quantrs2-core 0.1.3

// ADAPT-VQE: Adaptive Derivative-Assembled Pseudo-Trotter VQE
//
// A state-of-the-art quantum chemistry algorithm that adaptively constructs
// the ansatz circuit during optimization, avoiding the barren plateau problem
// and reducing circuit depth.
//
// Reference: Grimsley, H. R., et al. (2019). "An adaptive variational algorithm for exact molecular simulations on a quantum computer"
// Nature Communications 10, 3007

use crate::error::QuantRS2Error;
use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::{Complex64};
use scirs2_core::random::prelude::*;
use scirs2_core::ndarray::ndarray_linalg::Solve;
use scirs2_optimize::{Optimizer, OptimizerConfig, OptimizerMethod};
use std::collections::HashMap;

/// Fermionic operator pool for quantum chemistry
///
/// Contains the complete set of single and double excitation operators
/// that can be used to construct the ADAPT-VQE ansatz.
#[derive(Debug, Clone)]
pub struct FermionicOperatorPool {
    /// Single excitation operators (a†_p a_q)
    pub single_excitations: Vec<FermionicOperator>,
    /// Double excitation operators (a†_p a†_q a_r a_s)
    pub double_excitations: Vec<FermionicOperator>,
    /// Number of spin orbitals
    pub num_orbitals: usize,
}

impl FermionicOperatorPool {
    /// Create a new operator pool for a given number of spin orbitals
    pub fn new(num_orbitals: usize) -> Self {
        let mut single_excitations = Vec::new();
        let mut double_excitations = Vec::new();

        // Generate all single excitations
        for p in 0..num_orbitals {
            for q in 0..num_orbitals {
                if p != q {
                    single_excitations.push(FermionicOperator::single_excitation(p, q));
                }
            }
        }

        // Generate all double excitations
        for p in 0..num_orbitals {
            for q in p + 1..num_orbitals {
                for r in 0..num_orbitals {
                    for s in r + 1..num_orbitals {
                        if (p, q) != (r, s) {
                            double_excitations.push(
                                FermionicOperator::double_excitation(p, q, r, s)
                            );
                        }
                    }
                }
            }
        }

        Self {
            single_excitations,
            double_excitations,
            num_orbitals,
        }
    }

    /// Get all operators in the pool
    pub fn all_operators(&self) -> Vec<FermionicOperator> {
        let mut operators = Vec::new();
        operators.extend(self.single_excitations.clone());
        operators.extend(self.double_excitations.clone());
        operators
    }

    /// Get operator count
    pub fn size(&self) -> usize {
        self.single_excitations.len() + self.double_excitations.len()
    }
}

/// Fermionic operator representation
#[derive(Debug, Clone, PartialEq)]
pub struct FermionicOperator {
    /// Creation operator indices
    pub creation_ops: Vec<usize>,
    /// Annihilation operator indices
    pub annihilation_ops: Vec<usize>,
    /// Operator label for identification
    pub label: String,
}

impl FermionicOperator {
    /// Create a single excitation operator a†_p a_q
    pub fn single_excitation(p: usize, q: usize) -> Self {
        Self {
            creation_ops: vec![p],
            annihilation_ops: vec![q],
            label: format!("E_{{{},{}}}", p, q),
        }
    }

    /// Create a double excitation operator a†_p a†_q a_r a_s
    pub fn double_excitation(p: usize, q: usize, r: usize, s: usize) -> Self {
        Self {
            creation_ops: vec![p, q],
            annihilation_ops: vec![r, s],
            label: format!("E_{{{},{},{},{}}}", p, q, r, s),
        }
    }

    /// Convert to Pauli string representation using Jordan-Wigner transformation
    pub fn to_pauli_string(&self, num_qubits: usize) -> PauliString {
        // Simplified Jordan-Wigner transformation
        // Full implementation would require more sophisticated mapping
        let mut pauli_ops = vec![PauliOp::I; num_qubits];

        // Apply creation operators
        for &idx in &self.creation_ops {
            if idx < num_qubits {
                pauli_ops[idx] = PauliOp::X;
            }
        }

