scirs2_integrate/specialized/quantum/

algorithms.rs

//! Quantum algorithms and advanced quantum computing methods
//!
//! This module contains quantum algorithms including quantum annealing,
//! variational quantum eigensolvers, quantum error correction, and other
//! advanced quantum computational methods.

use crate::error::{IntegrateError, IntegrateResult as Result};
use scirs2_core::constants::PI;
use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::numeric::Complex64;
use scirs2_core::random::Rng;
use std::collections::HashMap;

/// Quantum annealing solver for optimization problems
pub struct QuantumAnnealer {
    /// Number of qubits
    pub n_qubits: usize,
    /// Annealing schedule
    pub schedule: Vec<(f64, f64)>, // (time, annealing_parameter)
    /// Temperature for thermal fluctuations
    pub temperature: f64,
    /// Number of sweeps per schedule point
    pub sweeps_per_point: usize,
}

impl QuantumAnnealer {
    /// Create a new quantum annealer
    pub fn new(n_qubits: usize, annealing_time: f64, n_schedulepoints: usize) -> Self {
        let mut schedule = Vec::with_capacity(n_schedulepoints);
        for i in 0..n_schedulepoints {
            let t = i as f64 / (n_schedulepoints - 1) as f64;
            let s = t * annealing_time;
            let annealing_param = t; // Linear schedule from 0 to 1
            schedule.push((s, annealing_param));
        }

        Self {
            n_qubits,
            schedule,
            temperature: 0.1,
            sweeps_per_point: 1000,
        }
    }

    /// Solve an Ising model using quantum annealing
    /// J: coupling matrix, h: local fields
    pub fn solve_ising(
        &self,
        j_matrix: &Array2<f64>,
        h_fields: &Array1<f64>,
    ) -> Result<(Array1<i8>, f64)> {
        let mut rng = scirs2_core::random::rng();

        // Initialize random spin configuration
        let mut spins: Array1<i8> = Array1::zeros(self.n_qubits);
        for spin in spins.iter_mut() {
            *spin = if rng.random::<bool>() { 1 } else { -1 };
        }

        let mut best_energy = self.compute_ising_energy(&spins, j_matrix, h_fields);
        let mut best_spins = spins.clone();

        // Perform annealing schedule
        for &(_time, s) in &self.schedule {
            let gamma = (1.0 - s) * 10.0; // Transverse field strength
            let beta = 1.0 / (self.temperature * (1.0 + s)); // Inverse temperature

            // Monte Carlo sweeps at this annealing point
            for _ in 0..self.sweeps_per_point {
                // Try flipping each spin
                for i in 0..self.n_qubits {
                    let old_energy = self.compute_local_energy(i, &spins, j_matrix, h_fields);

                    // Flip spin
                    spins[i] *= -1;
                    let new_energy = self.compute_local_energy(i, &spins, j_matrix, h_fields);

                    // Quantum tunneling effect (simplified)
                    let tunneling_probability = (-gamma * 0.1).exp();
                    let thermal_probability = (-(new_energy - old_energy) * beta).exp();

                    let acceptance_prob = tunneling_probability.max(thermal_probability);

                    if rng.random::<f64>() > acceptance_prob {
                        // Reject: flip back
                        spins[i] *= -1;
                    }
                }

                // Check if this is the best configuration so far
                let current_energy = self.compute_ising_energy(&spins, j_matrix, h_fields);
                if current_energy < best_energy {
                    best_energy = current_energy;
                    best_spins = spins.clone();
                }
            }
        }

        Ok((best_spins, best_energy))
    }

    fn compute_ising_energy(
        &self,
        spins: &Array1<i8>,
        j_matrix: &Array2<f64>,
        h_fields: &Array1<f64>,
    ) -> f64 {
        let mut energy = 0.0;

        // Interaction energy
        for i in 0..self.n_qubits {
            for j in (i + 1)..self.n_qubits {
                energy -= j_matrix[[i, j]] * spins[i] as f64 * spins[j] as f64;
            }
            // Local field energy
            energy -= h_fields[i] * spins[i] as f64;
        }

        energy
    }

    fn compute_local_energy(
        &self,
        site: usize,
        spins: &Array1<i8>,
        j_matrix: &Array2<f64>,
        h_fields: &Array1<f64>,
    ) -> f64 {
        let mut energy = 0.0;

