated_step.confidence_scores.mean().unwrap()
            );
        }
    }

    let avg_adaptive_improvement =
        training_history.iter().sum::<f64>() / training_history.len() as f64;
    println!(
        "   Average adaptive improvement: {:.1}%",
        avg_adaptive_improvement * 100.0
    );

    // Step 8: Demonstrate specialized mitigation techniques
    println!("\n8. Demonstrating specialized mitigation techniques...");

    // Zero Noise Extrapolation
    let zne_demo = demonstrate_zne_mitigation(&test_circuit, &noise_model)?;
    println!("   Zero Noise Extrapolation:");
    println!(
        "     - Extrapolated fidelity: {:.4}",
        zne_demo.extrapolated_fidelity
    );
    println!(
        "     - Confidence interval: [{:.4}, {:.4}]",
        zne_demo.confidence_interval.0, zne_demo.confidence_interval.1
    );

    // Readout Error Mitigation
    let readout_demo = demonstrate_readout_mitigation(&test_circuit, &noise_model)?;
    println!("   Readout Error Mitigation:");
    println!(
        "     - Correction accuracy: {:.1}%",
        readout_demo.correction_accuracy * 100.0
    );
    println!(
        "     - Assignment matrix condition number: {:.2}",
        readout_demo.condition_number
    );

    // Clifford Data Regression
    let cdr_demo = demonstrate_cdr_mitigation(&test_circuit, &noise_model)?;
    println!("   Clifford Data Regression:");
    println!("     - Regression R²: {:.3}", cdr_demo.r_squared);
    println!(
        "     - Prediction accuracy: {:.1}%",
        cdr_demo.prediction_accuracy * 100.0
    );

    // Virtual Distillation
    let vd_demo = demonstrate_virtual_distillation(&test_circuit, &noise_model)?;
    println!("   Virtual Distillation:");
    println!(
        "     - Distillation fidelity: {:.4}",
        vd_demo.distillation_fidelity
    );
    println!(
        "     - Resource overhead: {:.1}x",
        vd_demo.resource_overhead
    );

    // Step 9: ML-based error mitigation
    println!("\n9. Demonstrating ML-based error mitigation...");

    let ml_mitigation_demo = demonstrate_ml_mitigation(&test_circuit, &noise_model)?;
    println!("   Machine Learning-based Mitigation:");
    println!(
        "     - Neural network accuracy: {:.1}%",
        ml_mitigation_demo.nn_accuracy * 100.0
    );
    println!(
        "     - Noise prediction MSE: {:.6}",
        ml_mitigation_demo.prediction_mse
    );
    println!(
        "     - Correction effectiveness: {:.1}%",
        ml_mitigation_demo.correction_effectiveness * 100.0
    );

    // Step 10: Real-time adaptive mitigation
    println!("\n10. Real-time adaptive mitigation simulation...");

    let realtime_results = simulate_realtime_mitigation(&test_circuit, &noise_model)?;
    println!("    Real-time Adaptation Results:");
    println!(
        "    - Response time: {:.1} ms",
        realtime_results.response_time_ms
    );
    println!(
        "    - Adaptation accuracy: {:.1}%",
        realtime_results.adaptation_accuracy * 100.0
    );
    println!(
        "    - Overall performance gain: {:.1}%",
        realtime_results.performance_gain * 100.0
    );

    // Step 11: Error mitigation for inference
    println!("\n11. Error mitigation for quantum ML inference...");

    let inference_measurements = simulate_inference_measurements(&test_circuit, 500)?;

    let best_strategy = &strategies[sorted_results[0].0];
    let mut inference_mitigator =
        QuantumMLErrorMitigator::new(best_strategy.clone(), noise_model.clone())?;

    let mitigated_inference =
        inference_mitigator.mitigate_inference_errors(&test_circuit, &inference_measurements)?;

    println!("    Inference Mitigation Results:");
    println!(
        "    - Uncertainty reduction: {:.1}%",
        (1.0 - mitigated_inference.uncertainty.mean().unwrap()) * 100.0
    );
    println!(
        "    - Reliability score: {:.3}",
        mitigated_inference.reliability_score
    );
    println!(
        "    - Prediction confidence: {:.1}%",
        calculate_prediction_confidence(&mitigated_inference.measurements) * 100.0
    );