        // Apply annihilation operators
        for &idx in &self.annihilation_ops {
            if idx < num_qubits {
                pauli_ops[idx] = PauliOp::Y;
            }
        }

        PauliString {
            operators: pauli_ops,
            coefficient: Complex64::new(1.0, 0.0),
        }
    }
}

/// Pauli operator types
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum PauliOp {
    I, // Identity
    X, // Pauli-X
    Y, // Pauli-Y
    Z, // Pauli-Z
}

/// Pauli string representation of a quantum operator
#[derive(Debug, Clone)]
pub struct PauliString {
    /// Pauli operators for each qubit
    pub operators: Vec<PauliOp>,
    /// Overall coefficient
    pub coefficient: Complex64,
}

impl PauliString {
    /// Compute expectation value <ψ|P|ψ> for this Pauli string
    pub fn expectation_value(&self, state: &Array1<Complex64>) -> Complex64 {
        // Apply Pauli operator to state and compute overlap
        let transformed = self.apply_to_state(state);
        state.iter()
            .zip(transformed.iter())
            .map(|(a, b)| a.conj() * b)
            .sum::<Complex64>()
            * self.coefficient
    }

    /// Apply Pauli string to a quantum state
    pub fn apply_to_state(&self, state: &Array1<Complex64>) -> Array1<Complex64> {
        let n = self.operators.len();
        let dim = 1 << n;
        let mut result = Array1::<Complex64>::zeros(dim);

        for i in 0..dim {
            let mut new_index = i;
            let mut phase = Complex64::new(1.0, 0.0);

            for (qubit, &op) in self.operators.iter().enumerate() {
                let bit = (i >> qubit) & 1;
                match op {
                    PauliOp::I => {},
                    PauliOp::X => {
                        new_index ^= 1 << qubit; // Flip bit
                    },
                    PauliOp::Y => {
                        new_index ^= 1 << qubit;
                        phase *= if bit == 0 {
                            Complex64::new(0.0, 1.0)
                        } else {
                            Complex64::new(0.0, -1.0)
                        };
                    },
                    PauliOp::Z => {
                        if bit == 1 {
                            phase *= Complex64::new(-1.0, 0.0);
                        }
                    },
                }
            }

            result[new_index] += phase * state[i];
        }

        result
    }

    /// Compute commutator [H, P] where H is the Hamiltonian
    pub fn commutator_with_hamiltonian(
        &self,
        hamiltonian: &MolecularHamiltonian,
        state: &Array1<Complex64>,
    ) -> Complex64 {
        // [H, P] = HP - PH
        let hp_state = hamiltonian.apply_to_state(&self.apply_to_state(state));
        let ph_state = self.apply_to_state(&hamiltonian.apply_to_state(state));

        state.iter()
            .zip(hp_state.iter().zip(ph_state.iter()))
            .map(|(psi, (hp, ph))| psi.conj() * (hp - ph))
            .sum()
    }
}

/// Molecular Hamiltonian in second-quantized form
#[derive(Debug, Clone)]
pub struct MolecularHamiltonian {
    /// One-electron integrals
    pub one_electron_integrals: Array2<f64>,
    /// Two-electron integrals (4D tensor flattened)
    pub two_electron_integrals: HashMap<(usize, usize, usize, usize), f64>,
    /// Nuclear repulsion energy
    pub nuclear_repulsion: f64,
    /// Number of spin orbitals
    pub num_orbitals: usize,
}

impl MolecularHamiltonian {
    /// Create a new molecular Hamiltonian
    pub fn new(
        one_electron: Array2<f64>,
        two_electron: HashMap<(usize, usize, usize, usize), f64>,
        nuclear_repulsion: f64,
    ) -> Self {
        let num_orbitals = one_electron.nrows();
        Self {
            one_electron_integrals: one_electron,
            two_electron_integrals: two_electron,
            nuclear_repulsion,
            num_orbitals,
        }
    }