        // Interaction with neighbors
        for j in 0..self.n_qubits {
            if j != site {
                energy -= j_matrix[[site, j]] * spins[site] as f64 * spins[j] as f64;
            }
        }

        // Local field
        energy -= h_fields[site] * spins[site] as f64;

        energy
    }
}

/// Variational Quantum Eigensolver (VQE) for quantum chemistry
pub struct VariationalQuantumEigensolver {
    /// Number of qubits
    pub n_qubits: usize,
    /// Ansatz circuit depth
    pub circuit_depth: usize,
    /// Optimization tolerance
    pub tolerance: f64,
    /// Maximum optimization iterations
    pub max_iterations: usize,
}

impl VariationalQuantumEigensolver {
    /// Create a new VQE solver
    pub fn new(n_qubits: usize, circuitdepth: usize) -> Self {
        Self {
            n_qubits,
            circuit_depth: circuitdepth,
            tolerance: 1e-6,
            max_iterations: 1000,
        }
    }

    /// Find ground state energy using VQE
    pub fn find_ground_state(&self, hamiltonian: &Array2<Complex64>) -> Result<(f64, Array1<f64>)> {
        let mut rng = scirs2_core::random::rng();

        // Initialize random variational parameters
        let n_params = self.n_qubits * self.circuit_depth * 3; // 3 angles per layer per qubit
        let mut params: Array1<f64> = Array1::zeros(n_params);
        for param in params.iter_mut() {
            *param = rng.random::<f64>() * 2.0 * PI;
        }

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

        // Optimization using gradient descent with finite differences
        let learning_rate = 0.01;
        let epsilon = 1e-8;

        for _iteration in 0..self.max_iterations {
            let current_energy = self.compute_expectation_value(&params, hamiltonian)?;

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

            // Compute numerical gradients
            let mut gradients = Array1::zeros(n_params);
            for i in 0..n_params {
                params[i] += epsilon;
                let energy_plus = self.compute_expectation_value(&params, hamiltonian)?;

                params[i] -= 2.0 * epsilon;
                let energy_minus = self.compute_expectation_value(&params, hamiltonian)?;

                params[i] += epsilon; // Restore original value

                gradients[i] = (energy_plus - energy_minus) / (2.0 * epsilon);
            }

            // Update parameters
            for i in 0..n_params {
                params[i] -= learning_rate * gradients[i];
            }

            // Check convergence
            let gradient_norm: f64 = gradients.iter().map(|&g| g * g).sum::<f64>().sqrt();
            if gradient_norm < self.tolerance {
                break;
            }
        }

        Ok((best_energy, best_params))
    }

    /// Compute expectation value of Hamiltonian for given parameters
    fn compute_expectation_value(
        &self,
        params: &Array1<f64>,
        hamiltonian: &Array2<Complex64>,
    ) -> Result<f64> {
        // Create ansatz state vector
        let state_vector = self.create_ansatz_state(params)?;

        // Compute <ψ|H|ψ>
        let h_psi = hamiltonian.dot(&state_vector);
        let expectation: Complex64 = state_vector
            .iter()
            .zip(h_psi.iter())
            .map(|(&psi, &h_psi)| psi.conj() * h_psi)
            .sum();

        Ok(expectation.re)
    }

    /// Create ansatz state vector from variational parameters
    fn create_ansatz_state(&self, params: &Array1<f64>) -> Result<Array1<Complex64>> {
        let n_states = 1 << self.n_qubits;
        let mut state = Array1::zeros(n_states);
        state[0] = Complex64::new(1.0, 0.0); // Start with |00...0⟩

        // Apply parameterized quantum circuit
        let mut param_idx = 0;
        for _layer in 0..self.circuit_depth {
            // Apply rotation gates to each qubit
            for qubit in 0..self.n_qubits {
                let rx_angle = params[param_idx];
                let ry_angle = params[param_idx + 1];
                let rz_angle = params[param_idx + 2];
                param_idx += 3;

                // Apply rotations (simplified implementation)
                state = self.apply_rotation_gates(&state, qubit, rx_angle, ry_angle, rz_angle)?;
            }

            // Apply entangling gates
            for qubit in 0..self.n_qubits - 1 {
                state = self.apply_cnot(&state, qubit, qubit + 1)?;
            }
        }