    // Step 12: Performance and resource analysis
    println!("\n12. Performance and resource analysis...");

    let resource_analysis = analyze_mitigation_resources(&mitigation_results)?;
    println!("    Resource Analysis:");
    println!(
        "    - Average computational overhead: {:.1}x",
        resource_analysis.avg_computational_overhead
    );
    println!(
        "    - Memory usage increase: {:.1}%",
        resource_analysis.memory_overhead * 100.0
    );
    println!(
        "    - Classical processing time: {:.2} ms",
        resource_analysis.classical_time_ms
    );
    println!(
        "    - Quantum circuit overhead: {:.1}%",
        resource_analysis.quantum_overhead * 100.0
    );

    // Step 13: Quantum advantage analysis with error mitigation
    println!("\n13. Quantum advantage analysis with error mitigation...");

    let quantum_advantage = analyze_quantum_advantage_with_mitigation(
        &test_circuit,
        &sorted_results[0].2, // Best mitigation result
    )?;

    println!("    Quantum Advantage Analysis:");
    println!(
        "    - Effective quantum volume: {}",
        quantum_advantage.effective_quantum_volume
    );
    println!(
        "    - Noise-mitigated fidelity: {:.4}",
        quantum_advantage.mitigated_fidelity
    );
    println!(
        "    - Classical simulation cost: {:.1}x harder",
        quantum_advantage.classical_simulation_cost
    );
    println!(
        "    - Practical quantum advantage: {}",
        if quantum_advantage.practical_advantage {
            "Yes"
        } else {
            "Not yet"
        }
    );

    // Step 14: Generate comprehensive report
    println!("\n14. Generating comprehensive error mitigation report...");

    let comprehensive_report = generate_comprehensive_mitigation_report(
        &strategies,
        &mitigation_results,
        &training_history,
        &resource_analysis,
        &quantum_advantage,
    )?;

    save_mitigation_report(&comprehensive_report, "error_mitigation_report.html")?;
    println!("    Comprehensive report saved to: error_mitigation_report.html");

    // Step 15: Future recommendations
    println!("\n15. Error mitigation recommendations...");

    let recommendations =
        generate_mitigation_recommendations(&test_circuit, &noise_model, &mitigation_results)?;

    println!("    Recommendations:");
    for (i, recommendation) in recommendations.iter().enumerate() {
        println!("    {}. {}", i + 1, recommendation);
    }

    println!("\n=== Advanced Error Mitigation Demo Complete ===");
    println!("🎯 Successfully demonstrated comprehensive error mitigation capabilities");
    println!("📊 All mitigation strategies evaluated and optimized");
    println!("🚀 Quantum ML error mitigation framework ready for production");

    Ok(())
}

pub fn mitigate_training_errors( &mut self, circuit: &QuantumCircuit, parameters: &Array1<f64>, measurement_results: &Array2<f64>, gradient_estimates: &Array1<f64>, ) -> Result<MitigatedTrainingData>

Apply error mitigation to quantum ML training

Examples found in repository

examples/advanced_error_mitigation_demo.rs (lines 102-107)

fn main() -> Result<()> {
    println!("=== Advanced Quantum ML Error Mitigation Demo ===\n");

    // Step 1: Initialize noise model and calibration data
    println!("1. Setting up noise model and calibration data...");

    let noise_model = create_realistic_noise_model()?;
    println!(
        "   - Noise model configured with {} gate types",
        noise_model.gate_errors.len()
    );
    println!(
        "   - Average gate error rate: {:.4}",
        calculate_average_error_rate(&noise_model)
    );
    println!(
        "   - Measurement fidelity: {:.3}",
        noise_model.measurement_errors.readout_fidelity
    );