    /// Apply Hamiltonian to a quantum state
    pub fn apply_to_state(&self, state: &Array1<Complex64>) -> Array1<Complex64> {
        // Simplified: In practice, would convert to Pauli decomposition
        // and apply each term. For now, returns a placeholder.
        state.clone()
    }

    /// Compute energy expectation value <ψ|H|ψ>
    pub fn expectation_value(&self, state: &Array1<Complex64>) -> f64 {
        let h_psi = self.apply_to_state(state);
        let energy: Complex64 = state.iter()
            .zip(h_psi.iter())
            .map(|(a, b)| a.conj() * b)
            .sum();

        energy.re + self.nuclear_repulsion
    }
}

/// ADAPT-VQE algorithm configuration
#[derive(Debug, Clone)]
pub struct AdaptVQEConfig {
    /// Gradient threshold for operator selection
    pub gradient_threshold: f64,
    /// Maximum number of ADAPT iterations
    pub max_iterations: usize,
    /// Energy convergence threshold
    pub energy_threshold: f64,
    /// Maximum VQE optimization steps per iteration
    pub max_vqe_steps: usize,
    /// Optimizer for parameter optimization
    pub optimizer_method: OptimizerMethod,
}

impl Default for AdaptVQEConfig {
    fn default() -> Self {
        Self {
            gradient_threshold: 1e-3,
            max_iterations: 50,
            energy_threshold: 1e-6,
            max_vqe_steps: 100,
            optimizer_method: OptimizerMethod::LBFGS,
        }
    }
}

/// ADAPT-VQE ansatz built adaptively
#[derive(Debug, Clone)]
pub struct AdaptAnsatz {
    /// Selected operators in order
    pub operators: Vec<FermionicOperator>,
    /// Optimized parameters for each operator
    pub parameters: Vec<f64>,
    /// Energy at each iteration
    pub energy_history: Vec<f64>,
}

impl AdaptAnsatz {
    /// Create an empty ansatz
    pub const fn new() -> Self {
        Self {
            operators: Vec::new(),
            parameters: Vec::new(),
            energy_history: Vec::new(),
        }
    }

    /// Add a new operator to the ansatz
    pub fn add_operator(&mut self, operator: FermionicOperator, parameter: f64) {
        self.operators.push(operator);
        self.parameters.push(parameter);
    }

    /// Get current circuit depth (number of operators)
    pub fn depth(&self) -> usize {
        self.operators.len()
    }

    /// Apply ansatz to a reference state
    pub fn apply_to_state(&self, reference_state: &Array1<Complex64>, num_qubits: usize) -> Array1<Complex64> {
        let mut state = reference_state.clone();

        for (operator, &theta) in self.operators.iter().zip(self.parameters.iter()) {
            let pauli_string = operator.to_pauli_string(num_qubits);

            // Apply exp(-iθP) using Pauli rotation
            // In practice, would use Trotter decomposition or other methods
            let rotation = self.apply_pauli_rotation(&pauli_string, theta);
            state = rotation.dot(&state);
        }

        state
    }

    /// Apply Pauli rotation exp(-iθP)
    fn apply_pauli_rotation(&self, pauli: &PauliString, theta: f64) -> Array2<Complex64> {
        let n = pauli.operators.len();
        let dim = 1 << n;

        // Simplified: construct rotation matrix
        // Full implementation would use efficient Pauli rotation circuits
        let mut rotation = Array2::<Complex64>::zeros((dim, dim));

        for i in 0..dim {
            for j in 0..dim {
                if i == j {
                    rotation[[i, j]] = Complex64::new((theta / 2.0).cos(), 0.0);
                }
            }
        }

        rotation
    }
}

impl Default for AdaptAnsatz {
    fn default() -> Self {
        Self::new()
    }
}

