quantrs2-ml 0.1.3

//! Barren Plateau Detection for Quantum Machine Learning
//!
//! This module implements methods to detect and analyze barren plateaus
//! in quantum neural networks and variational circuits.

use crate::error::MLError;
use quantrs2_circuit::prelude::*;
use scirs2_core::random::prelude::*;
use std::f64::consts::PI;

/// Variance threshold below which we consider a gradient to be in a barren plateau
const BARREN_PLATEAU_THRESHOLD: f64 = 1e-6;

/// Result of barren plateau analysis
#[derive(Debug, Clone)]
pub struct BarrenPlateauAnalysis {
    /// Layer-wise gradient variances
    pub layer_variances: Vec<f64>,
    /// Overall gradient variance
    pub overall_variance: f64,
    /// Whether the circuit is in a barren plateau
    pub is_barren: bool,
    /// Problematic layers (indices)
    pub problematic_layers: Vec<usize>,
    /// Suggested mitigation strategies
    pub mitigation_strategies: Vec<String>,
}

/// Barren plateau detector
pub struct BarrenPlateauDetector {
    /// Number of samples for variance estimation
    pub num_samples: usize,
    /// Random seed for reproducibility
    pub seed: u64,
}

impl Default for BarrenPlateauDetector {
    fn default() -> Self {
        Self {
            num_samples: 100,
            seed: 42,
        }
    }
}

impl BarrenPlateauDetector {
    /// Create a new barren plateau detector
    pub fn new(num_samples: usize) -> Self {
        Self {
            num_samples,
            seed: 42,
        }
    }

    /// Analyze a parameterized quantum circuit for barren plateaus
    pub fn analyze_circuit<const N: usize>(
        &self,
        circuit_builder: impl Fn(&[f64]) -> Result<Circuit<N>, MLError>,
        num_params: usize,
        num_layers: usize,
    ) -> Result<BarrenPlateauAnalysis, MLError> {
        let mut rng = scirs2_core::random::ChaCha8Rng::seed_from_u64(self.seed);
        let mut layer_variances = vec![0.0; num_layers];
        let mut all_gradients = Vec::new();

        // Sample random parameter configurations
        for _ in 0..self.num_samples {
            // Generate random parameters
            let params: Vec<f64> = (0..num_params)
                .map(|_| rng.random::<f64>() * 2.0 * PI)
                .collect();

            // Compute gradients for this configuration
            let gradients = self.compute_gradients(&circuit_builder, &params)?;

            // Store gradients for analysis
            all_gradients.extend(gradients.clone());

            // Accumulate layer-wise variances
            let params_per_layer = num_params / num_layers;
            for (layer_idx, chunk) in gradients.chunks(params_per_layer).enumerate() {
                if layer_idx < num_layers {
                    let layer_var = variance(chunk);
                    layer_variances[layer_idx] += layer_var;
                }
            }
        }

        // Average the variances
        for var in &mut layer_variances {
            *var /= self.num_samples as f64;
        }

        // Compute overall variance
        let overall_variance = variance(&all_gradients);

        // Identify problematic layers
        let problematic_layers: Vec<usize> = layer_variances
            .iter()
            .enumerate()
            .filter(|(_, &var)| var < BARREN_PLATEAU_THRESHOLD)
            .map(|(idx, _)| idx)
            .collect();

        // Determine if circuit is in barren plateau
        let is_barren = overall_variance < BARREN_PLATEAU_THRESHOLD
            || problematic_layers.len() > num_layers / 2;

        // Generate mitigation strategies
        let mitigation_strategies =
            self.suggest_mitigation_strategies(&layer_variances, overall_variance, num_layers, N);

        Ok(BarrenPlateauAnalysis {
            layer_variances,
            overall_variance,
            is_barren,
            problematic_layers,
            mitigation_strategies,
        })
    }

    /// Compute gradients using parameter shift rule
    fn compute_gradients<const N: usize>(
        &self,
        circuit_builder: &impl Fn(&[f64]) -> Result<Circuit<N>, MLError>,
        params: &[f64],
    ) -> Result<Vec<f64>, MLError> {
        let shift = PI / 2.0;
        let mut gradients = vec![0.0; params.len()];

        for i in 0..params.len() {
            // Positive shift
            let mut params_plus = params.to_vec();
            params_plus[i] += shift;
            let circuit_plus = circuit_builder(&params_plus)?;
            let exp_plus = self.compute_expectation(&circuit_plus)?;

            // Negative shift
            let mut params_minus = params.to_vec();
            params_minus[i] -= shift;
            let circuit_minus = circuit_builder(&params_minus)?;
            let exp_minus = self.compute_expectation(&circuit_minus)?;

            // Parameter shift gradient
            gradients[i] = (exp_plus - exp_minus) / 2.0;
        }

        Ok(gradients)
    }

    /// Compute expectation value (simplified - returns random value for demo)
    fn compute_expectation<const N: usize>(&self, _circuit: &Circuit<N>) -> Result<f64, MLError> {
        // In a real implementation, this would:
        // 1. Simulate the circuit
        // 2. Measure an observable
        // 3. Return the expectation value

        // For demo purposes, return a small random value
        let mut rng = scirs2_core::random::ChaCha8Rng::seed_from_u64(self.seed);
        Ok(rng.random::<f64>() * 0.1)
    }

    /// Suggest mitigation strategies based on analysis
    fn suggest_mitigation_strategies(
        &self,
        layer_variances: &[f64],
        overall_variance: f64,
        num_layers: usize,
        num_qubits: usize,
    ) -> Vec<String> {
        let mut strategies = Vec::new();

