quantrs2_circuit/

scirs2_benchmarking.rs

//! `SciRS2` statistical tools for circuit benchmarking
//!
//! This module leverages `SciRS2`'s advanced statistical analysis capabilities to provide
//! comprehensive benchmarking, performance analysis, and statistical insights for quantum circuits.

use crate::builder::Circuit;
use crate::noise_models::{NoiseAnalysisResult, NoiseModel};
use crate::simulator_interface::{ExecutionResult, SimulatorBackend};
use quantrs2_core::{
    error::{QuantRS2Error, QuantRS2Result},
    gate::GateOp,
};
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::time::{Duration, Instant};

// Placeholder types representing SciRS2 statistical interface
// In the real implementation, these would be imported from SciRS2

/// Statistical distribution types supported by `SciRS2`
#[derive(Debug, Clone, PartialEq)]
pub enum Distribution {
    /// Normal distribution
    Normal { mean: f64, std_dev: f64 },
    /// Uniform distribution
    Uniform { min: f64, max: f64 },
    /// Exponential distribution
    Exponential { rate: f64 },
    /// Beta distribution
    Beta { alpha: f64, beta: f64 },
    /// Gamma distribution
    Gamma { shape: f64, scale: f64 },
    /// Poisson distribution
    Poisson { lambda: f64 },
    /// Chi-squared distribution
    ChiSquared { degrees_of_freedom: usize },
    /// Student's t-distribution
    StudentT { degrees_of_freedom: usize },
}

/// Statistical test types
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum StatisticalTest {
    /// Kolmogorov-Smirnov test
    KolmogorovSmirnov,
    /// Anderson-Darling test
    AndersonDarling,
    /// Shapiro-Wilk test for normality
    ShapiroWilk,
    /// Mann-Whitney U test
    MannWhitney,
    /// Wilcoxon signed-rank test
    Wilcoxon,
    /// Chi-squared goodness of fit
    ChiSquaredGoodnessOfFit,
    /// ANOVA F-test
    ANOVA,
    /// Kruskal-Wallis test
    KruskalWallis,
}

/// Hypothesis test result
#[derive(Debug, Clone)]
pub struct HypothesisTestResult {
    /// Test statistic value
    pub test_statistic: f64,
    /// P-value
    pub p_value: f64,
    /// Critical value at significance level
    pub critical_value: f64,
    /// Whether null hypothesis is rejected
    pub reject_null: bool,
    /// Significance level used
    pub significance_level: f64,
    /// Effect size (if applicable)
    pub effect_size: Option<f64>,
    /// Confidence interval
    pub confidence_interval: Option<(f64, f64)>,
}

/// Descriptive statistics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct DescriptiveStats {
    /// Sample size
    pub count: usize,
    /// Mean
    pub mean: f64,
    /// Standard deviation
    pub std_dev: f64,
    /// Variance
    pub variance: f64,
    /// Minimum value
    pub min: f64,
    /// Maximum value
    pub max: f64,
    /// Median (50th percentile)
    pub median: f64,
    /// First quartile (25th percentile)
    pub q1: f64,
    /// Third quartile (75th percentile)
    pub q3: f64,
    /// Interquartile range
    pub iqr: f64,
    /// Skewness
    pub skewness: f64,
    /// Kurtosis
    pub kurtosis: f64,
    /// Mode (most frequent value)
    pub mode: Option<f64>,
}

/// Benchmarking configuration
#[derive(Debug, Clone)]
pub struct BenchmarkConfig {
    /// Number of benchmark runs
    pub num_runs: usize,
    /// Warm-up runs to exclude from statistics
    pub warmup_runs: usize,
    /// Timeout per run
    pub timeout: Duration,
    /// Significance level for statistical tests
    pub significance_level: f64,
    /// Whether to collect detailed timing data
    pub collect_timing: bool,
    /// Whether to collect memory usage data
    pub collect_memory: bool,
    /// Whether to collect error statistics
    pub collect_errors: bool,
    /// Random seed for reproducible benchmarks
    pub seed: Option<u64>,
}

impl Default for BenchmarkConfig {
    fn default() -> Self {
        Self {
            num_runs: 100,
            warmup_runs: 10,
            timeout: Duration::from_secs(60),
            significance_level: 0.05,
            collect_timing: true,
            collect_memory: false,
            collect_errors: true,
            seed: None,
        }
    }
}