/// Main ADAPT-VQE algorithm implementation
#[derive(Debug)]
pub struct AdaptVQE {
    /// Molecular Hamiltonian
    pub hamiltonian: MolecularHamiltonian,
    /// Operator pool
    pub operator_pool: FermionicOperatorPool,
    /// Configuration
    pub config: AdaptVQEConfig,
    /// Current ansatz
    pub ansatz: AdaptAnsatz,
    /// Number of qubits required
    pub num_qubits: usize,
}

impl AdaptVQE {
    /// Create a new ADAPT-VQE instance
    pub fn new(
        hamiltonian: MolecularHamiltonian,
        num_qubits: usize,
        config: AdaptVQEConfig,
    ) -> Self {
        let operator_pool = FermionicOperatorPool::new(hamiltonian.num_orbitals);
        let ansatz = AdaptAnsatz::new();

        Self {
            hamiltonian,
            operator_pool,
            config,
            ansatz,
            num_qubits,
        }
    }

    /// Run the ADAPT-VQE algorithm
    pub fn run(&mut self, initial_state: &Array1<Complex64>) -> Result<AdaptVQEResult, QuantRS2Error> {
        let mut current_state = initial_state.clone();
        let mut iteration = 0;
        let mut converged = false;

        while iteration < self.config.max_iterations && !converged {
            // Step 1: Compute gradients for all operators in the pool
            let gradients = self.compute_operator_gradients(&current_state)?;

            // Step 2: Select operator with largest gradient magnitude
            let (max_gradient_idx, max_gradient) = gradients.iter()
                .enumerate()
                .max_by(|(_, a), (_, b)| a.abs().partial_cmp(&b.abs()).unwrap_or(std::cmp::Ordering::Equal))
                .ok_or_else(|| QuantRS2Error::InvalidState("No gradients computed".to_string()))?;

            // Check convergence: if max gradient is below threshold, we're done
            if max_gradient.abs() < self.config.gradient_threshold {
                converged = true;
                break;
            }

            // Step 3: Add selected operator to ansatz with initial parameter = 0
            let selected_operator = self.operator_pool.all_operators()[max_gradient_idx].clone();
            self.ansatz.add_operator(selected_operator, 0.0);

            // Step 4: Optimize all parameters in the current ansatz
            let optimized_params = self.optimize_parameters(&current_state)?;
            self.ansatz.parameters = optimized_params;

            // Step 5: Update state and energy
            current_state = self.ansatz.apply_to_state(initial_state, self.num_qubits);
            let energy = self.hamiltonian.expectation_value(&current_state);
            self.ansatz.energy_history.push(energy);

            // Check energy convergence
            if iteration > 0 {
                let energy_change = (self.ansatz.energy_history[iteration] -
                                    self.ansatz.energy_history[iteration - 1]).abs();
                if energy_change < self.config.energy_threshold {
                    converged = true;
                }
            }

            iteration += 1;
        }

        Ok(AdaptVQEResult {
            final_energy: self.ansatz.energy_history.last().copied().unwrap_or(0.0),
            final_state: current_state,
            ansatz: self.ansatz.clone(),
            num_iterations: iteration,
            converged,
        })
    }

    /// Compute gradients for all operators in the pool
    fn compute_operator_gradients(&self, state: &Array1<Complex64>) -> Result<Vec<f64>, QuantRS2Error> {
        let mut gradients = Vec::new();

        for operator in self.operator_pool.all_operators() {
            let pauli_string = operator.to_pauli_string(self.num_qubits);

            // Gradient = <ψ|[H, A]|ψ> where A is the operator
            let gradient = pauli_string.commutator_with_hamiltonian(&self.hamiltonian, state);
            gradients.push(gradient.re);
        }

        Ok(gradients)
    }

    /// Optimize all parameters in the ansatz
    fn optimize_parameters(&self, initial_state: &Array1<Complex64>) -> Result<Vec<f64>, QuantRS2Error> {
        // Use SciRS2 optimizer
        let mut optimizer = Optimizer::new(OptimizerConfig {
            method: self.config.optimizer_method.clone(),
            max_iterations: self.config.max_vqe_steps,
            tolerance: 1e-6,
            ..Default::default()
        });

        // Initial guess: current parameters
        let initial_params = Array1::from_vec(self.ansatz.parameters.clone());

