quantrs2_core/

qpca.rs

//! Quantum Principal Component Analysis (qPCA)
//!
//! This module implements quantum principal component analysis for
//! efficient dimensionality reduction and eigenvalue estimation.

use crate::error::QuantRS2Error;
use ndarray::{Array1, Array2};
use num_complex::Complex64;
use std::f64::consts::PI;

/// Parameters for quantum PCA
#[derive(Debug, Clone)]
pub struct QPCAParams {
    /// Number of precision qubits for phase estimation
    pub precision_qubits: usize,
    /// Number of samples for density matrix estimation
    pub num_samples: usize,
    /// Threshold for eigenvalue selection
    pub eigenvalue_threshold: f64,
    /// Maximum number of iterations for quantum phase estimation
    pub max_iterations: usize,
}

impl Default for QPCAParams {
    fn default() -> Self {
        Self {
            precision_qubits: 8,
            num_samples: 1000,
            eigenvalue_threshold: 0.01,
            max_iterations: 100,
        }
    }
}

/// Quantum Principal Component Analysis implementation
pub struct QuantumPCA {
    params: QPCAParams,
    data_matrix: Array2<f64>,
    density_matrix: Option<Array2<Complex64>>,
    eigenvalues: Option<Array1<f64>>,
    eigenvectors: Option<Array2<Complex64>>,
}

impl QuantumPCA {
    /// Create new qPCA instance with data matrix
    pub fn new(data: Array2<f64>, params: QPCAParams) -> Self {
        Self {
            params,
            data_matrix: data,
            density_matrix: None,
            eigenvalues: None,
            eigenvectors: None,
        }
    }

    /// Compute the quantum density matrix from classical data
    pub fn compute_density_matrix(&mut self) -> Result<&Array2<Complex64>, QuantRS2Error> {
        let (n_samples, n_features) = (self.data_matrix.nrows(), self.data_matrix.ncols());

        // Center the data
        let mean = self
            .data_matrix
            .mean_axis(ndarray::Axis(0))
            .ok_or_else(|| {
                QuantRS2Error::UnsupportedOperation("Failed to compute mean".to_string())
            })?;

        let centered_data = &self.data_matrix - &mean;

        // Compute covariance matrix
        let cov_matrix = centered_data.t().dot(&centered_data) / (n_samples - 1) as f64;

        // Convert to complex density matrix and normalize
        let mut density = Array2::<Complex64>::zeros((n_features, n_features));
        for i in 0..n_features {
            for j in 0..n_features {
                density[[i, j]] = Complex64::new(cov_matrix[[i, j]], 0.0);
            }
        }

        // Normalize to trace 1
        let trace: Complex64 = (0..n_features).map(|i| density[[i, i]]).sum();
        if trace.norm() > 1e-10 {
            density /= trace;
        }

        self.density_matrix = Some(density);
        self.density_matrix
            .as_ref()
            .ok_or(QuantRS2Error::UnsupportedOperation(
                "Failed to create density matrix".to_string(),
            ))
    }

    /// Quantum phase estimation for eigenvalue extraction
    pub fn quantum_phase_estimation(
        &self,
        unitary: &Array2<Complex64>,
        state: &Array1<Complex64>,
    ) -> Result<f64, QuantRS2Error> {
        let precision = self.params.precision_qubits;
        let _n = 1 << precision;

        // Simulate quantum phase estimation
        // In a real quantum computer, this would use controlled-U operations
        let mut phase_estimate = 0.0;

        // Apply inverse QFT and measure
        for k in 0..precision {
            // Simplified simulation of controlled unitary application
            let controlled_phase = self.estimate_controlled_phase(unitary, state, 1 << k)?;
            phase_estimate += controlled_phase * (1.0 / (1 << (precision - k - 1)) as f64);
        }

        Ok(phase_estimate)
    }

    /// Estimate phase from controlled unitary (simplified simulation)
    fn estimate_controlled_phase(
        &self,
        unitary: &Array2<Complex64>,
        state: &Array1<Complex64>,
        power: usize,
    ) -> Result<f64, QuantRS2Error> {
        // Compute U^power
        let mut u_power = unitary.clone();
        for _ in 1..power {
            u_power = u_power.dot(unitary);
        }

        // Apply to state and extract phase
        let result = u_power.dot(state);
        let inner_product: Complex64 = state
            .iter()
            .zip(result.iter())
            .map(|(a, b)| a.conj() * b)
            .sum();

        Ok(inner_product.arg() / (2.0 * PI))
    }

    /// Extract principal components using quantum algorithm
    pub fn extract_components(&mut self) -> Result<(), QuantRS2Error> {
        // Ensure density matrix is computed
        if self.density_matrix.is_none() {
            self.compute_density_matrix()?;
        }

        let density = self.density_matrix.as_ref().unwrap();
        let dim = density.nrows();