    // Step 2: Create different mitigation strategies
    println!("\n2. Creating error mitigation strategies...");

    let strategies = create_mitigation_strategies()?;
    println!(
        "   - Created {} different mitigation strategies",
        strategies.len()
    );

    for (i, strategy) in strategies.iter().enumerate() {
        println!("   {}. {}", i + 1, get_strategy_name(strategy));
    }

    // Step 3: Initialize quantum ML circuit for testing
    println!("\n3. Initializing quantum ML circuit...");

    let test_circuit = create_test_qml_circuit(4, 3)?; // 4 qubits, 3 layers
    let initial_parameters = Array1::from_vec(vec![0.1, 0.2, 0.3, 0.4, 0.5, 0.6]);

    println!(
        "   - Circuit: {} qubits, {} parameters",
        test_circuit.num_qubits(),
        initial_parameters.len()
    );
    println!(
        "   - Circuit depth: approximately {} gates",
        estimate_circuit_depth(&test_circuit)
    );

    // Step 4: Simulate noisy measurements
    println!("\n4. Simulating noisy quantum measurements...");

    let noisy_measurements = simulate_noisy_measurements(&test_circuit, &noise_model, 1000)?;
    let noisy_gradients =
        simulate_noisy_gradients(&test_circuit, &initial_parameters, &noise_model)?;

    println!(
        "   - Generated {} measurement shots",
        noisy_measurements.nrows()
    );
    println!(
        "   - Noise level in measurements: {:.3}",
        assess_noise_level(&noisy_measurements)
    );
    println!(
        "   - Gradient noise standard deviation: {:.4}",
        noisy_gradients.std(0.0)
    );

    // Step 5: Apply different mitigation strategies
    println!("\n5. Applying different error mitigation strategies...");

    let mut mitigation_results = Vec::new();

    for (strategy_idx, strategy) in strategies.iter().enumerate() {
        println!(
            "   Testing strategy {}: {}",
            strategy_idx + 1,
            get_strategy_name(strategy)
        );

        let mut mitigator = QuantumMLErrorMitigator::new(strategy.clone(), noise_model.clone())?;

        let mitigated_data = mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &noisy_measurements,
            &noisy_gradients,
        )?;

        let improvement = calculate_improvement(&noisy_measurements, &mitigated_data.measurements)?;
        println!(
            "     - Measurement improvement: {:.1}%",
            improvement * 100.0
        );
        println!(
            "     - Confidence score: {:.3}",
            mitigated_data.confidence_scores.mean().unwrap()
        );
        println!(
            "     - Mitigation overhead: {:.1}%",
            mitigated_data.mitigation_overhead * 100.0
        );

        mitigation_results.push((strategy_idx, improvement, mitigated_data));
    }

    // Step 6: Compare mitigation effectiveness
    println!("\n6. Comparing mitigation effectiveness...");

    let mut sorted_results = mitigation_results.clone();
    sorted_results.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());

    println!("   Ranking by improvement:");
    for (rank, (strategy_idx, improvement, _)) in sorted_results.iter().enumerate() {
        println!(
            "   {}. {}: {:.1}% improvement",
            rank + 1,
            get_strategy_name(&strategies[*strategy_idx]),
            improvement * 100.0
        );
    }

    // Step 7: Demonstrate adaptive mitigation
    println!("\n7. Demonstrating adaptive error mitigation...");

    let adaptive_strategy = MitigationStrategy::AdaptiveMultiStrategy {
        strategies: strategies.clone(),
        selection_policy: create_smart_selection_policy()?,
        performance_tracker: create_performance_tracker()?,
    };

    let mut adaptive_mitigator =
        QuantumMLErrorMitigator::new(adaptive_strategy, noise_model.clone())?;