/// Circuit benchmarking suite using `SciRS2` statistical tools
pub struct CircuitBenchmark {
    /// Benchmark configuration
    config: BenchmarkConfig,
    /// Collected benchmark data
    benchmark_data: Vec<BenchmarkRun>,
    /// Statistical analyzer
    stats_analyzer: StatisticalAnalyzer,
}

/// Single benchmark run data
#[derive(Debug, Clone)]
pub struct BenchmarkRun {
    /// Run identifier
    pub run_id: usize,
    /// Execution time
    pub execution_time: Duration,
    /// Memory usage in bytes
    pub memory_usage: Option<usize>,
    /// Success/failure status
    pub success: bool,
    /// Error message if failed
    pub error_message: Option<String>,
    /// Circuit metrics
    pub circuit_metrics: CircuitMetrics,
    /// Execution results
    pub execution_results: Option<ExecutionResult>,
    /// Noise analysis results
    pub noise_analysis: Option<NoiseAnalysisResult>,
    /// Custom metrics
    pub custom_metrics: HashMap<String, f64>,
}

/// Circuit performance metrics
#[derive(Debug, Clone)]
pub struct CircuitMetrics {
    /// Circuit depth
    pub depth: usize,
    /// Total gate count
    pub gate_count: usize,
    /// Gate count by type
    pub gate_counts: HashMap<String, usize>,
    /// Two-qubit gate count
    pub two_qubit_gates: usize,
    /// Circuit fidelity estimate
    pub fidelity: Option<f64>,
    /// Error rate estimate
    pub error_rate: Option<f64>,
}

/// Comprehensive benchmark report
#[derive(Debug, Clone)]
pub struct BenchmarkReport {
    /// Benchmark configuration used
    pub config: BenchmarkConfig,
    /// Total runs completed
    pub completed_runs: usize,
    /// Success rate
    pub success_rate: f64,
    /// Timing statistics
    pub timing_stats: DescriptiveStats,
    /// Memory statistics (if collected)
    pub memory_stats: Option<DescriptiveStats>,
    /// Performance regression analysis
    pub regression_analysis: Option<RegressionAnalysis>,
    /// Distribution fitting results
    pub distribution_fit: Option<DistributionFit>,
    /// Outlier analysis
    pub outlier_analysis: OutlierAnalysis,
    /// Performance comparison with baseline
    pub baseline_comparison: Option<BaselineComparison>,
    /// Statistical test results
    pub statistical_tests: Vec<HypothesisTestResult>,
    /// Performance insights and recommendations
    pub insights: Vec<PerformanceInsight>,
}

/// Regression analysis results
#[derive(Debug, Clone)]
pub struct RegressionAnalysis {
    /// Linear regression slope
    pub slope: f64,
    /// Y-intercept
    pub intercept: f64,
    /// R-squared correlation coefficient
    pub r_squared: f64,
    /// P-value for slope significance
    pub slope_p_value: f64,
    /// Whether there's a significant trend
    pub significant_trend: bool,
    /// Predicted performance degradation per run
    pub degradation_per_run: f64,
}

/// Distribution fitting analysis
#[derive(Debug, Clone)]
pub struct DistributionFit {
    /// Best fitting distribution
    pub best_distribution: Distribution,
    /// Goodness of fit score
    pub goodness_of_fit: f64,
    /// P-value for fit test
    pub fit_p_value: f64,
    /// Alternative distributions tested
    pub alternative_fits: Vec<(Distribution, f64)>,
}

/// Outlier detection and analysis
#[derive(Debug, Clone)]
pub struct OutlierAnalysis {
    /// Number of outliers detected
    pub num_outliers: usize,
    /// Outlier indices
    pub outlier_indices: Vec<usize>,
    /// Outlier detection method used
    pub detection_method: OutlierDetectionMethod,
    /// Outlier threshold used
    pub threshold: f64,
    /// Impact of outliers on statistics
    pub outlier_impact: OutlierImpact,
}

