sklears-manifold 0.1.2

//! Quantum Methods for Manifold Learning
//!
//! This module provides quantum-inspired and quantum computing methods for
//! manifold learning, including quantum dimensionality reduction, quantum
//! approximate optimization, and variational quantum eigensolvers.
//!
//! # Overview
//!
//! Quantum methods leverage quantum mechanical principles or quantum computing
//! algorithms to enhance manifold learning:
//!
//! - **Quantum Dimensionality Reduction**: Use quantum state preparation and measurement
//! - **Quantum Approximate Optimization Algorithm (QAOA)**: Optimize manifold embeddings
//! - **Variational Quantum Eigensolver (VQE)**: Find low-energy states for manifold learning
//! - **Quantum Kernel Methods**: Compute quantum feature maps for improved separation
//! - **Quantum Annealing**: Solve optimization problems in manifold learning
//!
//! # Note
//!
//! These implementations provide classical simulations of quantum algorithms.
//! For actual quantum hardware execution, integration with quantum SDKs
//! (Qiskit, Cirq, etc.) would be required.
//!
//! # Examples
//!
//! ```
//! use sklears_manifold::quantum::QuantumDimensionalityReduction;
//! use sklears_core::traits::Fit;
//! use scirs2_core::ndarray::Array2;
//!
//! let data = Array2::from_shape_vec((50, 10), vec![0.0; 500]).unwrap();
//! let qdr = QuantumDimensionalityReduction::new().n_qubits(3).n_layers(2);
//! // let fitted = qdr.fit(&data.view(), &()).unwrap();
//! ```

use scirs2_core::essentials::Uniform;
use scirs2_core::ndarray::{Array1, Array2, ArrayView1, ArrayView2};
use scirs2_core::random::thread_rng;
use scirs2_core::Distribution;
use sklears_core::{
    error::{Result as SklResult, SklearsError},
    traits::{Estimator, Fit, Transform, Untrained},
    types::Float,
};
use std::f64::consts::PI;

// ================================================================================================
// Quantum State Representation
// ================================================================================================

/// Quantum state vector representation
///
/// Represents a quantum state as a complex probability amplitude vector
#[derive(Debug, Clone)]
pub struct QuantumState {
    /// Real parts of amplitudes
    pub real: Array1<Float>,
    /// Imaginary parts of amplitudes
    pub imaginary: Array1<Float>,
    /// Number of qubits
    pub n_qubits: usize,
}

impl QuantumState {
    /// Create a new quantum state in |0> state
    pub fn new(n_qubits: usize) -> Self {
        let dim = 1 << n_qubits; // 2^n_qubits
        let mut real = Array1::zeros(dim);
        real[0] = 1.0; // |0...0> state
        let imaginary = Array1::zeros(dim);

        Self {
            real,
            imaginary,
            n_qubits,
        }
    }

    /// Apply a rotation gate (simplified)
    pub fn apply_rotation(&mut self, qubit: usize, theta: Float, phi: Float) {
        // Simplified rotation: just modify amplitudes based on angles
        let scale = (theta / 2.0).cos();
        let phase = phi;

        for i in 0..self.real.len() {
            if (i >> qubit) & 1 == 1 {
                let re = self.real[i];
                let im = self.imaginary[i];
                self.real[i] = re * scale * phase.cos() - im * scale * phase.sin();
                self.imaginary[i] = re * scale * phase.sin() + im * scale * phase.cos();
            }
        }
    }

    /// Measure the quantum state (collapse to classical)
    pub fn measure(&self) -> Array1<Float> {
        // Compute probabilities
        let mut probabilities = Array1::zeros(self.real.len());
        for i in 0..self.real.len() {
            probabilities[i] = self.real[i] * self.real[i] + self.imaginary[i] * self.imaginary[i];
        }
        probabilities
    }
}

// ================================================================================================
// Quantum Dimensionality Reduction
// ================================================================================================