    // Simulate training loop with adaptive mitigation
    println!("   Simulating training with adaptive mitigation:");
    let num_training_steps = 10;
    let mut training_history = Vec::new();

    for step in 0..num_training_steps {
        // Simulate changing noise conditions
        let dynamic_noise = simulate_dynamic_noise(&noise_model, step)?;
        adaptive_mitigator.noise_model = dynamic_noise;

        let step_measurements = simulate_training_step_measurements(&test_circuit, step)?;
        let step_gradients = simulate_training_step_gradients(&test_circuit, step)?;

        let mitigated_step = adaptive_mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &step_measurements,
            &step_gradients,
        )?;

        let step_improvement =
            calculate_improvement(&step_measurements, &mitigated_step.measurements)?;
        training_history.push(step_improvement);

        if step % 3 == 0 {
            println!(
                "     Step {}: {:.1}% improvement, confidence: {:.3}",
                step + 1,
                step_improvement * 100.0,
                mitigated_step.confidence_scores.mean().unwrap()
            );
        }
    }

    let avg_adaptive_improvement =
        training_history.iter().sum::<f64>() / training_history.len() as f64;
    println!(
        "   Average adaptive improvement: {:.1}%",
        avg_adaptive_improvement * 100.0
    );

    // Step 8: Demonstrate specialized mitigation techniques
    println!("\n8. Demonstrating specialized mitigation techniques...");

    // Zero Noise Extrapolation
    let zne_demo = demonstrate_zne_mitigation(&test_circuit, &noise_model)?;
    println!("   Zero Noise Extrapolation:");
    println!(
        "     - Extrapolated fidelity: {:.4}",
        zne_demo.extrapolated_fidelity
    );
    println!(
        "     - Confidence interval: [{:.4}, {:.4}]",
        zne_demo.confidence_interval.0, zne_demo.confidence_interval.1
    );

    // Readout Error Mitigation
    let readout_demo = demonstrate_readout_mitigation(&test_circuit, &noise_model)?;
    println!("   Readout Error Mitigation:");
    println!(
        "     - Correction accuracy: {:.1}%",
        readout_demo.correction_accuracy * 100.0
    );
    println!(
        "     - Assignment matrix condition number: {:.2}",
        readout_demo.condition_number
    );

    // Clifford Data Regression
    let cdr_demo = demonstrate_cdr_mitigation(&test_circuit, &noise_model)?;
    println!("   Clifford Data Regression:");
    println!("     - Regression R²: {:.3}", cdr_demo.r_squared);
    println!(
        "     - Prediction accuracy: {:.1}%",
        cdr_demo.prediction_accuracy * 100.0
    );

    // Virtual Distillation
    let vd_demo = demonstrate_virtual_distillation(&test_circuit, &noise_model)?;
    println!("   Virtual Distillation:");
    println!(
        "     - Distillation fidelity: {:.4}",
        vd_demo.distillation_fidelity
    );
    println!(
        "     - Resource overhead: {:.1}x",
        vd_demo.resource_overhead
    );

    // Step 9: ML-based error mitigation
    println!("\n9. Demonstrating ML-based error mitigation...");

    let ml_mitigation_demo = demonstrate_ml_mitigation(&test_circuit, &noise_model)?;
    println!("   Machine Learning-based Mitigation:");
    println!(
        "     - Neural network accuracy: {:.1}%",
        ml_mitigation_demo.nn_accuracy * 100.0
    );
    println!(
        "     - Noise prediction MSE: {:.6}",
        ml_mitigation_demo.prediction_mse
    );
    println!(
        "     - Correction effectiveness: {:.1}%",
        ml_mitigation_demo.correction_effectiveness * 100.0
    );

    // Step 10: Real-time adaptive mitigation
    println!("\n10. Real-time adaptive mitigation simulation...");

    let realtime_results = simulate_realtime_mitigation(&test_circuit, &noise_model)?;
    println!("    Real-time Adaptation Results:");
    println!(
        "    - Response time: {:.1} ms",
        realtime_results.response_time_ms
    );
    println!(
        "    - Adaptation accuracy: {:.1}%",
        realtime_results.adaptation_accuracy * 100.0
    );
    println!(
        "    - Overall performance gain: {:.1}%",
        realtime_results.performance_gain * 100.0
    );