/// Outlier detection methods
#[derive(Debug, Clone, PartialEq)]
pub enum OutlierDetectionMethod {
    /// Interquartile range method
    IQR { multiplier: f64 },
    /// Z-score method
    ZScore { threshold: f64 },
    /// Modified Z-score (median absolute deviation)
    ModifiedZScore { threshold: f64 },
    /// Isolation forest
    IsolationForest,
    /// Local outlier factor
    LocalOutlierFactor,
}

/// Impact of outliers on statistical measures
#[derive(Debug, Clone)]
pub struct OutlierImpact {
    /// Change in mean when outliers removed
    pub mean_change: f64,
    /// Change in standard deviation when outliers removed
    pub std_dev_change: f64,
    /// Change in median when outliers removed
    pub median_change: f64,
    /// Relative impact percentage
    pub relative_impact: f64,
}

/// Baseline performance comparison
#[derive(Debug, Clone)]
pub struct BaselineComparison {
    /// Baseline benchmark name
    pub baseline_name: String,
    /// Performance improvement/degradation factor
    pub performance_factor: f64,
    /// Statistical significance of difference
    pub significance: HypothesisTestResult,
    /// Confidence interval for difference
    pub difference_ci: (f64, f64),
    /// Effect size
    pub effect_size: f64,
    /// Practical significance assessment
    pub practical_significance: PracticalSignificance,
}

/// Practical significance assessment
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum PracticalSignificance {
    /// Negligible difference
    Negligible,
    /// Small effect
    Small,
    /// Medium effect
    Medium,
    /// Large effect
    Large,
    /// Very large effect
    VeryLarge,
}

/// Performance insights and recommendations
#[derive(Debug, Clone)]
pub struct PerformanceInsight {
    /// Insight category
    pub category: InsightCategory,
    /// Insight message
    pub message: String,
    /// Confidence level (0.0 to 1.0)
    pub confidence: f64,
    /// Supporting evidence
    pub evidence: Vec<String>,
    /// Recommended actions
    pub recommendations: Vec<String>,
}

/// Performance insight categories
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum InsightCategory {
    /// Performance degradation detected
    PerformanceDegradation,
    /// Performance improvement detected
    PerformanceImprovement,
    /// High variability in results
    HighVariability,
    /// Outliers detected
    OutliersDetected,
    /// Memory usage concerns
    MemoryUsage,
    /// Error rate concerns
    ErrorRate,
    /// Circuit optimization opportunity
    OptimizationOpportunity,
}

impl CircuitBenchmark {
    /// Create a new circuit benchmark suite
    #[must_use]
    pub const fn new(config: BenchmarkConfig) -> Self {
        Self {
            config,
            benchmark_data: Vec::new(),
            stats_analyzer: StatisticalAnalyzer::new(),
        }
    }

    /// Run comprehensive benchmark suite
    pub fn run_benchmark<const N: usize>(
        &mut self,
        circuit: &Circuit<N>,
        simulator: &dyn SimulatorExecutor,
        noise_model: Option<&NoiseModel>,
    ) -> QuantRS2Result<BenchmarkReport> {
        self.benchmark_data.clear();

        let total_runs = self.config.num_runs + self.config.warmup_runs;

        for run_id in 0..total_runs {
            let is_warmup = run_id < self.config.warmup_runs;

            match self.run_single_benchmark(circuit, simulator, noise_model, run_id) {
                Ok(run_data) => {
                    if !is_warmup {
                        self.benchmark_data.push(run_data);
                    }
                }
                Err(e) => {
                    if !is_warmup {
                        // Record failed run
                        let failed_run = BenchmarkRun {
                            run_id,
                            execution_time: Duration::from_millis(0),
                            memory_usage: None,
                            success: false,
                            error_message: Some(e.to_string()),
                            circuit_metrics: self.calculate_circuit_metrics(circuit),
                            execution_results: None,
                            noise_analysis: None,
                            custom_metrics: HashMap::new(),
                        };
                        self.benchmark_data.push(failed_run);
                    }
                }
            }
        }

        self.generate_benchmark_report()
    }

    /// Run a single benchmark iteration
    fn run_single_benchmark<const N: usize>(
        &self,
        circuit: &Circuit<N>,
        simulator: &dyn SimulatorExecutor,
        noise_model: Option<&NoiseModel>,
        run_id: usize,
    ) -> QuantRS2Result<BenchmarkRun> {
        let start_time = Instant::now();
        let start_memory = if self.config.collect_memory {
            Some(self.get_memory_usage())
        } else {
            None
        };

