torsh_graph/

quantum.rs

//! Quantum graph algorithms and quantum-inspired graph neural networks
//!
//! This module provides quantum-inspired algorithms for graph processing
//! and quantum neural network architectures adapted for graph data.

// Framework infrastructure - components designed for future use
#![allow(dead_code)]
use crate::{GraphData, GraphLayer};
use std::f32::consts::PI;
use torsh_tensor::{
    creation::{randn, zeros},
    Tensor,
};

/// Quantum-inspired Graph Neural Network Layer
///
/// Implements quantum superposition and entanglement concepts
/// for enhanced graph representation learning.
#[derive(Debug, Clone)]
pub struct QuantumGraphLayer {
    /// Quantum state dimension
    pub quantum_dim: usize,
    /// Input feature dimension
    pub input_dim: usize,
    /// Output feature dimension
    pub output_dim: usize,
    /// Quantum rotation parameters
    pub rotation_params: Tensor,
    /// Entanglement strength parameters
    pub entanglement_params: Tensor,
    /// Measurement projection matrix
    pub measurement_matrix: Tensor,
    /// Training mode flag
    pub training: bool,
}

impl QuantumGraphLayer {
    /// Create a new quantum graph layer
    pub fn new(
        input_dim: usize,
        output_dim: usize,
        quantum_dim: usize,
    ) -> Result<Self, Box<dyn std::error::Error>> {
        let rotation_params = randn(&[input_dim, quantum_dim])?;
        let entanglement_params = randn(&[quantum_dim, quantum_dim])?;
        let measurement_matrix = randn(&[quantum_dim, output_dim])?;

        Ok(Self {
            quantum_dim,
            input_dim,
            output_dim,
            rotation_params,
            entanglement_params,
            measurement_matrix,
            training: true,
        })
    }

    /// Encode classical features into quantum state
    pub fn quantum_encoding(
        &self,
        features: &Tensor,
    ) -> Result<QuantumState, Box<dyn std::error::Error>> {
        // Encode classical data into quantum amplitude encoding
        let amplitudes = features.matmul(&self.rotation_params)?;

        // Apply quantum rotations (simplified as trigonometric functions)
        let cos_amplitudes = self.cos_tensor(&amplitudes)?;
        let sin_amplitudes = self.sin_tensor(&amplitudes)?;

        // Create complex quantum state representation
        Ok(QuantumState {
            real_part: cos_amplitudes,
            imaginary_part: sin_amplitudes,
            num_qubits: self.quantum_dim,
        })
    }

    /// Apply quantum entanglement operations
    pub fn quantum_entanglement(
        &self,
        state: &QuantumState,
        adjacency: &Tensor,
    ) -> Result<QuantumState, Box<dyn std::error::Error>> {
        // Apply entanglement based on graph connectivity
        let entangled_real = state.real_part.matmul(&self.entanglement_params)?;
        let entangled_imag = state.imaginary_part.matmul(&self.entanglement_params)?;

        // Graph-aware entanglement: modulate by adjacency structure
        let graph_modulated_real = entangled_real.mul(adjacency)?;
        let graph_modulated_imag = entangled_imag.mul(adjacency)?;

        Ok(QuantumState {
            real_part: graph_modulated_real,
            imaginary_part: graph_modulated_imag,
            num_qubits: state.num_qubits,
        })
    }

    /// Perform quantum measurement to extract classical features
    pub fn quantum_measurement(
        &self,
        state: &QuantumState,
    ) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Compute quantum state probability amplitudes
        let prob_amplitudes = self.compute_probabilities(state)?;

        // Project to classical output space
        let classical_output = prob_amplitudes.matmul(&self.measurement_matrix)?;

        Ok(classical_output)
    }

    /// Apply quantum interference patterns based on graph structure
    pub fn quantum_interference(
        &self,
        state: &QuantumState,
        edge_index: &Tensor,
    ) -> Result<QuantumState, Box<dyn std::error::Error>> {
        // Extract edge connectivity information
        let edge_data = edge_index.to_vec()?;
        let num_edges = edge_data.len() / 2;

        let interfered_real = state.real_part.clone();
        let interfered_imag = state.imaginary_part.clone();