    // Step 11: Error mitigation for inference
    println!("\n11. Error mitigation for quantum ML inference...");

    let inference_measurements = simulate_inference_measurements(&test_circuit, 500)?;

    let best_strategy = &strategies[sorted_results[0].0];
    let mut inference_mitigator =
        QuantumMLErrorMitigator::new(best_strategy.clone(), noise_model.clone())?;

    let mitigated_inference =
        inference_mitigator.mitigate_inference_errors(&test_circuit, &inference_measurements)?;

    println!("    Inference Mitigation Results:");
    println!(
        "    - Uncertainty reduction: {:.1}%",
        (1.0 - mitigated_inference.uncertainty.mean().unwrap()) * 100.0
    );
    println!(
        "    - Reliability score: {:.3}",
        mitigated_inference.reliability_score
    );
    println!(
        "    - Prediction confidence: {:.1}%",
        calculate_prediction_confidence(&mitigated_inference.measurements) * 100.0
    );

    // Step 12: Performance and resource analysis
    println!("\n12. Performance and resource analysis...");

    let resource_analysis = analyze_mitigation_resources(&mitigation_results)?;
    println!("    Resource Analysis:");
    println!(
        "    - Average computational overhead: {:.1}x",
        resource_analysis.avg_computational_overhead
    );
    println!(
        "    - Memory usage increase: {:.1}%",
        resource_analysis.memory_overhead * 100.0
    );
    println!(
        "    - Classical processing time: {:.2} ms",
        resource_analysis.classical_time_ms
    );
    println!(
        "    - Quantum circuit overhead: {:.1}%",
        resource_analysis.quantum_overhead * 100.0
    );

    // Step 13: Quantum advantage analysis with error mitigation
    println!("\n13. Quantum advantage analysis with error mitigation...");

    let quantum_advantage = analyze_quantum_advantage_with_mitigation(
        &test_circuit,
        &sorted_results[0].2, // Best mitigation result
    )?;

    println!("    Quantum Advantage Analysis:");
    println!(
        "    - Effective quantum volume: {}",
        quantum_advantage.effective_quantum_volume
    );
    println!(
        "    - Noise-mitigated fidelity: {:.4}",
        quantum_advantage.mitigated_fidelity
    );
    println!(
        "    - Classical simulation cost: {:.1}x harder",
        quantum_advantage.classical_simulation_cost
    );
    println!(
        "    - Practical quantum advantage: {}",
        if quantum_advantage.practical_advantage {
            "Yes"
        } else {
            "Not yet"
        }
    );

    // Step 14: Generate comprehensive report
    println!("\n14. Generating comprehensive error mitigation report...");

    let comprehensive_report = generate_comprehensive_mitigation_report(
        &strategies,
        &mitigation_results,
        &training_history,
        &resource_analysis,
        &quantum_advantage,
    )?;

    save_mitigation_report(&comprehensive_report, "error_mitigation_report.html")?;
    println!("    Comprehensive report saved to: error_mitigation_report.html");

    // Step 15: Future recommendations
    println!("\n15. Error mitigation recommendations...");

    let recommendations =
        generate_mitigation_recommendations(&test_circuit, &noise_model, &mitigation_results)?;

    println!("    Recommendations:");
    for (i, recommendation) in recommendations.iter().enumerate() {
        println!("    {}. {}", i + 1, recommendation);
    }

    println!("\n=== Advanced Error Mitigation Demo Complete ===");
    println!("🎯 Successfully demonstrated comprehensive error mitigation capabilities");
    println!("📊 All mitigation strategies evaluated and optimized");
    println!("🚀 Quantum ML error mitigation framework ready for production");

    Ok(())
}

pub fn mitigate_inference_errors( &mut self, circuit: &QuantumCircuit, measurement_results: &Array2<f64>, ) -> Result<MitigatedInferenceData>

Apply error mitigation to quantum ML inference

Examples found in repository

examples/advanced_error_mitigation_demo.rs (line 289)

fn main() -> Result<()> {
    println!("=== Advanced Quantum ML Error Mitigation Demo ===\n");

