quantrs2_device/process_tomography/reconstruction/

machine_learning.rs

//! Machine learning based reconstruction method

use scirs2_core::ndarray::{Array1, Array2, Array4};
use scirs2_core::Complex64;

use super::super::core::SciRS2ProcessTomographer;
use super::super::results::{ExperimentalData, ReconstructionQuality};
use super::utils::calculate_reconstruction_quality;
use crate::DeviceResult;

/// Machine learning reconstruction implementation
pub fn reconstruct_machine_learning(
    tomographer: &SciRS2ProcessTomographer,
    experimental_data: &ExperimentalData,
) -> DeviceResult<(Array4<Complex64>, ReconstructionQuality)> {
    let num_qubits = (experimental_data.input_states[0].dim().0 as f64).log2() as usize;
    let dim = 1 << num_qubits;

    // Extract features from experimental data
    let features = extract_features(experimental_data)?;

    // Apply ML model (simplified neural network simulation)
    let ml_output = apply_ml_model(&features)?;

    // Convert ML output to process matrix
    let process_matrix = ml_output_to_process_matrix(&ml_output, dim)?;

    let log_likelihood = calculate_ml_log_likelihood(&process_matrix, experimental_data)?;
    let reconstruction_quality =
        calculate_reconstruction_quality(&process_matrix, experimental_data, log_likelihood);

    Ok((process_matrix, reconstruction_quality))
}

/// Extract features from experimental data for ML
fn extract_features(experimental_data: &ExperimentalData) -> DeviceResult<Array1<f64>> {
    let num_measurements = experimental_data.measurement_results.len();
    let num_states = experimental_data.input_states.len();
    let num_operators = experimental_data.measurement_operators.len();

    let mut features = Vec::new();

    // Statistical features
    let mean_result =
        experimental_data.measurement_results.iter().sum::<f64>() / num_measurements as f64;
    let var_result = experimental_data
        .measurement_results
        .iter()
        .map(|&x| (x - mean_result).powi(2))
        .sum::<f64>()
        / num_measurements as f64;

    features.push(mean_result);
    features.push(var_result.sqrt());
    features.push(num_measurements as f64);
    features.push(num_states as f64);
    features.push(num_operators as f64);

    // Add measurement results as features (truncated/padded to fixed size)
    let max_features = 100;
    for i in 0..max_features {
        if i < experimental_data.measurement_results.len() {
            features.push(experimental_data.measurement_results[i]);
        } else {
            features.push(0.0);
        }
    }

    Ok(Array1::from_vec(features))
}

/// Apply ML model to features (simplified neural network simulation)
fn apply_ml_model(features: &Array1<f64>) -> DeviceResult<Array1<f64>> {
    let input_size = features.len();
    let hidden_size = 64;
    let output_size = 16; // Simplified output for 2x2x2x2 process matrix

    // Simplified neural network forward pass
    let mut hidden_layer = Array1::zeros(hidden_size);

    // Hidden layer computation (simplified)
    for i in 0..hidden_size {
        let mut sum = 0.0;
        for j in 0..input_size {
            // Simplified weights (in practice, these would be learned)
            let weight = 0.1 * ((i + j) as f64).sin();
            sum += features[j] * weight;
        }
        hidden_layer[i] = tanh_activation(sum);
    }

    // Output layer computation
    let mut output = Array1::zeros(output_size);
    for i in 0..output_size {
        let mut sum = 0.0;
        for j in 0..hidden_size {
            let weight = 0.1 * ((i * hidden_size + j) as f64).cos();
            sum += hidden_layer[j] * weight;
        }
        output[i] = sigmoid_activation(sum);
    }

    Ok(output)
}

/// Convert ML output to process matrix
fn ml_output_to_process_matrix(
    ml_output: &Array1<f64>,
    dim: usize,
) -> DeviceResult<Array4<Complex64>> {
    let mut process_matrix = Array4::zeros((dim, dim, dim, dim));

    // Map ML output to process matrix elements
    let mut idx = 0;
    for i in 0..dim {
        for j in 0..dim {
            for k in 0..dim {
                for l in 0..dim {
                    if idx < ml_output.len() {
                        // Convert real output to complex with appropriate scaling
                        let real_part = ml_output[idx].mul_add(2.0, -1.0); // Scale from [0,1] to [-1,1]
                        let imag_part = if idx + 1 < ml_output.len() {
                            ml_output[idx + 1].mul_add(2.0, -1.0)
                        } else {
                            0.0
                        };
                        process_matrix[[i, j, k, l]] = Complex64::new(real_part, imag_part);
                        idx += 1;
                    } else {
                        // Default to identity-like behavior for missing elements
                        if i == j && k == l && i == k {
                            process_matrix[[i, j, k, l]] = Complex64::new(1.0, 0.0);
                        }
                    }
                }
            }
        }
    }

    // Normalize to ensure trace preservation
    let mut trace = Complex64::new(0.0, 0.0);
    for i in 0..dim {
        for j in 0..dim {
            trace += process_matrix[[i, j, i, j]];
        }
    }

    if trace.norm() > 1e-12 {
        let scale_factor = Complex64::new(1.0, 0.0) / trace;
        for i in 0..dim {
            for j in 0..dim {
                for k in 0..dim {
                    for l in 0..dim {
                        process_matrix[[i, j, k, l]] *= scale_factor;
                    }
                }
            }
        }
    }

    Ok(process_matrix)
}

/// Calculate ML-specific log-likelihood
fn calculate_ml_log_likelihood(
    process_matrix: &Array4<Complex64>,
    experimental_data: &ExperimentalData,
) -> DeviceResult<f64> {
    let mut log_likelihood = 0.0;

    for (observed, &uncertainty) in experimental_data
        .measurement_results
        .iter()
        .zip(experimental_data.measurement_uncertainties.iter())
    {
        let predicted = 0.5; // Placeholder prediction from ML model
        let diff = observed - predicted;
        let variance = uncertainty * uncertainty;
        log_likelihood -= 0.5 * (diff * diff / variance);
    }

    Ok(log_likelihood)
}

/// Activation functions
fn tanh_activation(x: f64) -> f64 {
    x.tanh()
}

fn sigmoid_activation(x: f64) -> f64 {
    1.0 / (1.0 + (-x).exp())
}

const fn relu_activation(x: f64) -> f64 {
    x.max(0.0)
}