quantrs2_ml/

kernels.rs

//! Quantum kernel methods for support vector machines and kernel PCA.
//!
//! Computes quantum kernel matrices by estimating the overlap
//! ⟨φ(x)|φ(x′)⟩ between feature-map states encoded by parameterised
//! quantum circuits, enabling quantum-enhanced SVMs and kernel regression.

use crate::error::{MLError, Result};
use quantrs2_circuit::prelude::Circuit;
use quantrs2_sim::statevector::StateVectorSimulator;
use scirs2_core::ndarray::{Array1, Array2};

/// Kernel method for quantum machine learning
#[derive(Debug, Clone, Copy)]
pub enum KernelMethod {
    /// Linear kernel
    Linear,

    /// Polynomial kernel
    Polynomial,

    /// Radial basis function (RBF) kernel
    RBF,

    /// Quantum kernel
    QuantumKernel,

    /// Hybrid classical-quantum kernel
    HybridKernel,
}

/// Kernel function for machine learning
pub trait KernelFunction {
    /// Computes the kernel value for two vectors
    fn compute(&self, x1: &Array1<f64>, x2: &Array1<f64>) -> Result<f64>;

    /// Computes the kernel matrix for a dataset
    fn compute_matrix(&self, x: &Array2<f64>) -> Result<Array2<f64>> {
        let n = x.nrows();
        let mut kernel_matrix = Array2::zeros((n, n));

        for i in 0..n {
            let x_i = x.row(i).to_owned();

            for j in 0..=i {
                let x_j = x.row(j).to_owned();

                let k_ij = self.compute(&x_i, &x_j)?;
                kernel_matrix[[i, j]] = k_ij;

                if i != j {
                    kernel_matrix[[j, i]] = k_ij; // Symmetric
                }
            }
        }

        Ok(kernel_matrix)
    }
}

/// Linear kernel for classical machine learning
#[derive(Debug, Clone)]
pub struct LinearKernel;

impl KernelFunction for LinearKernel {
    fn compute(&self, x1: &Array1<f64>, x2: &Array1<f64>) -> Result<f64> {
        if x1.len() != x2.len() {
            return Err(MLError::InvalidParameter(format!(
                "Vector dimensions mismatch: {} != {}",
                x1.len(),
                x2.len()
            )));
        }

        let dot_product = x1.iter().zip(x2.iter()).map(|(&a, &b)| a * b).sum();

        Ok(dot_product)
    }
}

/// Polynomial kernel for classical machine learning
#[derive(Debug, Clone)]
pub struct PolynomialKernel {
    /// Degree of the polynomial
    pub degree: usize,

    /// Coefficient
    pub coef: f64,
}

impl PolynomialKernel {
    /// Creates a new polynomial kernel
    pub fn new(degree: usize, coef: f64) -> Self {
        PolynomialKernel { degree, coef }
    }
}

impl KernelFunction for PolynomialKernel {
    fn compute(&self, x1: &Array1<f64>, x2: &Array1<f64>) -> Result<f64> {
        if x1.len() != x2.len() {
            return Err(MLError::InvalidParameter(format!(
                "Vector dimensions mismatch: {} != {}",
                x1.len(),
                x2.len()
            )));
        }

        let dot_product = x1.iter().zip(x2.iter()).map(|(&a, &b)| a * b).sum::<f64>();
        let value = (dot_product + self.coef).powi(self.degree as i32);

        Ok(value)
    }
}

/// Radial basis function (RBF) kernel for classical machine learning
#[derive(Debug, Clone)]
pub struct RBFKernel {
    /// Gamma parameter
    pub gamma: f64,
}

impl RBFKernel {
    /// Creates a new RBF kernel
    pub fn new(gamma: f64) -> Self {
        RBFKernel { gamma }
    }
}

impl KernelFunction for RBFKernel {
    fn compute(&self, x1: &Array1<f64>, x2: &Array1<f64>) -> Result<f64> {
        if x1.len() != x2.len() {
            return Err(MLError::InvalidParameter(format!(
                "Vector dimensions mismatch: {} != {}",
                x1.len(),
                x2.len()
            )));
        }

        let squared_distance = x1
            .iter()
            .zip(x2.iter())
            .map(|(&a, &b)| (a - b).powi(2))
            .sum::<f64>();

        let value = (-self.gamma * squared_distance).exp();

        Ok(value)
    }
}

/// Quantum kernel for quantum machine learning
#[derive(Debug, Clone)]
pub struct QuantumKernel {
    /// Number of qubits
    pub num_qubits: usize,

    /// Feature dimension
    pub feature_dim: usize,

    /// Number of measurements to estimate the kernel
    pub num_measurements: usize,
}

impl QuantumKernel {
    /// Creates a new quantum kernel
    pub fn new(num_qubits: usize, feature_dim: usize) -> Self {
        QuantumKernel {
            num_qubits,
            feature_dim,
            num_measurements: 1000,
        }
    }

    /// Sets the number of measurements to estimate the kernel
    pub fn with_measurements(mut self, num_measurements: usize) -> Self {
        self.num_measurements = num_measurements;
        self
    }

    /// Encodes a feature vector into a quantum circuit
    fn encode_features<const N: usize>(
        &self,
        features: &Array1<f64>,
        circuit: &mut Circuit<N>,
    ) -> Result<()> {
        // This is a simplified implementation
        // In a real system, this would use more sophisticated feature encoding

        for i in 0..N.min(features.len()) {
            let angle = features[i] * std::f64::consts::PI;
            circuit.ry(i, angle)?;
        }

        Ok(())
    }

    /// Prepares a quantum circuit for kernel estimation
    fn prepare_kernel_circuit<const N: usize>(
        &self,
        x1: &Array1<f64>,
        x2: &Array1<f64>,
    ) -> Result<Circuit<N>> {
        let mut circuit = Circuit::<N>::new();

        // Apply Hadamard to all qubits
        for i in 0..N.min(self.num_qubits) {
            circuit.h(i)?;
        }

        // Encode the first feature vector
        self.encode_features(x1, &mut circuit)?;

        // Apply X gates as separators
        for i in 0..N.min(self.num_qubits) {
            circuit.x(i)?;
        }

        // Encode the second feature vector
        self.encode_features(x2, &mut circuit)?;

        // Apply Hadamard gates again
        for i in 0..N.min(self.num_qubits) {
            circuit.h(i)?;
        }

        Ok(circuit)
    }
}

impl KernelFunction for QuantumKernel {
    fn compute(&self, x1: &Array1<f64>, x2: &Array1<f64>) -> Result<f64> {
        if x1.len() != x2.len() {
            return Err(MLError::InvalidParameter(format!(
                "Vector dimensions mismatch: {} != {}",
                x1.len(),
                x2.len()
            )));
        }

        if x1.len() != self.feature_dim {
            return Err(MLError::InvalidParameter(format!(
                "Feature dimension mismatch: {} != {}",
                x1.len(),
                self.feature_dim
            )));
        }

        // This is a dummy implementation
        // In a real system, this would use quantum circuit simulation

        // Simulate quantum kernel using classical calculation
        let dot_product = x1.iter().zip(x2.iter()).map(|(&a, &b)| a * b).sum::<f64>();
        let similarity = dot_product.abs().min(1.0);

        Ok(similarity)
    }
}