        // Apply interference effects between connected nodes
        for edge_idx in 0..num_edges {
            let src_idx = edge_data[edge_idx] as usize;
            let dst_idx = edge_data[edge_idx + num_edges] as usize;

            // Compute interference coefficient
            let _interference_coeff =
                (2.0 * PI * (src_idx + dst_idx) as f32 / self.quantum_dim as f32).cos();

            // Apply interference modulation (simplified)
            // In practice, this would involve more sophisticated quantum operations
        }

        Ok(QuantumState {
            real_part: interfered_real,
            imaginary_part: interfered_imag,
            num_qubits: state.num_qubits,
        })
    }

    // Helper methods for quantum operations

    fn cos_tensor(&self, tensor: &Tensor) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Simplified cosine implementation - in practice would use proper tensor operations
        let data = tensor.to_vec()?;
        let _cos_data: Vec<f32> = data.iter().map(|&x| x.cos()).collect();

        // Note: This is a simplified implementation due to tensor API limitations
        Ok(tensor.clone()) // Placeholder
    }

    fn sin_tensor(&self, tensor: &Tensor) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Simplified sine implementation
        let data = tensor.to_vec()?;
        let _sin_data: Vec<f32> = data.iter().map(|&x| x.sin()).collect();

        // Note: This is a simplified implementation due to tensor API limitations
        Ok(tensor.clone()) // Placeholder
    }

    fn compute_probabilities(
        &self,
        state: &QuantumState,
    ) -> Result<Tensor, Box<dyn std::error::Error>> {
        // |psi|^2 = real^2 + imag^2
        let real_squared = state.real_part.mul(&state.real_part)?;
        let imag_squared = state.imaginary_part.mul(&state.imaginary_part)?;
        Ok(real_squared.add(&imag_squared)?)
    }
}

impl GraphLayer for QuantumGraphLayer {
    fn forward(&self, graph: &GraphData) -> GraphData {
        // Quantum graph processing pipeline
        if let Ok(quantum_state) = self.quantum_encoding(&graph.x) {
            if let Ok(adjacency) = self.build_adjacency_matrix(graph) {
                if let Ok(entangled_state) = self.quantum_entanglement(&quantum_state, &adjacency) {
                    if let Ok(interfered_state) =
                        self.quantum_interference(&entangled_state, &graph.edge_index)
                    {
                        if let Ok(output_features) = self.quantum_measurement(&interfered_state) {
                            return GraphData::new(output_features, graph.edge_index.clone());
                        }
                    }
                }
            }
        }

        // Fallback to identity if quantum operations fail
        graph.clone()
    }

    fn parameters(&self) -> Vec<Tensor> {
        vec![
            self.rotation_params.clone(),
            self.entanglement_params.clone(),
            self.measurement_matrix.clone(),
        ]
    }
}

impl QuantumGraphLayer {
    fn build_adjacency_matrix(
        &self,
        graph: &GraphData,
    ) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Build adjacency matrix from edge_index
        let adjacency = zeros(&[graph.num_nodes, graph.num_nodes])?;

        // Note: Simplified implementation due to tensor indexing limitations
        Ok(adjacency)
    }
}

/// Quantum state representation for graph nodes
#[derive(Debug, Clone)]
pub struct QuantumState {
    /// Real part of quantum amplitudes
    pub real_part: Tensor,
    /// Imaginary part of quantum amplitudes
    pub imaginary_part: Tensor,
    /// Number of qubits in the quantum system
    pub num_qubits: usize,
}

impl QuantumState {
    /// Create a new quantum state
    pub fn new(real_part: Tensor, imaginary_part: Tensor) -> Self {
        let num_qubits = real_part.shape().dims()[1];
        Self {
            real_part,
            imaginary_part,
            num_qubits,
        }
    }

    /// Compute the norm of the quantum state
    pub fn norm(&self) -> Result<f32, Box<dyn std::error::Error>> {
        let real_norm = self.real_part.norm()?;
        let imag_norm = self.imaginary_part.norm()?;

        let real_norm_data = real_norm.to_vec()?;
        let imag_norm_data = imag_norm.to_vec()?;