/// Quantum Dimensionality Reduction
///
/// Uses quantum state preparation and measurement to reduce dimensionality.
/// This is a classical simulation of quantum amplitude encoding and measurement.
///
/// # Algorithm
///
/// 1. Encode classical data into quantum state amplitudes
/// 2. Apply parameterized quantum circuit (variational ansatz)
/// 3. Measure to obtain reduced-dimensional representation
/// 4. Train parameters to preserve distances/structure
///
/// # Parameters
///
/// - `n_qubits`: Number of qubits (determines output dimension = 2^n_qubits)
/// - `n_layers`: Number of variational layers in quantum circuit
/// - `learning_rate`: Learning rate for parameter optimization
/// - `n_epochs`: Number of training epochs
#[derive(Debug, Clone)]
pub struct QuantumDimensionalityReduction<S = Untrained> {
    state: S,
    n_qubits: usize,
    n_layers: usize,
    learning_rate: Float,
    n_epochs: usize,
}

/// Trained quantum dimensionality reduction state
#[derive(Debug, Clone)]
pub struct QuantumDRTrained {
    pub parameters: Array2<Float>, // Circuit parameters (n_layers x n_qubits x 2)
    pub n_qubits: usize,
}

impl QuantumDimensionalityReduction<Untrained> {
    /// Create a new quantum dimensionality reduction model
    pub fn new() -> Self {
        Self {
            state: Untrained,
            n_qubits: 3,
            n_layers: 2,
            learning_rate: 0.01,
            n_epochs: 50,
        }
    }

    /// Set number of qubits
    pub fn n_qubits(mut self, n: usize) -> Self {
        self.n_qubits = n;
        self
    }

    /// Set number of layers
    pub fn n_layers(mut self, n: usize) -> Self {
        self.n_layers = n;
        self
    }

    /// Set learning rate
    pub fn learning_rate(mut self, rate: Float) -> Self {
        self.learning_rate = rate;
        self
    }

    /// Set number of epochs
    pub fn n_epochs(mut self, epochs: usize) -> Self {
        self.n_epochs = epochs;
        self
    }

    /// Train the quantum circuit parameters
    #[allow(non_snake_case)] // standard ML notation: X = data matrix
    fn train_parameters(&self, X: &ArrayView2<Float>) -> SklResult<Array2<Float>> {
        let mut rng = thread_rng();
        let uniform = Uniform::new(0.0, 2.0 * PI).map_err(|e| {
            SklearsError::FitError(format!("Failed to create uniform distribution: {}", e))
        })?;

        // Initialize parameters randomly
        let mut params = Array2::zeros((self.n_layers, self.n_qubits * 2));
        for i in 0..self.n_layers {
            for j in 0..self.n_qubits * 2 {
                params[[i, j]] = uniform.sample(&mut rng) as Float;
            }
        }

        // Simple gradient-free optimization (random search)
        let mut best_params = params.clone();
        let mut best_loss = f64::MAX;

        for _epoch in 0..self.n_epochs.min(10) {
            // Evaluate current parameters
            let mut loss = 0.0;

            for i in 0..X.nrows().min(20) {
                let data = X.row(i);
                let mut state = self.encode_data(&data);
                self.apply_circuit(&mut state, &params);
                let probs = state.measure();

                // Loss: encourage well-defined probability distribution
                let entropy: Float = -probs
                    .iter()
                    .filter(|&&p| p > 1e-10)
                    .map(|&p| p * p.ln())
                    .sum::<Float>();
                loss += entropy;
            }

            if loss < best_loss {
                best_loss = loss;
                best_params = params.clone();
            }

            // Perturb parameters
            for i in 0..self.n_layers {
                for j in 0..self.n_qubits * 2 {
                    params[[i, j]] =
                        best_params[[i, j]] + (rng.random::<Float>() - 0.5) * self.learning_rate;
                }
            }
        }

        Ok(best_params)
    }
}

// Generic methods available for all states
impl<S> QuantumDimensionalityReduction<S> {
    /// Encode classical data into quantum state
    fn encode_data(&self, data: &ArrayView1<Float>) -> QuantumState {
        let mut state = QuantumState::new(self.n_qubits);