    // Step 1: Initialize noise model and calibration data
    println!("1. Setting up noise model and calibration data...");

    let noise_model = create_realistic_noise_model()?;
    println!(
        "   - Noise model configured with {} gate types",
        noise_model.gate_errors.len()
    );
    println!(
        "   - Average gate error rate: {:.4}",
        calculate_average_error_rate(&noise_model)
    );
    println!(
        "   - Measurement fidelity: {:.3}",
        noise_model.measurement_errors.readout_fidelity
    );

    // Step 2: Create different mitigation strategies
    println!("\n2. Creating error mitigation strategies...");

    let strategies = create_mitigation_strategies()?;
    println!(
        "   - Created {} different mitigation strategies",
        strategies.len()
    );

    for (i, strategy) in strategies.iter().enumerate() {
        println!("   {}. {}", i + 1, get_strategy_name(strategy));
    }

    // Step 3: Initialize quantum ML circuit for testing
    println!("\n3. Initializing quantum ML circuit...");

    let test_circuit = create_test_qml_circuit(4, 3)?; // 4 qubits, 3 layers
    let initial_parameters = Array1::from_vec(vec![0.1, 0.2, 0.3, 0.4, 0.5, 0.6]);

    println!(
        "   - Circuit: {} qubits, {} parameters",
        test_circuit.num_qubits(),
        initial_parameters.len()
    );
    println!(
        "   - Circuit depth: approximately {} gates",
        estimate_circuit_depth(&test_circuit)
    );

    // Step 4: Simulate noisy measurements
    println!("\n4. Simulating noisy quantum measurements...");

    let noisy_measurements = simulate_noisy_measurements(&test_circuit, &noise_model, 1000)?;
    let noisy_gradients =
        simulate_noisy_gradients(&test_circuit, &initial_parameters, &noise_model)?;

    println!(
        "   - Generated {} measurement shots",
        noisy_measurements.nrows()
    );
    println!(
        "   - Noise level in measurements: {:.3}",
        assess_noise_level(&noisy_measurements)
    );
    println!(
        "   - Gradient noise standard deviation: {:.4}",
        noisy_gradients.std(0.0)
    );

    // Step 5: Apply different mitigation strategies
    println!("\n5. Applying different error mitigation strategies...");

    let mut mitigation_results = Vec::new();

    for (strategy_idx, strategy) in strategies.iter().enumerate() {
        println!(
            "   Testing strategy {}: {}",
            strategy_idx + 1,
            get_strategy_name(strategy)
        );

        let mut mitigator = QuantumMLErrorMitigator::new(strategy.clone(), noise_model.clone())?;

        let mitigated_data = mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &noisy_measurements,
            &noisy_gradients,
        )?;

        let improvement = calculate_improvement(&noisy_measurements, &mitigated_data.measurements)?;
        println!(
            "     - Measurement improvement: {:.1}%",
            improvement * 100.0
        );
        println!(
            "     - Confidence score: {:.3}",
            mitigated_data.confidence_scores.mean().unwrap()
        );
        println!(
            "     - Mitigation overhead: {:.1}%",
            mitigated_data.mitigation_overhead * 100.0
        );

        mitigation_results.push((strategy_idx, improvement, mitigated_data));
    }

    // Step 6: Compare mitigation effectiveness
    println!("\n6. Comparing mitigation effectiveness...");

    let mut sorted_results = mitigation_results.clone();
    sorted_results.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());

    println!("   Ranking by improvement:");
    for (rank, (strategy_idx, improvement, _)) in sorted_results.iter().enumerate() {
        println!(
            "   {}. {}: {:.1}% improvement",
            rank + 1,
            get_strategy_name(&strategies[*strategy_idx]),
            improvement * 100.0
        );
    }

    // Step 7: Demonstrate adaptive mitigation
    println!("\n7. Demonstrating adaptive error mitigation...");

    let adaptive_strategy = MitigationStrategy::AdaptiveMultiStrategy {
        strategies: strategies.clone(),
        selection_policy: create_smart_selection_policy()?,
        performance_tracker: create_performance_tracker()?,
    };

    let mut adaptive_mitigator =
        QuantumMLErrorMitigator::new(adaptive_strategy, noise_model.clone())?;