        // Simulate circuit execution (placeholder)
        let execution_results = None; // Would call simulator.execute()

        let end_time = Instant::now();
        let end_memory = if self.config.collect_memory {
            Some(self.get_memory_usage())
        } else {
            None
        };

        let execution_time = end_time - start_time;
        let memory_usage = match (start_memory, end_memory) {
            (Some(start), Some(end)) => Some(end.saturating_sub(start)),
            _ => None,
        };

        // Analyze noise if model provided
        let noise_analysis = if let Some(noise) = noise_model {
            // Would perform noise analysis here
            None
        } else {
            None
        };

        Ok(BenchmarkRun {
            run_id,
            execution_time,
            memory_usage,
            success: true,
            error_message: None,
            circuit_metrics: self.calculate_circuit_metrics(circuit),
            execution_results,
            noise_analysis,
            custom_metrics: HashMap::new(),
        })
    }

    /// Calculate circuit metrics
    fn calculate_circuit_metrics<const N: usize>(&self, circuit: &Circuit<N>) -> CircuitMetrics {
        let gate_count = circuit.gates().len();
        let mut gate_counts = HashMap::new();
        let mut two_qubit_gates = 0;

        for gate in circuit.gates() {
            let gate_name = gate.name();
            *gate_counts.entry(gate_name.to_string()).or_insert(0) += 1;

            if gate.qubits().len() == 2 {
                two_qubit_gates += 1;
            }
        }

        CircuitMetrics {
            depth: gate_count, // Simplified depth calculation
            gate_count,
            gate_counts,
            two_qubit_gates,
            fidelity: None,
            error_rate: None,
        }
    }

    /// Get current memory usage (placeholder)
    const fn get_memory_usage(&self) -> usize {
        // In real implementation, this would use system APIs to get memory usage
        0
    }

    /// Generate comprehensive benchmark report
    fn generate_benchmark_report(&self) -> QuantRS2Result<BenchmarkReport> {
        let completed_runs = self.benchmark_data.len();
        let successful_runs: Vec<_> = self
            .benchmark_data
            .iter()
            .filter(|run| run.success)
            .collect();

        let success_rate = successful_runs.len() as f64 / completed_runs as f64;

        // Extract timing data
        let timing_data: Vec<f64> = successful_runs
            .iter()
            .map(|run| run.execution_time.as_secs_f64())
            .collect();

        let timing_stats = self
            .stats_analyzer
            .calculate_descriptive_stats(&timing_data)?;

        // Extract memory data if available
        let memory_stats = if self.config.collect_memory {
            let memory_data: Vec<f64> = successful_runs
                .iter()
                .filter_map(|run| run.memory_usage.map(|m| m as f64))
                .collect();

            if memory_data.is_empty() {
                None
            } else {
                Some(
                    self.stats_analyzer
                        .calculate_descriptive_stats(&memory_data)?,
                )
            }
        } else {
            None
        };

        // Perform regression analysis to detect performance trends
        let regression_analysis = self
            .stats_analyzer
            .perform_regression_analysis(&timing_data)?;

        // Fit distributions to timing data
        let distribution_fit = self.stats_analyzer.fit_distributions(&timing_data)?;

        // Detect outliers
        let outlier_analysis = self.stats_analyzer.detect_outliers(
            &timing_data,
            OutlierDetectionMethod::IQR { multiplier: 1.5 },
        )?;

        // Generate insights
        let insights = self.generate_performance_insights(
            &timing_stats,
            &regression_analysis,
            &outlier_analysis,
            success_rate,
        );

        Ok(BenchmarkReport {
            config: self.config.clone(),
            completed_runs,
            success_rate,
            timing_stats,
            memory_stats,
            regression_analysis: Some(regression_analysis),
            distribution_fit: Some(distribution_fit),
            outlier_analysis,
            baseline_comparison: None,
            statistical_tests: Vec::new(),
            insights,
        })
    }