        Ok(state)
    }

    /// Apply rotation gates to a qubit (simplified implementation)
    fn apply_rotation_gates(
        &self,
        state: &Array1<Complex64>,
        _qubit: usize,
        _rx_angle: f64,
        _ry_angle: f64,
        _rz_angle: f64,
    ) -> Result<Array1<Complex64>> {
        // Simplified: just return the input state
        // In a real implementation, this would apply the rotation matrices
        Ok(state.clone())
    }

    /// Apply CNOT gate between two qubits
    fn apply_cnot(
        &self,
        state: &Array1<Complex64>,
        _control: usize,
        _target: usize,
    ) -> Result<Array1<Complex64>> {
        // Simplified: just return the input state
        // In a real implementation, this would apply the CNOT gate
        Ok(state.clone())
    }
}

/// Quantum error correction codes
#[derive(Debug, Clone, Copy)]
pub enum ErrorCorrectionCode {
    /// Steane 7-qubit code
    Steane7,
    /// Surface code
    Surface,
    /// Repetition code
    Repetition,
}

/// Noise parameters for quantum error correction
#[derive(Debug, Clone)]
pub struct NoiseParameters {
    /// Single-qubit error rate
    pub single_qubit_error_rate: f64,
    /// Two-qubit gate error rate
    pub two_qubit_error_rate: f64,
    /// Measurement error rate
    pub measurement_error_rate: f64,
    /// Decoherence time
    pub decoherence_time: f64,
}

impl Default for NoiseParameters {
    fn default() -> Self {
        Self {
            single_qubit_error_rate: 1e-4,
            two_qubit_error_rate: 1e-3,
            measurement_error_rate: 1e-3,
            decoherence_time: 100e-6, // 100 microseconds
        }
    }
}

/// Quantum error correction system
pub struct QuantumErrorCorrection {
    /// Number of logical qubits
    pub n_logical_qubits: usize,
    /// Error correction code
    pub code: ErrorCorrectionCode,
    /// Noise parameters
    pub noise_parameters: NoiseParameters,
    /// Syndrome history for improved decoding
    pub syndrome_history: Vec<Array1<i8>>,
}

impl QuantumErrorCorrection {
    /// Create new quantum error correction system
    pub fn new(n_logicalqubits: usize, code: ErrorCorrectionCode) -> Self {
        Self {
            n_logical_qubits: n_logicalqubits,
            code,
            noise_parameters: NoiseParameters::default(),
            syndrome_history: Vec::new(),
        }
    }

    /// Encode logical state into physical qubits
    pub fn encode(&self, logicalstate: &Array1<Complex64>) -> Result<Array1<Complex64>> {
        let n_physical = self.get_physical_qubit_count();
        let mut physical_state = Array1::zeros(1 << n_physical);

        match self.code {
            ErrorCorrectionCode::Steane7 => {
                // Steane code encoding
                self.encode_steane7(logicalstate, &mut physical_state)?;
            }
            ErrorCorrectionCode::Surface => {
                // Surface code encoding
                self.encode_surface(logicalstate, &mut physical_state)?;
            }
            ErrorCorrectionCode::Repetition => {
                // Repetition code encoding
                self.encode_repetition(logicalstate, &mut physical_state)?;
            }
        }

        Ok(physical_state)
    }

    /// Get number of physical qubits needed
    fn get_physical_qubit_count(&self) -> usize {
        match self.code {
            ErrorCorrectionCode::Steane7 => 7 * self.n_logical_qubits,
            ErrorCorrectionCode::Surface => 9 * self.n_logical_qubits, // Simplified
            ErrorCorrectionCode::Repetition => 3 * self.n_logical_qubits,
        }
    }

    /// Encode using Steane 7-qubit code
    fn encode_steane7(
        &self,
        logical_state: &Array1<Complex64>,
        physical_state: &mut Array1<Complex64>,
    ) -> Result<()> {
        // Simplified Steane encoding
        if logical_state.len() != (1 << self.n_logical_qubits) {
            return Err(IntegrateError::InvalidInput(
                "Logical state dimension mismatch".to_string(),
            ));
        }

        // For simplicity, just copy logical state to first positions
        for (i, &amp) in logical_state.iter().enumerate() {
            if i < physical_state.len() {
                physical_state[i] = amp;
            }
        }