        // Objective function: energy expectation value
        let objective = |params: &Array1<f64>| -> f64 {
            let mut ansatz_copy = self.ansatz.clone();
            ansatz_copy.parameters = params.to_vec();
            let state = ansatz_copy.apply_to_state(initial_state, self.num_qubits);
            self.hamiltonian.expectation_value(&state)
        };

        // Run optimization
        match optimizer.minimize(&objective, &initial_params) {
            Ok(result) => Ok(result.x.to_vec()),
            Err(_) => Err(QuantRS2Error::OptimizationFailed(
                "Parameter optimization failed".to_string()
            ))
        }
    }

    /// Get current circuit depth
    pub fn get_circuit_depth(&self) -> usize {
        self.ansatz.depth()
    }

    /// Get operator pool size
    pub fn get_pool_size(&self) -> usize {
        self.operator_pool.size()
    }
}

/// Result from ADAPT-VQE algorithm
#[derive(Debug, Clone)]
pub struct AdaptVQEResult {
    /// Final ground state energy
    pub final_energy: f64,
    /// Final quantum state
    pub final_state: Array1<Complex64>,
    /// Constructed ansatz
    pub ansatz: AdaptAnsatz,
    /// Number of ADAPT iterations performed
    pub num_iterations: usize,
    /// Whether the algorithm converged
    pub converged: bool,
}

impl AdaptVQEResult {
    /// Get circuit depth of the final ansatz
    pub fn circuit_depth(&self) -> usize {
        self.ansatz.depth()
    }

    /// Get energy lowering from initial to final
    pub fn energy_lowering(&self) -> Option<f64> {
        if self.ansatz.energy_history.len() >= 2 {
            Some(self.ansatz.energy_history[0] - self.final_energy)
        } else {
            None
        }
    }

    /// Get convergence rate (energy change per iteration)
    pub fn convergence_rate(&self) -> f64 {
        if self.num_iterations > 1 {
            let energy_change = (self.ansatz.energy_history.first().unwrap_or(&0.0) -
                               self.final_energy).abs();
            energy_change / self.num_iterations as f64
        } else {
            0.0
        }
    }
}

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

    #[test]
    fn test_fermionic_operator_pool() {
        let pool = FermionicOperatorPool::new(4);

        // For 4 orbitals: 4*3 = 12 single excitations
        assert_eq!(pool.single_excitations.len(), 12);

        // Double excitations: C(4,2) * C(4,2) - overlaps
        assert!(pool.double_excitations.len() > 0);

        assert_eq!(pool.size(), pool.single_excitations.len() + pool.double_excitations.len());
    }

    #[test]
    fn test_pauli_string_application() {
        let pauli = PauliString {
            operators: vec![PauliOp::X, PauliOp::I],
            coefficient: Complex64::new(1.0, 0.0),
        };

        let state = Array1::from_vec(vec![
            Complex64::new(1.0, 0.0),
            Complex64::new(0.0, 0.0),
            Complex64::new(0.0, 0.0),
            Complex64::new(0.0, 0.0),
        ]);

        let result = pauli.apply_to_state(&state);

        // X on qubit 0 should flip |00⟩ to |01⟩
        assert!((result[0].re - 0.0).abs() < 1e-10);
        assert!((result[1].re - 1.0).abs() < 1e-10);
    }

    #[test]
    fn test_adapt_ansatz() {
        let mut ansatz = AdaptAnsatz::new();

        assert_eq!(ansatz.depth(), 0);

        let op = FermionicOperator::single_excitation(0, 1);
        ansatz.add_operator(op, 0.1);

        assert_eq!(ansatz.depth(), 1);
        assert_eq!(ansatz.parameters.len(), 1);
    }

    #[test]
    fn test_molecular_hamiltonian() {
        let h_one = Array2::from_shape_fn((2, 2), |(i, j)| {
            if i == j { -1.0 } else { 0.0 }
        });

        let h_two = HashMap::new();
        let nuclear = 0.5;

        let hamiltonian = MolecularHamiltonian::new(h_one, h_two, nuclear);
        assert_eq!(hamiltonian.num_orbitals, 2);
        assert!((hamiltonian.nuclear_repulsion - 0.5).abs() < 1e-10);
    }
}