    // Simulate training loop with adaptive mitigation
    println!("   Simulating training with adaptive mitigation:");
    let num_training_steps = 10;
    let mut training_history = Vec::new();

    for step in 0..num_training_steps {
        // Simulate changing noise conditions
        let dynamic_noise = simulate_dynamic_noise(&noise_model, step)?;
        adaptive_mitigator.noise_model = dynamic_noise;

        let step_measurements = simulate_training_step_measurements(&test_circuit, step)?;
        let step_gradients = simulate_training_step_gradients(&test_circuit, step)?;

        let mitigated_step = adaptive_mitigator.mitigate_training_errors(
            &test_circuit,
            &initial_parameters,
            &step_measurements,
            &step_gradients,
        )?;

        let step_improvement =
            calculate_improvement(&step_measurements, &mitigated_step.measurements)?;
        training_history.push(step_improvement);

        if step % 3 == 0 {
            println!(
                "     Step {}: {:.1}% improvement, confidence: {:.3}",
                step + 1,
                step_improvement * 100.0,
                mitigated_step.confidence_scores.mean().unwrap()
            );
        }
    }

    let avg_adaptive_improvement =
        training_history.iter().sum::<f64>() / training_history.len() as f64;
    println!(
        "   Average adaptive improvement: {:.1}%",
        avg_adaptive_improvement * 100.0
    );

    // Step 8: Demonstrate specialized mitigation techniques
    println!("\n8. Demonstrating specialized mitigation techniques...");

    // Zero Noise Extrapolation
    let zne_demo = demonstrate_zne_mitigation(&test_circuit, &noise_model)?;
    println!("   Zero Noise Extrapolation:");
    println!(
        "     - Extrapolated fidelity: {:.4}",
        zne_demo.extrapolated_fidelity
    );
    println!(
        "     - Confidence interval: [{:.4}, {:.4}]",
        zne_demo.confidence_interval.0, zne_demo.confidence_interval.1
    );

    // Readout Error Mitigation
    let readout_demo = demonstrate_readout_mitigation(&test_circuit, &noise_model)?;
    println!("   Readout Error Mitigation:");
    println!(
        "     - Correction accuracy: {:.1}%",
        readout_demo.correction_accuracy * 100.0
    );
    println!(
        "     - Assignment matrix condition number: {:.2}",
        readout_demo.condition_number
    );

    // Clifford Data Regression
    let cdr_demo = demonstrate_cdr_mitigation(&test_circuit, &noise_model)?;
    println!("   Clifford Data Regression:");
    println!("     - Regression R²: {:.3}", cdr_demo.r_squared);
    println!(
        "     - Prediction accuracy: {:.1}%",
        cdr_demo.prediction_accuracy * 100.0
    );

    // Virtual Distillation
    let vd_demo = demonstrate_virtual_distillation(&test_circuit, &noise_model)?;
    println!("   Virtual Distillation:");
    println!(
        "     - Distillation fidelity: {:.4}",
        vd_demo.distillation_fidelity
    );
    println!(
        "     - Resource overhead: {:.1}x",
        vd_demo.resource_overhead
    );

    // Step 9: ML-based error mitigation
    println!("\n9. Demonstrating ML-based error mitigation...");

    let ml_mitigation_demo = demonstrate_ml_mitigation(&test_circuit, &noise_model)?;
    println!("   Machine Learning-based Mitigation:");
    println!(
        "     - Neural network accuracy: {:.1}%",
        ml_mitigation_demo.nn_accuracy * 100.0
    );
    println!(
        "     - Noise prediction MSE: {:.6}",
        ml_mitigation_demo.prediction_mse
    );
    println!(
        "     - Correction effectiveness: {:.1}%",
        ml_mitigation_demo.correction_effectiveness * 100.0
    );