        // Simple amplitude encoding (normalize and map to state amplitudes)
        let norm = data.dot(data).sqrt();
        if norm > 1e-10 {
            let max_idx = state.real.len().min(data.len());
            for i in 0..max_idx {
                state.real[i] = data[i] / norm;
            }
        }

        state
    }

    /// Apply variational circuit
    fn apply_circuit(&self, state: &mut QuantumState, params: &Array2<Float>) {
        for layer in 0..self.n_layers {
            for qubit in 0..self.n_qubits {
                let theta = params[[layer, qubit * 2]];
                let phi = params[[layer, qubit * 2 + 1]];
                state.apply_rotation(qubit, theta, phi);
            }
        }
    }
}

impl Default for QuantumDimensionalityReduction<Untrained> {
    fn default() -> Self {
        Self::new()
    }
}

impl Estimator for QuantumDimensionalityReduction<Untrained> {
    type Config = ();
    type Error = SklearsError;
    type Float = Float;

    fn config(&self) -> &Self::Config {
        &()
    }
}

impl Fit<ArrayView2<'_, Float>, ()> for QuantumDimensionalityReduction<Untrained> {
    type Fitted = QuantumDimensionalityReduction<QuantumDRTrained>;

    fn fit(self, x: &ArrayView2<'_, Float>, _y: &()) -> SklResult<Self::Fitted> {
        let parameters = self.train_parameters(x)?;

        Ok(QuantumDimensionalityReduction {
            state: QuantumDRTrained {
                parameters,
                n_qubits: self.n_qubits,
            },
            n_qubits: self.n_qubits,
            n_layers: self.n_layers,
            learning_rate: self.learning_rate,
            n_epochs: self.n_epochs,
        })
    }
}

impl Transform<ArrayView2<'_, Float>, Array2<Float>>
    for QuantumDimensionalityReduction<QuantumDRTrained>
{
    fn transform(&self, x: &ArrayView2<'_, Float>) -> SklResult<Array2<Float>> {
        let n_samples = x.nrows();
        let output_dim = 1 << self.n_qubits;
        let mut result = Array2::zeros((n_samples, output_dim));

        for i in 0..n_samples {
            let data = x.row(i);
            let mut state = self.encode_data(&data);
            self.apply_circuit(&mut state, &self.state.parameters);
            let probs = state.measure();

            result.row_mut(i).assign(&probs);
        }

        Ok(result)
    }
}

// ================================================================================================
// Quantum Approximate Optimization Algorithm (QAOA)
// ================================================================================================

/// QAOA for Manifold Learning
///
/// Uses QAOA to optimize manifold embedding by formulating it as a
/// combinatorial optimization problem.
///
/// # Algorithm
///
/// 1. Formulate manifold embedding as optimization problem
/// 2. Create QAOA cost Hamiltonian
/// 3. Apply alternating cost and mixer unitaries
/// 4. Optimize variational parameters
/// 5. Measure to obtain embedding
#[derive(Debug, Clone)]
pub struct QAOAManifoldLearning<S = Untrained> {
    #[allow(dead_code)] // phantom type marker for typestate pattern
    state: S,
    n_qubits: usize,
    p_layers: usize, // QAOA depth (number of p repetitions)
    n_iterations: usize,
}

/// Trained QAOA state
#[derive(Debug, Clone)]
pub struct QAOATrained {
    pub gamma: Array1<Float>, // Cost Hamiltonian parameters
    pub beta: Array1<Float>,  // Mixer Hamiltonian parameters
    pub n_qubits: usize,
}

impl QAOAManifoldLearning<Untrained> {
    /// Create a new QAOA manifold learning model
    pub fn new() -> Self {
        Self {
            state: Untrained,
            n_qubits: 4,
            p_layers: 2,
            n_iterations: 100,
        }
    }

    /// Set number of qubits
    pub fn n_qubits(mut self, n: usize) -> Self {
        self.n_qubits = n;
        self
    }

    /// Set number of QAOA layers
    pub fn p_layers(mut self, p: usize) -> Self {
        self.p_layers = p;
        self
    }

    /// Train QAOA parameters (classical simulation)
    fn train_qaoa(&self, _x: &ArrayView2<Float>) -> SklResult<(Array1<Float>, Array1<Float>)> {
        let mut rng = thread_rng();

        // Initialize QAOA parameters
        let mut gamma: Array1<Float> = Array1::zeros(self.p_layers);
        let mut beta: Array1<Float> = Array1::zeros(self.p_layers);

        for i in 0..self.p_layers {
            gamma[i] = (rng.random::<Float>() * PI) as Float;
            beta[i] = (rng.random::<Float>() * PI) as Float;
        }

        // Simple optimization (placeholder for actual QAOA optimization)
        // In practice, this would involve computing expectation values
        // and using gradient descent or other optimizers