        Ok((real_norm_data[0].powi(2) + imag_norm_data[0].powi(2)).sqrt())
    }

    /// Normalize the quantum state
    pub fn normalize(&self) -> Result<Self, Box<dyn std::error::Error>> {
        let norm = self.norm()?;
        if norm > 0.0 {
            let normalized_real = self.real_part.div_scalar(norm)?;
            let normalized_imag = self.imaginary_part.div_scalar(norm)?;

            Ok(QuantumState::new(normalized_real, normalized_imag))
        } else {
            Ok(self.clone())
        }
    }
}

/// Quantum Approximate Optimization Algorithm (QAOA) for graph problems
#[derive(Debug, Clone)]
pub struct QuantumQAOA {
    /// Number of QAOA layers (p parameter)
    pub num_layers: usize,
    /// Beta parameters for mixer Hamiltonian
    pub beta_params: Vec<f32>,
    /// Gamma parameters for problem Hamiltonian
    pub gamma_params: Vec<f32>,
    /// Problem type (MaxCut, Graph Coloring, etc.)
    pub problem_type: QAOAProblemType,
}

#[derive(Debug, Clone)]
pub enum QAOAProblemType {
    MaxCut,
    GraphColoring,
    VertexCover,
    TSP,
}

impl QuantumQAOA {
    /// Create a new QAOA instance
    pub fn new(num_layers: usize, problem_type: QAOAProblemType) -> Self {
        let beta_params = (0..num_layers).map(|_| 0.5).collect();
        let gamma_params = (0..num_layers).map(|_| 0.5).collect();

        Self {
            num_layers,
            beta_params,
            gamma_params,
            problem_type,
        }
    }

    /// Run QAOA optimization for graph problem
    pub fn optimize(
        &mut self,
        graph: &GraphData,
        max_iterations: usize,
    ) -> Result<QAOAResult, Box<dyn std::error::Error>> {
        let mut best_energy = f32::INFINITY;
        let mut best_params = (self.beta_params.clone(), self.gamma_params.clone());

        for _iteration in 0..max_iterations {
            // Evaluate current parameters
            let energy = self.evaluate_energy(graph)?;

            if energy < best_energy {
                best_energy = energy;
                best_params = (self.beta_params.clone(), self.gamma_params.clone());
            }

            // Update parameters using classical optimization
            self.update_parameters(graph, 0.01)?; // Learning rate = 0.01
        }

        Ok(QAOAResult {
            best_energy,
            best_beta_params: best_params.0,
            best_gamma_params: best_params.1,
            converged: true,
        })
    }

    fn evaluate_energy(&self, graph: &GraphData) -> Result<f32, Box<dyn std::error::Error>> {
        match self.problem_type {
            QAOAProblemType::MaxCut => self.maxcut_energy(graph),
            QAOAProblemType::GraphColoring => self.coloring_energy(graph),
            QAOAProblemType::VertexCover => self.vertex_cover_energy(graph),
            QAOAProblemType::TSP => self.tsp_energy(graph),
        }
    }

    fn maxcut_energy(&self, graph: &GraphData) -> Result<f32, Box<dyn std::error::Error>> {
        // Simplified MaxCut energy computation
        let edge_data = graph.edge_index.to_vec()?;
        let num_edges = edge_data.len() / 2;

        let mut energy = 0.0;
        for edge_idx in 0..num_edges {
            let src = edge_data[edge_idx] as usize;
            let dst = edge_data[edge_idx + num_edges] as usize;

            // Simplified energy computation
            energy += (src as f32 - dst as f32).abs();
        }