    // Step 10: Real-time adaptive mitigation
    println!("\n10. Real-time adaptive mitigation simulation...");

    let realtime_results = simulate_realtime_mitigation(&test_circuit, &noise_model)?;
    println!("    Real-time Adaptation Results:");
    println!(
        "    - Response time: {:.1} ms",
        realtime_results.response_time_ms
    );
    println!(
        "    - Adaptation accuracy: {:.1}%",
        realtime_results.adaptation_accuracy * 100.0
    );
    println!(
        "    - Overall performance gain: {:.1}%",
        realtime_results.performance_gain * 100.0
    );

    // Step 11: Error mitigation for inference
    println!("\n11. Error mitigation for quantum ML inference...");

    let inference_measurements = simulate_inference_measurements(&test_circuit, 500)?;

    let best_strategy = &strategies[sorted_results[0].0];
    let mut inference_mitigator =
        QuantumMLErrorMitigator::new(best_strategy.clone(), noise_model.clone())?;

    let mitigated_inference =
        inference_mitigator.mitigate_inference_errors(&test_circuit, &inference_measurements)?;

    println!("    Inference Mitigation Results:");
    println!(
        "    - Uncertainty reduction: {:.1}%",
        (1.0 - mitigated_inference.uncertainty.mean().unwrap()) * 100.0
    );
    println!(
        "    - Reliability score: {:.3}",
        mitigated_inference.reliability_score
    );
    println!(
        "    - Prediction confidence: {:.1}%",
        calculate_prediction_confidence(&mitigated_inference.measurements) * 100.0
    );

    // Step 12: Performance and resource analysis
    println!("\n12. Performance and resource analysis...");

    let resource_analysis = analyze_mitigation_resources(&mitigation_results)?;
    println!("    Resource Analysis:");
    println!(
        "    - Average computational overhead: {:.1}x",
        resource_analysis.avg_computational_overhead
    );
    println!(
        "    - Memory usage increase: {:.1}%",
        resource_analysis.memory_overhead * 100.0
    );
    println!(
        "    - Classical processing time: {:.2} ms",
        resource_analysis.classical_time_ms
    );
    println!(
        "    - Quantum circuit overhead: {:.1}%",
        resource_analysis.quantum_overhead * 100.0
    );

    // Step 13: Quantum advantage analysis with error mitigation
    println!("\n13. Quantum advantage analysis with error mitigation...");

    let quantum_advantage = analyze_quantum_advantage_with_mitigation(
        &test_circuit,
        &sorted_results[0].2, // Best mitigation result
    )?;

    println!("    Quantum Advantage Analysis:");
    println!(
        "    - Effective quantum volume: {}",
        quantum_advantage.effective_quantum_volume
    );
    println!(
        "    - Noise-mitigated fidelity: {:.4}",
        quantum_advantage.mitigated_fidelity
    );
    println!(
        "    - Classical simulation cost: {:.1}x harder",
        quantum_advantage.classical_simulation_cost
    );
    println!(
        "    - Practical quantum advantage: {}",
        if quantum_advantage.practical_advantage {
            "Yes"
        } else {
            "Not yet"
        }
    );

    // Step 14: Generate comprehensive report
    println!("\n14. Generating comprehensive error mitigation report...");

    let comprehensive_report = generate_comprehensive_mitigation_report(
        &strategies,
        &mitigation_results,
        &training_history,
        &resource_analysis,
        &quantum_advantage,
    )?;

    save_mitigation_report(&comprehensive_report, "error_mitigation_report.html")?;
    println!("    Comprehensive report saved to: error_mitigation_report.html");

    // Step 15: Future recommendations
    println!("\n15. Error mitigation recommendations...");

    let recommendations =
        generate_mitigation_recommendations(&test_circuit, &noise_model, &mitigation_results)?;

    println!("    Recommendations:");
    for (i, recommendation) in recommendations.iter().enumerate() {
        println!("    {}. {}", i + 1, recommendation);
    }

    println!("\n=== Advanced Error Mitigation Demo Complete ===");
    println!("🎯 Successfully demonstrated comprehensive error mitigation capabilities");
    println!("📊 All mitigation strategies evaluated and optimized");
    println!("🚀 Quantum ML error mitigation framework ready for production");

    Ok(())
}