        Ok(())
    }

    /// Encode using surface code
    fn encode_surface(
        &self,
        logical_state: &Array1<Complex64>,
        physical_state: &mut Array1<Complex64>,
    ) -> Result<()> {
        // Simplified surface code encoding
        if logical_state.len() != (1 << self.n_logical_qubits) {
            return Err(IntegrateError::InvalidInput(
                "Logical state dimension mismatch".to_string(),
            ));
        }

        // For simplicity, just copy logical state to first positions
        for (i, &amp) in logical_state.iter().enumerate() {
            if i < physical_state.len() {
                physical_state[i] = amp;
            }
        }

        Ok(())
    }

    /// Encode using repetition code
    fn encode_repetition(
        &self,
        logical_state: &Array1<Complex64>,
        physical_state: &mut Array1<Complex64>,
    ) -> Result<()> {
        // Simplified repetition code encoding
        if logical_state.len() != (1 << self.n_logical_qubits) {
            return Err(IntegrateError::InvalidInput(
                "Logical state dimension mismatch".to_string(),
            ));
        }

        // For simplicity, just copy logical state to first positions
        for (i, &amp) in logical_state.iter().enumerate() {
            if i < physical_state.len() {
                physical_state[i] = amp;
            }
        }

        Ok(())
    }

    /// Apply quantum gates with error correction
    pub fn apply_logical_x(
        &self,
        state: &Array1<Complex64>,
        qubit: usize,
    ) -> Result<Array1<Complex64>> {
        // Apply logical X gate with error correction
        let mut result = state.clone();

        // For simplicity, apply a basic transformation
        let n_states = state.len();
        for i in 0..n_states {
            // Flip the specified qubit bit in the computational basis
            let flipped_i = i ^ (1 << qubit);
            if flipped_i < n_states {
                result[i] = state[flipped_i];
            }
        }

        Ok(result)
    }

    /// Apply Hadamard gate with error correction
    pub fn apply_hadamard(
        &self,
        state: &Array1<Complex64>,
        _qubit: usize,
    ) -> Result<Array1<Complex64>> {
        // Simplified Hadamard implementation
        let mut result = Array1::zeros(state.len());
        let sqrt_2_inv = 1.0 / 2.0_f64.sqrt();

        for (i, &amp) in state.iter().enumerate() {
            result[i] = amp * Complex64::new(sqrt_2_inv, 0.0);
        }

        Ok(result)
    }

    /// Apply Pauli-X gate with error correction
    pub fn apply_pauli_x(
        &self,
        state: &Array1<Complex64>,
        qubit: usize,
    ) -> Result<Array1<Complex64>> {
        self.apply_logical_x(state, qubit)
    }

    /// Apply CNOT gate with error correction
    pub fn apply_cnot(
        &self,
        state: &Array1<Complex64>,
        _control: usize,
        _target: usize,
    ) -> Result<Array1<Complex64>> {
        // Simplified CNOT implementation
        Ok(state.clone())
    }

    /// Perform error correction cycle
    pub fn error_correction_cycle(&mut self, state: &mut Array1<Complex64>) -> Result<f64> {
        // Measure syndromes
        let syndromes = self.measure_syndromes(state)?;

        // Store in history for improved decoding
        self.syndrome_history.push(syndromes.clone());

        // Decode and apply corrections
        let corrections = self.decode_syndromes(&syndromes)?;
        self.apply_corrections(state, &corrections)?;

        // Estimate error probability
        let error_prob = self.estimate_error_probability(&syndromes);

        Ok(error_prob)
    }

    /// Measure error syndromes
    fn measure_syndromes(&self, state: &Array1<Complex64>) -> Result<Array1<i8>> {
        let n_syndromes = match self.code {
            ErrorCorrectionCode::Steane7 => 6,
            ErrorCorrectionCode::Surface => 8,
            ErrorCorrectionCode::Repetition => 2,
        };

        // Simplified syndrome measurement
        let mut syndromes = Array1::zeros(n_syndromes);
        let mut rng = scirs2_core::random::rng();

        for syndrome in syndromes.iter_mut() {
            *syndrome = if rng.random::<f64>() < self.noise_parameters.measurement_error_rate {
                1
            } else {
                0
            };
        }

        Ok(syndromes)
    }

    /// Decode syndromes to determine corrections
    fn decode_syndromes(&self, syndromes: &Array1<i8>) -> Result<Array1<i8>> {
        let n_physical = self.get_physical_qubit_count();
        let mut corrections = Array1::zeros(n_physical);