    /// Generate performance insights based on statistical analysis
    fn generate_performance_insights(
        &self,
        timing_stats: &DescriptiveStats,
        regression: &RegressionAnalysis,
        outliers: &OutlierAnalysis,
        success_rate: f64,
    ) -> Vec<PerformanceInsight> {
        let mut insights = Vec::new();

        // Check for performance degradation
        if regression.significant_trend && regression.slope > 0.0 {
            insights.push(PerformanceInsight {
                category: InsightCategory::PerformanceDegradation,
                message: format!(
                    "Significant performance degradation detected: {:.4} seconds per run increase",
                    regression.degradation_per_run
                ),
                confidence: 1.0 - regression.slope_p_value,
                evidence: vec![
                    format!("Linear trend slope: {:.6}", regression.slope),
                    format!("R-squared: {:.4}", regression.r_squared),
                    format!("P-value: {:.4}", regression.slope_p_value),
                ],
                recommendations: vec![
                    "Investigate potential memory leaks".to_string(),
                    "Check for resource contention".to_string(),
                    "Profile execution to identify bottlenecks".to_string(),
                ],
            });
        }

        // Check for high variability
        let coefficient_of_variation = timing_stats.std_dev / timing_stats.mean;
        if coefficient_of_variation > 0.2 {
            insights.push(PerformanceInsight {
                category: InsightCategory::HighVariability,
                message: format!(
                    "High performance variability detected: CV = {:.2}%",
                    coefficient_of_variation * 100.0
                ),
                confidence: 0.8,
                evidence: vec![
                    format!("Standard deviation: {:.4} seconds", timing_stats.std_dev),
                    format!("Mean: {:.4} seconds", timing_stats.mean),
                    format!(
                        "Coefficient of variation: {:.2}%",
                        coefficient_of_variation * 100.0
                    ),
                ],
                recommendations: vec![
                    "Increase warm-up runs to stabilize performance".to_string(),
                    "Check for system load variations".to_string(),
                    "Consider running benchmarks in isolated environment".to_string(),
                ],
            });
        }

        // Check for outliers
        if outliers.num_outliers > 0 {
            let outlier_percentage =
                outliers.num_outliers as f64 / timing_stats.count as f64 * 100.0;
            insights.push(PerformanceInsight {
                category: InsightCategory::OutliersDetected,
                message: format!(
                    "Performance outliers detected: {} outliers ({:.1}% of runs)",
                    outliers.num_outliers, outlier_percentage
                ),
                confidence: 0.9,
                evidence: vec![
                    format!("Number of outliers: {}", outliers.num_outliers),
                    format!("Outlier percentage: {:.1}%", outlier_percentage),
                    format!("Detection method: {:?}", outliers.detection_method),
                ],
                recommendations: vec![
                    "Investigate causes of outlier runs".to_string(),
                    "Consider removing outliers from performance metrics".to_string(),
                    "Check for system interruptions during benchmarking".to_string(),
                ],
            });
        }

        // Check success rate
        if success_rate < 0.95 {
            insights.push(PerformanceInsight {
                category: InsightCategory::ErrorRate,
                message: format!("Low success rate detected: {:.1}%", success_rate * 100.0),
                confidence: 1.0,
                evidence: vec![
                    format!("Success rate: {:.1}%", success_rate * 100.0),
                    format!(
                        "Failed runs: {}",
                        timing_stats.count - (timing_stats.count as f64 * success_rate) as usize
                    ),
                ],
                recommendations: vec![
                    "Investigate failure causes".to_string(),
                    "Check circuit validity and simulator compatibility".to_string(),
                    "Increase timeout limits if timeouts are occurring".to_string(),
                ],
            });
        }

        insights
    }

    /// Compare with baseline benchmark
    pub fn compare_with_baseline(
        &self,
        baseline: &BenchmarkReport,
    ) -> QuantRS2Result<BaselineComparison> {
        if self.benchmark_data.is_empty() {
            return Err(QuantRS2Error::InvalidInput(
                "No benchmark data available for comparison".to_string(),
            ));
        }

        let current_timing: Vec<f64> = self
            .benchmark_data
            .iter()
            .filter(|run| run.success)
            .map(|run| run.execution_time.as_secs_f64())
            .collect();

        let baseline_mean = baseline.timing_stats.mean;
        let current_mean = self
            .stats_analyzer
            .calculate_descriptive_stats(&current_timing)?
            .mean;

        let performance_factor = current_mean / baseline_mean;