        // Use quantum phase estimation to find eigenvalues
        // In practice, this would be done on a quantum computer
        let (eigenvalues, eigenvectors) = self.quantum_eigendecomposition(density)?;

        // Filter by threshold
        let mut filtered_indices: Vec<usize> = eigenvalues
            .iter()
            .enumerate()
            .filter(|(_, &val)| val.abs() > self.params.eigenvalue_threshold)
            .map(|(idx, _)| idx)
            .collect();

        // Sort by eigenvalue magnitude (descending)
        filtered_indices.sort_by(|&a, &b| {
            eigenvalues[b]
                .abs()
                .partial_cmp(&eigenvalues[a].abs())
                .unwrap()
        });

        // Extract filtered eigenvalues and eigenvectors
        let n_components = filtered_indices.len();
        let mut filtered_eigenvalues = Array1::zeros(n_components);
        let mut filtered_eigenvectors = Array2::zeros((dim, n_components));

        for (new_idx, &old_idx) in filtered_indices.iter().enumerate() {
            filtered_eigenvalues[new_idx] = eigenvalues[old_idx];
            for i in 0..dim {
                filtered_eigenvectors[[i, new_idx]] = eigenvectors[[i, old_idx]];
            }
        }

        self.eigenvalues = Some(filtered_eigenvalues);
        self.eigenvectors = Some(filtered_eigenvectors);

        Ok(())
    }

    /// Quantum eigendecomposition (simulated)
    fn quantum_eigendecomposition(
        &self,
        matrix: &Array2<Complex64>,
    ) -> Result<(Array1<f64>, Array2<Complex64>), QuantRS2Error> {
        // In a real implementation, this would use quantum phase estimation
        // For now, we use a simplified eigendecomposition approach

        // Ensure matrix is Hermitian
        let hermitian = (matrix + &matrix.t().mapv(|x| x.conj())) / Complex64::new(2.0, 0.0);

        // Convert to real symmetric matrix if possible
        let is_real = hermitian.iter().all(|x| x.im.abs() < 1e-10);

        if is_real {
            let n = hermitian.nrows();
            let real_matrix = hermitian.mapv(|x| x.re);

            // Use power iteration method for finding dominant eigenvalues
            // This is a simplified approach - in practice use proper eigensolvers
            let mut eigenvalues = Vec::with_capacity(n);
            let mut eigenvectors = Array2::<Complex64>::zeros((n, n));

            // For demonstration, we'll just extract a few principal components
            let num_components = n.min(self.params.precision_qubits);

            for comp in 0..num_components {
                // Power iteration for finding dominant eigenvector
                let mut v = Array1::from_vec(vec![1.0 / (n as f64).sqrt(); n]);
                let mut eigenvalue = 0.0;

                for _ in 0..self.params.max_iterations {
                    let av = real_matrix.dot(&v);
                    eigenvalue = v.dot(&av);
                    let norm = av.dot(&av).sqrt();
                    if norm > 1e-10 {
                        v = av / norm;
                    }
                }

                eigenvalues.push(eigenvalue);
                for i in 0..n {
                    eigenvectors[[i, comp]] = Complex64::new(v[i], 0.0);
                }
            }

            // Fill remaining with zeros
            eigenvalues.extend(vec![0.0; n - num_components]);

            Ok((Array1::from_vec(eigenvalues), eigenvectors))
        } else {
            // For complex Hermitian matrices, we need specialized algorithms
            // This is a placeholder - in practice, use quantum phase estimation
            Err(QuantRS2Error::UnsupportedOperation(
                "Complex eigendecomposition not yet implemented".to_string(),
            ))
        }
    }

    /// Project data onto principal components
    pub fn transform(&self, data: &Array2<f64>) -> Result<Array2<f64>, QuantRS2Error> {
        let eigenvectors =
            self.eigenvectors
                .as_ref()
                .ok_or(QuantRS2Error::UnsupportedOperation(
                    "Components not yet extracted".to_string(),
                ))?;

        // Center the data
        let mean = self
            .data_matrix
            .mean_axis(ndarray::Axis(0))
            .ok_or_else(|| {
                QuantRS2Error::UnsupportedOperation("Failed to compute mean".to_string())
            })?;

        let centered_data = data - &mean;

        // Project onto principal components
        let n_components = eigenvectors.ncols();
        let n_samples = centered_data.nrows();
        let mut transformed = Array2::zeros((n_samples, n_components));

        for i in 0..n_samples {
            for j in 0..n_components {
                let mut sum = 0.0;
                for k in 0..centered_data.ncols() {
                    sum += centered_data[[i, k]] * eigenvectors[[k, j]].re;
                }
                transformed[[i, j]] = sum;
            }
        }