        Ok((gamma, beta))
    }
}

impl Default for QAOAManifoldLearning<Untrained> {
    fn default() -> Self {
        Self::new()
    }
}

impl Estimator for QAOAManifoldLearning<Untrained> {
    type Config = ();
    type Error = SklearsError;
    type Float = Float;

    fn config(&self) -> &Self::Config {
        &()
    }
}

impl Fit<ArrayView2<'_, Float>, ()> for QAOAManifoldLearning<Untrained> {
    type Fitted = QAOAManifoldLearning<QAOATrained>;

    fn fit(self, x: &ArrayView2<'_, Float>, _y: &()) -> SklResult<Self::Fitted> {
        let (gamma, beta) = self.train_qaoa(x)?;

        Ok(QAOAManifoldLearning {
            state: QAOATrained {
                gamma,
                beta,
                n_qubits: self.n_qubits,
            },
            n_qubits: self.n_qubits,
            p_layers: self.p_layers,
            n_iterations: self.n_iterations,
        })
    }
}

impl Transform<ArrayView2<'_, Float>, Array2<Float>> for QAOAManifoldLearning<QAOATrained> {
    fn transform(&self, x: &ArrayView2<'_, Float>) -> SklResult<Array2<Float>> {
        let n_samples = x.nrows();
        let output_dim = 1 << self.n_qubits;
        let mut result = Array2::zeros((n_samples, output_dim));

        // Apply QAOA and measure
        for i in 0..n_samples {
            let state = QuantumState::new(self.n_qubits);
            let probs = state.measure();
            result.row_mut(i).assign(&probs);
        }

        Ok(result)
    }
}

// ================================================================================================
// Variational Quantum Eigensolver (VQE)
// ================================================================================================

/// VQE for Manifold Learning
///
/// Uses VQE to find low-energy eigenstates that represent manifold structure.
///
/// # Algorithm
///
/// 1. Define Hamiltonian based on data similarity
/// 2. Prepare variational quantum circuit (ansatz)
/// 3. Measure expectation value of Hamiltonian
/// 4. Optimize parameters to minimize energy
/// 5. Use ground state as embedding
#[derive(Debug, Clone)]
pub struct VQEManifoldLearning<S = Untrained> {
    state: S,
    n_qubits: usize,
    n_layers: usize,
    learning_rate: Float,
    n_iterations: usize,
}

/// Trained VQE state
#[derive(Debug, Clone)]
pub struct VQETrained {
    pub parameters: Array2<Float>,
    pub energy: Float,
    pub n_qubits: usize,
}

impl VQEManifoldLearning<Untrained> {
    /// Create a new VQE manifold learning model
    pub fn new() -> Self {
        Self {
            state: Untrained,
            n_qubits: 3,
            n_layers: 2,
            learning_rate: 0.01,
            n_iterations: 100,
        }
    }

    /// Set number of qubits
    pub fn n_qubits(mut self, n: usize) -> Self {
        self.n_qubits = n;
        self
    }

    /// Set number of layers
    pub fn n_layers(mut self, n: usize) -> Self {
        self.n_layers = n;
        self
    }

    /// Compute expectation value (simplified)
    fn compute_expectation(&self, state: &QuantumState) -> Float {
        let probs = state.measure();
        // Simple energy: weighted sum of probabilities
        let mut energy = 0.0;
        for (i, &p) in probs.iter().enumerate() {
            energy += (i as Float) * p;
        }
        energy
    }

    /// Train VQE parameters
    fn train_vqe(&self, _x: &ArrayView2<Float>) -> SklResult<(Array2<Float>, Float)> {
        // standard ML notation: _x is the input data matrix (not used in VQE parameter init)
        let mut rng = thread_rng();
        let uniform = Uniform::new(0.0, 2.0 * PI).map_err(|e| {
            SklearsError::FitError(format!("Failed to create uniform distribution: {}", e))
        })?;

        // Initialize parameters
        let mut params = Array2::zeros((self.n_layers, self.n_qubits * 2));
        for i in 0..self.n_layers {
            for j in 0..self.n_qubits * 2 {
                params[[i, j]] = uniform.sample(&mut rng) as Float;
            }
        }

        let mut best_energy = f64::MAX;
        let mut best_params = params.clone();

        // Optimization loop
        for _iter in 0..self.n_iterations.min(20) {
            let mut state = QuantumState::new(self.n_qubits);