        // Perform statistical test for significance
        let significance = self.stats_analyzer.mann_whitney_test(
            &current_timing,
            &[baseline_mean], // Simplified - would use actual baseline data
            self.config.significance_level,
        )?;

        // Calculate effect size (Cohen's d)
        let effect_size = (current_mean - baseline_mean) / baseline.timing_stats.std_dev;

        // Assess practical significance
        let practical_significance = match effect_size.abs() {
            x if x < 0.2 => PracticalSignificance::Negligible,
            x if x < 0.5 => PracticalSignificance::Small,
            x if x < 0.8 => PracticalSignificance::Medium,
            x if x < 1.2 => PracticalSignificance::Large,
            _ => PracticalSignificance::VeryLarge,
        };

        Ok(BaselineComparison {
            baseline_name: "baseline".to_string(),
            performance_factor,
            significance,
            difference_ci: (0.0, 0.0), // Would calculate proper CI
            effect_size,
            practical_significance,
        })
    }
}

/// Statistical analyzer using `SciRS2` capabilities
pub struct StatisticalAnalyzer;

impl StatisticalAnalyzer {
    /// Create a new statistical analyzer
    #[must_use]
    pub const fn new() -> Self {
        Self
    }

    /// Calculate descriptive statistics
    pub fn calculate_descriptive_stats(&self, data: &[f64]) -> QuantRS2Result<DescriptiveStats> {
        if data.is_empty() {
            return Err(QuantRS2Error::InvalidInput("Empty data".to_string()));
        }

        let mut sorted_data = data.to_vec();
        sorted_data.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));

        let count = data.len();
        let mean = data.iter().sum::<f64>() / count as f64;
        let variance = data.iter().map(|x| (x - mean).powi(2)).sum::<f64>() / count as f64;
        let std_dev = variance.sqrt();
        let min = sorted_data[0];
        let max = sorted_data[count - 1];

        let median = if count % 2 == 0 {
            f64::midpoint(sorted_data[count / 2 - 1], sorted_data[count / 2])
        } else {
            sorted_data[count / 2]
        };

        let q1 = self.percentile(&sorted_data, 0.25);
        let q3 = self.percentile(&sorted_data, 0.75);
        let iqr = q3 - q1;

        // Calculate skewness and kurtosis
        let skewness = self.calculate_skewness(data, mean, std_dev);
        let kurtosis = self.calculate_kurtosis(data, mean, std_dev);

        Ok(DescriptiveStats {
            count,
            mean,
            std_dev,
            variance,
            min,
            max,
            median,
            q1,
            q3,
            iqr,
            skewness,
            kurtosis,
            mode: None, // Would implement mode calculation
        })
    }

    /// Calculate percentile
    fn percentile(&self, sorted_data: &[f64], p: f64) -> f64 {
        let index = (p * (sorted_data.len() - 1) as f64).round() as usize;
        sorted_data[index.min(sorted_data.len() - 1)]
    }

    /// Calculate skewness
    fn calculate_skewness(&self, data: &[f64], mean: f64, std_dev: f64) -> f64 {
        let n = data.len() as f64;
        let skew_sum = data
            .iter()
            .map(|x| ((x - mean) / std_dev).powi(3))
            .sum::<f64>();
        skew_sum / n
    }

    /// Calculate kurtosis
    fn calculate_kurtosis(&self, data: &[f64], mean: f64, std_dev: f64) -> f64 {
        let n = data.len() as f64;
        let kurt_sum = data
            .iter()
            .map(|x| ((x - mean) / std_dev).powi(4))
            .sum::<f64>();
        kurt_sum / n - 3.0 // Excess kurtosis
    }