        // Check for exponentially vanishing gradients
        if overall_variance < BARREN_PLATEAU_THRESHOLD {
            strategies
                .push("Use hardware-efficient ansatz with limited entanglement depth".to_string());
            strategies
                .push("Implement layer-wise training to avoid deep circuit issues".to_string());
        }

        // Check for specific problematic layers
        let bad_layers = layer_variances
            .iter()
            .filter(|&&var| var < BARREN_PLATEAU_THRESHOLD)
            .count();

        if bad_layers > 0 {
            strategies.push(format!(
                "Consider removing or redesigning {} problematic layers",
                bad_layers
            ));
            strategies
                .push("Use variable structure ansätze that adapt during training".to_string());
        }

        // Circuit depth recommendations
        if num_layers > num_qubits {
            strategies.push(format!(
                "Reduce circuit depth from {} to around {} (number of qubits)",
                num_layers, num_qubits
            ));
        }

        // Initialization strategies
        strategies.push("Use smart initialization: small random values around 0".to_string());
        strategies.push("Consider pre-training with classical shadows".to_string());

        // Architecture recommendations
        if num_qubits > 10 {
            strategies.push(
                "For large systems, use local cost functions instead of global ones".to_string(),
            );
            strategies.push("Implement quantum convolutional architectures".to_string());
        }

        strategies
    }
}

/// Compute variance of a slice of values
fn variance(values: &[f64]) -> f64 {
    if values.is_empty() {
        return 0.0;
    }

    let mean = values.iter().sum::<f64>() / values.len() as f64;
    let var = values.iter().map(|&x| (x - mean).powi(2)).sum::<f64>() / values.len() as f64;

    var
}

/// Analyze gradient variance scaling with system size
pub struct VarianceScalingAnalyzer {
    /// Detector instance
    detector: BarrenPlateauDetector,
}

impl VarianceScalingAnalyzer {
    /// Create a new variance scaling analyzer
    pub fn new(num_samples: usize) -> Self {
        Self {
            detector: BarrenPlateauDetector::new(num_samples),
        }
    }

    /// Analyze how gradient variance scales with number of qubits
    pub fn analyze_scaling(
        &self,
        min_qubits: usize,
        max_qubits: usize,
        layers_per_qubit: usize,
    ) -> Result<Vec<(usize, f64)>, MLError> {
        let mut results = Vec::new();

        for n in min_qubits..=max_qubits {
            let variance = self.analyze_system_size(n, n * layers_per_qubit)?;
            results.push((n, variance));
        }

        Ok(results)
    }

    /// Analyze variance for a specific system size
    fn analyze_system_size(&self, num_qubits: usize, num_layers: usize) -> Result<f64, MLError> {
        // For demo, return exponentially decaying variance
        // In real implementation, would build and analyze actual circuits
        let variance = 1.0 / (2.0_f64.powf(num_qubits as f64));
        Ok(variance)
    }
}

/// Pre-training strategy to avoid barren plateaus
pub struct BarrenPlateauMitigation {
    /// Number of pre-training steps
    pub pretrain_steps: usize,
    /// Learning rate for pre-training
    pub learning_rate: f64,
}

impl BarrenPlateauMitigation {
    /// Create a new mitigation strategy
    pub fn new(pretrain_steps: usize, learning_rate: f64) -> Self {
        Self {
            pretrain_steps,
            learning_rate,
        }
    }

    /// Initialize parameters to avoid barren plateaus
    pub fn smart_initialization(&self, num_params: usize) -> Vec<f64> {
        let mut rng = scirs2_core::random::ChaCha8Rng::seed_from_u64(42);

        // Initialize with small random values
        (0..num_params)
            .map(|_| (rng.random::<f64>() - 0.5) * 0.1)
            .collect()
    }

    /// Layer-wise pre-training strategy
    pub fn layer_wise_pretrain<const N: usize>(
        &self,
        circuit_builder: impl Fn(&[f64]) -> Result<Circuit<N>, MLError>,
        num_params: usize,
        num_layers: usize,
    ) -> Result<Vec<f64>, MLError> {
        let params_per_layer = num_params / num_layers;
        let mut params = self.smart_initialization(num_params);

        // Train each layer separately
        for layer in 0..num_layers {
            let start_idx = layer * params_per_layer;
            let end_idx = (layer + 1) * params_per_layer;

            // Freeze other layers and train only this one
            for step in 0..self.pretrain_steps {
                // Simplified gradient descent
                let gradients = vec![0.1; params_per_layer]; // Dummy gradients

                for i in start_idx..end_idx {
                    params[i] -= self.learning_rate * gradients[i - start_idx];
                }
            }
        }

        Ok(params)
    }
}

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

    #[test]
    fn test_variance_computation() {
        let values = vec![1.0, 2.0, 3.0, 4.0, 5.0];
        let var = variance(&values);
        assert!((var - 2.0).abs() < 1e-10);
    }

    #[test]
    fn test_barren_plateau_detection() {
        let detector = BarrenPlateauDetector::new(10);

        // Simple circuit builder
        let circuit_builder = |params: &[f64]| -> Result<Circuit<4>, MLError> {
            let mut circuit = Circuit::<4>::new();
            for (i, &param) in params.iter().enumerate() {
                circuit.ry(i % 4, param)?;
            }
            Ok(circuit)
        };

        let analysis = detector
            .analyze_circuit(circuit_builder, 8, 2)
            .expect("analyze_circuit should succeed");

        assert_eq!(analysis.layer_variances.len(), 2);
        assert!(!analysis.mitigation_strategies.is_empty());
    }

    #[test]
    fn test_smart_initialization() {
        let mitigation = BarrenPlateauMitigation::new(100, 0.01);
        let params = mitigation.smart_initialization(10);

        assert_eq!(params.len(), 10);
        // Check all parameters are small
        for &p in &params {
            assert!(p.abs() < 0.1);
        }
    }
}