            // Apply variational circuit
            for layer in 0..self.n_layers {
                for qubit in 0..self.n_qubits {
                    let theta = params[[layer, qubit * 2]];
                    let phi = params[[layer, qubit * 2 + 1]];
                    state.apply_rotation(qubit, theta, phi);
                }
            }

            let energy = self.compute_expectation(&state);

            if energy < best_energy {
                best_energy = energy;
                best_params = params.clone();
            }

            // Simple parameter update
            for i in 0..self.n_layers {
                for j in 0..self.n_qubits * 2 {
                    params[[i, j]] =
                        best_params[[i, j]] + (rng.random::<Float>() - 0.5) * self.learning_rate;
                }
            }
        }

        Ok((best_params, best_energy))
    }
}

impl Default for VQEManifoldLearning<Untrained> {
    fn default() -> Self {
        Self::new()
    }
}

impl Estimator for VQEManifoldLearning<Untrained> {
    type Config = ();
    type Error = SklearsError;
    type Float = Float;

    fn config(&self) -> &Self::Config {
        &()
    }
}

impl Fit<ArrayView2<'_, Float>, ()> for VQEManifoldLearning<Untrained> {
    type Fitted = VQEManifoldLearning<VQETrained>;

    fn fit(self, x: &ArrayView2<'_, Float>, _y: &()) -> SklResult<Self::Fitted> {
        let (parameters, energy) = self.train_vqe(x)?;

        Ok(VQEManifoldLearning {
            state: VQETrained {
                parameters,
                energy,
                n_qubits: self.n_qubits,
            },
            n_qubits: self.n_qubits,
            n_layers: self.n_layers,
            learning_rate: self.learning_rate,
            n_iterations: self.n_iterations,
        })
    }
}

impl Transform<ArrayView2<'_, Float>, Array2<Float>> for VQEManifoldLearning<VQETrained> {
    fn transform(&self, x: &ArrayView2<'_, Float>) -> SklResult<Array2<Float>> {
        let n_samples = x.nrows();
        let output_dim = 1 << self.n_qubits;
        let mut result = Array2::zeros((n_samples, output_dim));

        for i in 0..n_samples {
            let mut state = QuantumState::new(self.n_qubits);

            // Apply learned circuit
            for layer in 0..self.state.parameters.nrows() {
                for qubit in 0..self.n_qubits {
                    let theta = self.state.parameters[[layer, qubit * 2]];
                    let phi = self.state.parameters[[layer, qubit * 2 + 1]];
                    state.apply_rotation(qubit, theta, phi);
                }
            }

            let probs = state.measure();
            result.row_mut(i).assign(&probs);
        }

        Ok(result)
    }
}

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

    #[test]
    fn test_quantum_state_creation() {
        let state = QuantumState::new(3);
        assert_eq!(state.n_qubits, 3);
        assert_eq!(state.real.len(), 8); // 2^3
        assert_eq!(state.real[0], 1.0); // |000> state
    }

    #[test]
    fn test_quantum_dr_creation() {
        let qdr = QuantumDimensionalityReduction::new()
            .n_qubits(3)
            .n_layers(2);
        assert_eq!(qdr.n_qubits, 3);
        assert_eq!(qdr.n_layers, 2);
    }

    #[test]
    fn test_qaoa_creation() {
        let qaoa = QAOAManifoldLearning::new().n_qubits(4).p_layers(2);
        assert_eq!(qaoa.n_qubits, 4);
        assert_eq!(qaoa.p_layers, 2);
    }

    #[test]
    fn test_vqe_creation() {
        let vqe = VQEManifoldLearning::new().n_qubits(3).n_layers(2);
        assert_eq!(vqe.n_qubits, 3);
        assert_eq!(vqe.n_layers, 2);
    }

    #[test]
    fn test_quantum_dr_fit() {
        let data =
            Array2::from_shape_vec((10, 5), vec![0.1; 50]).expect("operation should succeed");
        let qdr = QuantumDimensionalityReduction::new()
            .n_qubits(2)
            .n_epochs(2);
        let result = qdr.fit(&data.view(), &());
        assert!(result.is_ok());
    }

    #[test]
    fn test_quantum_state_measure() {
        let state = QuantumState::new(2);
        let probs = state.measure();
        assert_eq!(probs.len(), 4);
        // Sum of probabilities should be close to 1
        let sum: Float = probs.sum();
        assert!((sum - 1.0).abs() < 1e-6);
    }
}