    /// Perform linear regression analysis
    pub fn perform_regression_analysis(&self, data: &[f64]) -> QuantRS2Result<RegressionAnalysis> {
        if data.len() < 3 {
            return Err(QuantRS2Error::InvalidInput(
                "Insufficient data for regression".to_string(),
            ));
        }

        let n = data.len() as f64;
        let x_values: Vec<f64> = (0..data.len()).map(|i| i as f64).collect();

        let x_mean = x_values.iter().sum::<f64>() / n;
        let y_mean = data.iter().sum::<f64>() / n;

        let numerator: f64 = x_values
            .iter()
            .zip(data.iter())
            .map(|(x, y)| (x - x_mean) * (y - y_mean))
            .sum();

        let denominator: f64 = x_values.iter().map(|x| (x - x_mean).powi(2)).sum();

        let slope = numerator / denominator;
        let intercept = slope.mul_add(-x_mean, y_mean);

        // Calculate R-squared
        let ss_tot: f64 = data.iter().map(|y| (y - y_mean).powi(2)).sum();
        let ss_res: f64 = x_values
            .iter()
            .zip(data.iter())
            .map(|(x, y)| {
                let predicted = slope * x + intercept;
                (y - predicted).powi(2)
            })
            .sum();

        let r_squared = 1.0 - (ss_res / ss_tot);

        // Calculate p-value for slope (simplified)
        let slope_p_value = if slope.abs() > 0.001 { 0.05 } else { 0.5 };
        let significant_trend = slope_p_value < 0.05;

        Ok(RegressionAnalysis {
            slope,
            intercept,
            r_squared,
            slope_p_value,
            significant_trend,
            degradation_per_run: slope,
        })
    }

    /// Fit probability distributions to data
    pub fn fit_distributions(&self, data: &[f64]) -> QuantRS2Result<DistributionFit> {
        let stats = self.calculate_descriptive_stats(data)?;

        // Fit normal distribution
        let normal_dist = Distribution::Normal {
            mean: stats.mean,
            std_dev: stats.std_dev,
        };

        // Simple goodness of fit (would use proper statistical tests in SciRS2)
        let goodness_of_fit = 0.8; // Placeholder
        let fit_p_value = 0.3; // Placeholder

        Ok(DistributionFit {
            best_distribution: normal_dist,
            goodness_of_fit,
            fit_p_value,
            alternative_fits: Vec::new(),
        })
    }

    /// Detect outliers using specified method
    pub fn detect_outliers(
        &self,
        data: &[f64],
        method: OutlierDetectionMethod,
    ) -> QuantRS2Result<OutlierAnalysis> {
        let outlier_indices = match method {
            OutlierDetectionMethod::IQR { multiplier } => {
                self.detect_outliers_iqr(data, multiplier)?
            }
            OutlierDetectionMethod::ZScore { threshold } => {
                self.detect_outliers_zscore(data, threshold)?
            }
            _ => Vec::new(), // Other methods would be implemented
        };

        let num_outliers = outlier_indices.len();

        // Calculate outlier impact
        let outlier_impact = if num_outliers > 0 {
            self.calculate_outlier_impact(data, &outlier_indices)?
        } else {
            OutlierImpact {
                mean_change: 0.0,
                std_dev_change: 0.0,
                median_change: 0.0,
                relative_impact: 0.0,
            }
        };

        Ok(OutlierAnalysis {
            num_outliers,
            outlier_indices,
            detection_method: method,
            threshold: 1.5, // Would depend on method
            outlier_impact,
        })
    }

    /// Detect outliers using IQR method
    fn detect_outliers_iqr(&self, data: &[f64], multiplier: f64) -> QuantRS2Result<Vec<usize>> {
        let stats = self.calculate_descriptive_stats(data)?;
        let lower_bound = multiplier.mul_add(-stats.iqr, stats.q1);
        let upper_bound = multiplier.mul_add(stats.iqr, stats.q3);

        Ok(data
            .iter()
            .enumerate()
            .filter_map(|(i, &value)| {
                if value < lower_bound || value > upper_bound {
                    Some(i)
                } else {
                    None
                }
            })
            .collect())
    }

    /// Detect outliers using Z-score method
    fn detect_outliers_zscore(&self, data: &[f64], threshold: f64) -> QuantRS2Result<Vec<usize>> {
        let stats = self.calculate_descriptive_stats(data)?;

        Ok(data
            .iter()
            .enumerate()
            .filter_map(|(i, &value)| {
                let z_score = (value - stats.mean) / stats.std_dev;
                if z_score.abs() > threshold {
                    Some(i)
                } else {
                    None
                }
            })
            .collect())
    }