        Ok(transformed)
    }

    /// Get explained variance ratio for each component
    pub fn explained_variance_ratio(&self) -> Result<Array1<f64>, QuantRS2Error> {
        let eigenvalues = self
            .eigenvalues
            .as_ref()
            .ok_or(QuantRS2Error::UnsupportedOperation(
                "Components not yet extracted".to_string(),
            ))?;

        let total_variance: f64 = eigenvalues.sum();
        if total_variance.abs() < 1e-10 {
            return Err(QuantRS2Error::UnsupportedOperation(
                "Total variance is zero".to_string(),
            ));
        }

        Ok(eigenvalues / total_variance)
    }

    /// Get the number of components
    pub fn n_components(&self) -> Option<usize> {
        self.eigenvalues.as_ref().map(|e| e.len())
    }

    /// Get eigenvalues
    pub fn eigenvalues(&self) -> Option<&Array1<f64>> {
        self.eigenvalues.as_ref()
    }

    /// Get eigenvectors
    pub fn eigenvectors(&self) -> Option<&Array2<Complex64>> {
        self.eigenvectors.as_ref()
    }
}

/// Quantum-inspired PCA using density matrix formulation
pub struct DensityMatrixPCA {
    params: QPCAParams,
    pub trace_threshold: f64,
}

impl DensityMatrixPCA {
    /// Create new density matrix PCA
    pub fn new(params: QPCAParams) -> Self {
        Self {
            params,
            trace_threshold: 0.95, // Capture 95% of trace
        }
    }

    /// Compute low-rank approximation using quantum-inspired method
    pub fn fit_transform(
        &self,
        data: &Array2<f64>,
    ) -> Result<(Array2<f64>, Array1<f64>), QuantRS2Error> {
        let mut qpca = QuantumPCA::new(data.clone(), self.params.clone());

        // Compute density matrix and extract components
        qpca.compute_density_matrix()?;
        qpca.extract_components()?;

        // Find number of components to retain based on trace threshold
        let explained_variance = qpca.explained_variance_ratio()?;
        let mut cumsum = 0.0;
        let mut n_components_retain = 0;

        for (i, &var) in explained_variance.iter().enumerate() {
            cumsum += var;
            n_components_retain = i + 1;
            if cumsum >= self.trace_threshold {
                break;
            }
        }

        // Transform data
        let transformed = qpca.transform(data)?;

        // Return only the retained components
        let retained_transform = transformed
            .slice(ndarray::s![.., ..n_components_retain])
            .to_owned();
        let retained_variance = explained_variance
            .slice(ndarray::s![..n_components_retain])
            .to_owned();

        Ok((retained_transform, retained_variance))
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use ndarray::Array2;

    #[test]
    fn test_qpca_basic() {
        // Create simple test data
        let data = Array2::from_shape_vec(
            (5, 3),
            vec![
                1.0, 2.0, 3.0, 2.0, 4.0, 6.0, 3.0, 6.0, 9.0, 4.0, 8.0, 12.0, 5.0, 10.0, 15.0,
            ],
        )
        .unwrap();

        let params = QPCAParams::default();
        let mut qpca = QuantumPCA::new(data.clone(), params);

        // Compute density matrix
        let density = qpca.compute_density_matrix().unwrap();
        assert_eq!(density.shape(), &[3, 3]);

        // Extract components
        qpca.extract_components().unwrap();

        let eigenvalues = qpca.eigenvalues().unwrap();
        assert!(!eigenvalues.is_empty());

        // Check that eigenvalues are sorted in descending order
        for i in 1..eigenvalues.len() {
            assert!(eigenvalues[i - 1] >= eigenvalues[i]);
        }
    }

    #[test]
    fn test_density_matrix_pca() {
        // Create test data with clear principal components
        let mut data = Array2::zeros((10, 4));
        for i in 0..10 {
            data[[i, 0]] = i as f64;
            data[[i, 1]] = 2.0 * i as f64;
            data[[i, 2]] = 0.1 * ((i * 7) % 10) as f64 / 10.0;
            data[[i, 3]] = 0.1 * ((i * 13) % 10) as f64 / 10.0;
        }

        let params = QPCAParams::default();
        let pca = DensityMatrixPCA::new(params);

        let (transformed, variance) = pca.fit_transform(&data).unwrap();

        // Should retain at least one component
        assert!(transformed.ncols() >= 1);
        assert!(transformed.ncols() <= data.ncols());
        // Variance should be normalized
        assert!(variance.sum() <= 1.0 + 1e-6);
    }
}