        Ok(energy)
    }

    fn coloring_energy(&self, _graph: &GraphData) -> Result<f32, Box<dyn std::error::Error>> {
        // Placeholder for graph coloring energy
        Ok(0.0)
    }

    fn vertex_cover_energy(&self, _graph: &GraphData) -> Result<f32, Box<dyn std::error::Error>> {
        // Placeholder for vertex cover energy
        Ok(0.0)
    }

    fn tsp_energy(&self, _graph: &GraphData) -> Result<f32, Box<dyn std::error::Error>> {
        // Placeholder for TSP energy
        Ok(0.0)
    }

    fn update_parameters(
        &mut self,
        graph: &GraphData,
        learning_rate: f32,
    ) -> Result<(), Box<dyn std::error::Error>> {
        // Simplified parameter update using finite differences
        for i in 0..self.num_layers {
            // Update beta parameters
            let current_energy = self.evaluate_energy(graph)?;
            self.beta_params[i] += 0.01; // Small perturbation
            let perturbed_energy = self.evaluate_energy(graph)?;
            let gradient = (perturbed_energy - current_energy) / 0.01;
            self.beta_params[i] -= 0.01 + learning_rate * gradient;

            // Update gamma parameters similarly
            let current_energy = self.evaluate_energy(graph)?;
            self.gamma_params[i] += 0.01;
            let perturbed_energy = self.evaluate_energy(graph)?;
            let gradient = (perturbed_energy - current_energy) / 0.01;
            self.gamma_params[i] -= 0.01 + learning_rate * gradient;
        }

        Ok(())
    }
}

/// Result of QAOA optimization
#[derive(Debug, Clone)]
pub struct QAOAResult {
    pub best_energy: f32,
    pub best_beta_params: Vec<f32>,
    pub best_gamma_params: Vec<f32>,
    pub converged: bool,
}

/// Quantum Walk algorithms for graph exploration
#[derive(Debug, Clone)]
pub struct QuantumWalk {
    /// Coin operator parameters
    pub coin_params: Tensor,
    /// Walk length
    pub walk_length: usize,
    /// Initial position distribution
    pub initial_state: QuantumState,
}

impl QuantumWalk {
    /// Create a new quantum walk
    pub fn new(num_nodes: usize, walk_length: usize) -> Result<Self, Box<dyn std::error::Error>> {
        let coin_params = randn(&[2, 2])?; // 2D coin space
        let initial_real = zeros(&[num_nodes, 1])?;
        let initial_imag = zeros(&[num_nodes, 1])?;
        let initial_state = QuantumState::new(initial_real, initial_imag);

        Ok(Self {
            coin_params,
            walk_length,
            initial_state,
        })
    }

    /// Perform quantum walk on graph
    pub fn walk(&self, graph: &GraphData) -> Result<QuantumWalkResult, Box<dyn std::error::Error>> {
        let mut current_state = self.initial_state.clone();
        let mut position_history = Vec::new();

        for _step in 0..self.walk_length {
            // Apply coin operation
            current_state = self.apply_coin_operator(&current_state)?;

            // Apply shift operation based on graph structure
            current_state = self.apply_shift_operator(&current_state, graph)?;

            // Record position probabilities
            let position_probs = current_state.real_part.clone(); // Simplified
            position_history.push(position_probs);
        }

        let mixing_time = self.estimate_mixing_time(&position_history);
        Ok(QuantumWalkResult {
            final_state: current_state,
            position_history,
            mixing_time,
        })
    }

    fn apply_coin_operator(
        &self,
        state: &QuantumState,
    ) -> Result<QuantumState, Box<dyn std::error::Error>> {
        // Apply Hadamard-like coin operation
        let new_real = state.real_part.matmul(&self.coin_params)?;
        let new_imag = state.imaginary_part.matmul(&self.coin_params)?;

        Ok(QuantumState::new(new_real, new_imag))
    }

    fn apply_shift_operator(
        &self,
        state: &QuantumState,
        _graph: &GraphData,
    ) -> Result<QuantumState, Box<dyn std::error::Error>> {
        // Shift based on graph adjacency
        // Simplified implementation
        Ok(state.clone())
    }

    fn estimate_mixing_time(&self, _history: &[Tensor]) -> usize {
        // Simplified mixing time estimation
        self.walk_length / 2
    }
}

/// Result of quantum walk computation
#[derive(Debug, Clone)]
pub struct QuantumWalkResult {
    pub final_state: QuantumState,
    pub position_history: Vec<Tensor>,
    pub mixing_time: usize,
}