        // Simplified decoding based on syndrome pattern
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome != 0 && i < n_physical {
                corrections[i] = 1; // Apply X correction
            }
        }

        Ok(corrections)
    }

    /// Apply corrections to the quantum state
    fn apply_corrections(
        &self,
        state: &mut Array1<Complex64>,
        corrections: &Array1<i8>,
    ) -> Result<()> {
        // Apply corrections (simplified)
        for (qubit, &correction) in corrections.iter().enumerate() {
            if correction != 0 {
                // Apply Pauli correction
                let corrected_state = self.apply_pauli_x(state, qubit)?;
                *state = corrected_state;
            }
        }

        Ok(())
    }

    /// Estimate error probability from syndromes
    fn estimate_error_probability(&self, syndromes: &Array1<i8>) -> f64 {
        let error_count = syndromes.iter().filter(|&&s| s != 0).count();
        error_count as f64 / syndromes.len() as f64
    }

    /// Estimate logical error rate
    pub fn estimate_logical_error_rate(&self) -> f64 {
        match self.code {
            ErrorCorrectionCode::Steane7 => {
                // Simplified model for Steane code
                let p = self.noise_parameters.single_qubit_error_rate;
                35.0 * p.powi(3) // Third-order error suppression
            }
            ErrorCorrectionCode::Surface => {
                // Simplified model for surface code
                let p = self.noise_parameters.single_qubit_error_rate;
                0.1 * (p / 0.01).powi(2) // Threshold around 1%
            }
            ErrorCorrectionCode::Repetition => {
                // Simple repetition code
                let p = self.noise_parameters.single_qubit_error_rate;
                3.0 * p.powi(2) * (1.0 - p) + p.powi(3)
            }
        }
    }
}

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

    #[test]
    fn test_quantum_annealer() {
        let annealer = QuantumAnnealer::new(4, 10.0, 100);
        assert_eq!(annealer.n_qubits, 4);
        assert_eq!(annealer.schedule.len(), 100);

        // Test Ising problem
        let j_matrix = Array2::zeros((4, 4));
        let h_fields = Array1::from_vec(vec![0.1, -0.2, 0.3, -0.1]);

        let result = annealer.solve_ising(&j_matrix, &h_fields);
        assert!(result.is_ok());

        let (spins, energy) = result.unwrap();
        assert_eq!(spins.len(), 4);
        assert!(energy.is_finite());
    }

    #[test]
    fn test_vqe() {
        let vqe = VariationalQuantumEigensolver::new(2, 2);
        assert_eq!(vqe.n_qubits, 2);
        assert_eq!(vqe.circuit_depth, 2);

        // Test with simple Hamiltonian
        let mut hamiltonian = Array2::zeros((4, 4));
        hamiltonian[[0, 0]] = Complex64::new(-1.0, 0.0);
        hamiltonian[[1, 1]] = Complex64::new(0.0, 0.0);
        hamiltonian[[2, 2]] = Complex64::new(0.0, 0.0);
        hamiltonian[[3, 3]] = Complex64::new(1.0, 0.0);

        let result = vqe.find_ground_state(&hamiltonian);
        assert!(result.is_ok());

        let (energy, params) = result.unwrap();
        assert!(energy <= 0.0); // Should find ground state with negative energy
        assert_eq!(params.len(), vqe.n_qubits * vqe.circuit_depth * 3);
    }

    #[test]
    fn test_quantum_error_correction() {
        let mut qec = QuantumErrorCorrection::new(1, ErrorCorrectionCode::Steane7);

        // Test encoding
        let logical_state =
            Array1::from_vec(vec![Complex64::new(0.707, 0.0), Complex64::new(0.707, 0.0)]);

        let encoded = qec.encode(&logical_state);
        assert!(encoded.is_ok());

        let physical_state = encoded.unwrap();
        assert_eq!(physical_state.len(), 1 << qec.get_physical_qubit_count());

        // Test error correction cycle
        let mut test_state = physical_state;
        let error_prob = qec.error_correction_cycle(&mut test_state);
        assert!(error_prob.is_ok());

        let error_rate = qec.estimate_logical_error_rate();
        assert!((0.0..=1.0).contains(&error_rate));
    }
}