    /// Calculate impact of outliers on statistics
    fn calculate_outlier_impact(
        &self,
        data: &[f64],
        outlier_indices: &[usize],
    ) -> QuantRS2Result<OutlierImpact> {
        let original_stats = self.calculate_descriptive_stats(data)?;

        // Create data without outliers
        let filtered_data: Vec<f64> = data
            .iter()
            .enumerate()
            .filter_map(|(i, &value)| {
                if outlier_indices.contains(&i) {
                    None
                } else {
                    Some(value)
                }
            })
            .collect();

        let filtered_stats = self.calculate_descriptive_stats(&filtered_data)?;

        let mean_change = (original_stats.mean - filtered_stats.mean).abs();
        let std_dev_change = (original_stats.std_dev - filtered_stats.std_dev).abs();
        let median_change = (original_stats.median - filtered_stats.median).abs();
        let relative_impact = mean_change / original_stats.mean * 100.0;

        Ok(OutlierImpact {
            mean_change,
            std_dev_change,
            median_change,
            relative_impact,
        })
    }

    /// Perform Mann-Whitney U test
    pub fn mann_whitney_test(
        &self,
        sample1: &[f64],
        sample2: &[f64],
        significance_level: f64,
    ) -> QuantRS2Result<HypothesisTestResult> {
        // Simplified implementation - would use SciRS2's statistical functions
        let test_statistic = 0.0; // Placeholder
        let p_value = 0.1; // Placeholder
        let critical_value = 1.96; // Placeholder
        let reject_null = p_value < significance_level;

        Ok(HypothesisTestResult {
            test_statistic,
            p_value,
            critical_value,
            reject_null,
            significance_level,
            effect_size: None,
            confidence_interval: None,
        })
    }
}

/// Trait for simulator execution (placeholder)
pub trait SimulatorExecutor {
    fn execute(&self, circuit: &dyn std::any::Any) -> QuantRS2Result<ExecutionResult>;
}

impl Default for StatisticalAnalyzer {
    fn default() -> Self {
        Self::new()
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_descriptive_stats() {
        let analyzer = StatisticalAnalyzer::new();
        let data = vec![1.0, 2.0, 3.0, 4.0, 5.0];

        let stats = analyzer
            .calculate_descriptive_stats(&data)
            .expect("calculate_descriptive_stats should succeed");
        assert_eq!(stats.mean, 3.0);
        assert_eq!(stats.median, 3.0);
        assert_eq!(stats.min, 1.0);
        assert_eq!(stats.max, 5.0);
    }

    #[test]
    fn test_outlier_detection_iqr() {
        let analyzer = StatisticalAnalyzer::new();
        let data = vec![1.0, 2.0, 3.0, 4.0, 5.0, 100.0]; // 100.0 is an outlier

        let outliers = analyzer
            .detect_outliers_iqr(&data, 1.5)
            .expect("outlier detection should succeed");
        assert_eq!(outliers.len(), 1);
        assert_eq!(outliers[0], 5); // Index of 100.0
    }

    #[test]
    fn test_regression_analysis() {
        let analyzer = StatisticalAnalyzer::new();
        let data = vec![1.0, 2.0, 3.0, 4.0, 5.0]; // Perfect linear trend

        let regression = analyzer
            .perform_regression_analysis(&data)
            .expect("perform_regression_analysis should succeed");
        assert!((regression.slope - 1.0).abs() < 1e-10);
        assert!((regression.r_squared - 1.0).abs() < 1e-10);
    }

    #[test]
    fn test_benchmark_config() {
        let config = BenchmarkConfig::default();
        assert_eq!(config.num_runs, 100);
        assert_eq!(config.warmup_runs, 10);
        assert_eq!(config.significance_level, 0.05);
    }

    #[test]
    fn test_distribution_creation() {
        let normal = Distribution::Normal {
            mean: 0.0,
            std_dev: 1.0,
        };
        match normal {
            Distribution::Normal { mean, std_dev } => {
                assert_eq!(mean, 0.0);
                assert_eq!(std_dev, 1.0);
            }
            _ => panic!("Wrong distribution type"),
        }
    }
}