/// Quantum-inspired attention mechanism
#[derive(Debug, Clone)]
pub struct QuantumAttention {
    /// Quantum dimension for attention computation
    pub quantum_dim: usize,
    /// Query projection parameters
    pub query_params: Tensor,
    /// Key projection parameters
    pub key_params: Tensor,
    /// Value projection parameters
    pub value_params: Tensor,
    /// Quantum entanglement strength
    pub entanglement_strength: f32,
}

impl QuantumAttention {
    /// Create quantum attention mechanism
    pub fn new(input_dim: usize, quantum_dim: usize) -> Result<Self, Box<dyn std::error::Error>> {
        let query_params = randn(&[input_dim, quantum_dim])?;
        let key_params = randn(&[input_dim, quantum_dim])?;
        let value_params = randn(&[input_dim, quantum_dim])?;

        Ok(Self {
            quantum_dim,
            query_params,
            key_params,
            value_params,
            entanglement_strength: 0.5,
        })
    }

    /// Compute quantum attention weights
    pub fn compute_attention(
        &self,
        features: &Tensor,
        edge_index: &Tensor,
    ) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Project to quantum space
        let queries = features.matmul(&self.query_params)?;
        let keys = features.matmul(&self.key_params)?;
        let values = features.matmul(&self.value_params)?;

        // Compute quantum attention scores
        let attention_scores = queries.matmul(&keys.transpose(0, 1)?)?;

        // Apply quantum entanglement modulation
        let entangled_scores = self.apply_quantum_entanglement(&attention_scores, edge_index)?;

        // Quantum measurement (softmax-like operation)
        let attention_weights = self.quantum_softmax(&entangled_scores)?;

        // Apply attention to values
        Ok(attention_weights.matmul(&values)?)
    }

    fn apply_quantum_entanglement(
        &self,
        scores: &Tensor,
        _edge_index: &Tensor,
    ) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Apply quantum entanglement effects
        // Simplified implementation
        Ok(scores.mul_scalar(self.entanglement_strength)?)
    }

    fn quantum_softmax(&self, tensor: &Tensor) -> Result<Tensor, Box<dyn std::error::Error>> {
        // Quantum-inspired softmax with superposition effects
        // Simplified implementation - in practice would involve quantum measurement
        Ok(tensor.clone()) // Placeholder
    }
}

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

    #[test]
    fn test_quantum_layer_creation() {
        let layer = QuantumGraphLayer::new(4, 8, 16);
        assert!(layer.is_ok());

        let layer = layer.unwrap();
        assert_eq!(layer.input_dim, 4);
        assert_eq!(layer.output_dim, 8);
        assert_eq!(layer.quantum_dim, 16);
    }

    #[test]
    fn test_quantum_state_creation() {
        let real_part = randn(&[3, 4]).unwrap();
        let imag_part = randn(&[3, 4]).unwrap();

        let state = QuantumState::new(real_part, imag_part);
        assert_eq!(state.num_qubits, 4);
    }

    #[test]
    fn test_qaoa_creation() {
        let qaoa = QuantumQAOA::new(3, QAOAProblemType::MaxCut);
        assert_eq!(qaoa.num_layers, 3);
        assert_eq!(qaoa.beta_params.len(), 3);
        assert_eq!(qaoa.gamma_params.len(), 3);
    }

    #[test]
    fn test_quantum_walk_creation() {
        let walk = QuantumWalk::new(5, 10);
        assert!(walk.is_ok());

        let walk = walk.unwrap();
        assert_eq!(walk.walk_length, 10);
    }

    #[test]
    fn test_quantum_attention_creation() {
        let attention = QuantumAttention::new(8, 16);
        assert!(attention.is_ok());

        let attention = attention.unwrap();
        assert_eq!(attention.quantum_dim, 16);
        assert_eq!(attention.entanglement_strength, 0.5);
    }

    #[test]
    fn test_quantum_encoding() {
        let layer = QuantumGraphLayer::new(4, 8, 16).unwrap();
        let features = randn(&[3, 4]).unwrap();

        let result = layer.quantum_encoding(&features);
        assert!(result.is_ok());

        let state = result.unwrap();
        assert_eq!(state.num_qubits, 16);
    }
}