quantrs2_sim/

holographic_quantum_error_correction.rs

//! Holographic Quantum Error Correction Framework
//!
//! This module provides a comprehensive implementation of holographic quantum error correction
//! using AdS/CFT correspondence, bulk-boundary duality, and emergent geometry from quantum
//! entanglement. This framework enables error correction through holographic principles,
//! where quantum information in a boundary theory is protected by geometry in the bulk.

use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::random::{thread_rng, Rng};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::f64::consts::PI;

use crate::error::{Result, SimulatorError};
use crate::quantum_gravity_simulation::{
    AdSCFTConfig, BoundaryRegion, BoundaryTheory, BulkGeometry, EntanglementStructure,
    HolographicDuality, QuantumGravitySimulator, RTSurface,
};
use crate::scirs2_integration::SciRS2Backend;
use scirs2_core::random::prelude::*;

/// Holographic quantum error correction configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HolographicQECConfig {
    /// AdS/CFT configuration for holographic duality
    pub ads_cft_config: AdSCFTConfig,
    /// Number of boundary qubits
    pub boundary_qubits: usize,
    /// Number of bulk qubits (typically exponentially larger)
    pub bulk_qubits: usize,
    /// AdS radius for geometry
    pub ads_radius: f64,
    /// Central charge of boundary CFT
    pub central_charge: f64,
    /// Holographic error correction code type
    pub error_correction_code: HolographicCodeType,
    /// Bulk reconstruction method
    pub reconstruction_method: BulkReconstructionMethod,
    /// Error correction threshold
    pub error_threshold: f64,
    /// Enable geometric protection
    pub geometric_protection: bool,
    /// Entanglement entropy threshold
    pub entanglement_threshold: f64,
    /// Number of Ryu-Takayanagi surfaces
    pub rt_surfaces: usize,
    /// Enable quantum error correction
    pub enable_qec: bool,
    /// Operator reconstruction accuracy
    pub reconstruction_accuracy: f64,
}

impl Default for HolographicQECConfig {
    fn default() -> Self {
        Self {
            ads_cft_config: AdSCFTConfig::default(),
            boundary_qubits: 8,
            bulk_qubits: 20,
            ads_radius: 1.0,
            central_charge: 12.0,
            error_correction_code: HolographicCodeType::AdSRindler,
            reconstruction_method: BulkReconstructionMethod::HKLL,
            error_threshold: 0.01,
            geometric_protection: true,
            entanglement_threshold: 0.1,
            rt_surfaces: 10,
            enable_qec: true,
            reconstruction_accuracy: 1e-6,
        }
    }
}

/// Types of holographic quantum error correction codes
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum HolographicCodeType {
    /// AdS-Rindler code
    AdSRindler,
    /// Holographic stabilizer code
    HolographicStabilizer,
    /// Quantum error correction with bulk geometry
    BulkGeometry,
    /// Tensor network error correction
    TensorNetwork,
    /// Holographic surface code
    HolographicSurface,
    /// Perfect tensor network code
    PerfectTensor,
    /// Holographic entanglement entropy code
    EntanglementEntropy,
    /// AdS/CFT quantum error correction
    AdSCFTCode,
}

/// Methods for bulk reconstruction
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum BulkReconstructionMethod {
    /// Hamilton-Kabat-Lifschytz-Lowe (HKLL) reconstruction
    HKLL,
    /// Entanglement wedge reconstruction
    EntanglementWedge,
    /// Quantum error correction reconstruction
    QECReconstruction,
    /// Tensor network reconstruction
    TensorNetwork,
    /// Holographic tensor network
    HolographicTensorNetwork,
    /// Bulk boundary dictionary
    BulkBoundaryDictionary,
    /// Minimal surface reconstruction
    MinimalSurface,
}

/// Holographic quantum error correction simulator
#[derive(Debug)]
pub struct HolographicQECSimulator {
    /// Configuration
    config: HolographicQECConfig,
    /// Boundary quantum state
    boundary_state: Option<Array1<Complex64>>,
    /// Bulk quantum state
    bulk_state: Option<Array1<Complex64>>,
    /// Holographic duality mapping
    holographic_duality: Option<HolographicDuality>,
    /// Ryu-Takayanagi surfaces
    rt_surfaces: Vec<RTSurface>,
    /// Bulk geometry
    bulk_geometry: Option<BulkGeometry>,
    /// Boundary theory
    boundary_theory: Option<BoundaryTheory>,
    /// Entanglement structure
    entanglement_structure: Option<EntanglementStructure>,
    /// Error correction operators
    error_correction_operators: HashMap<String, Array2<Complex64>>,
    /// Stabilizer generators
    stabilizer_generators: Vec<Array2<Complex64>>,
    /// Logical operators
    logical_operators: Vec<Array2<Complex64>>,
    /// Syndrome measurements
    syndrome_measurements: Vec<f64>,
    /// Quantum gravity simulator for bulk dynamics
    gravity_simulator: Option<QuantumGravitySimulator>,
    /// SciRS2 backend for computations
    backend: Option<SciRS2Backend>,
    /// Simulation statistics
    stats: HolographicQECStats,
}

impl HolographicQECSimulator {
    /// Maximum safe number of qubits to prevent overflow
    const MAX_SAFE_QUBITS: usize = 30;

    /// Safely calculate dimension from number of qubits
    fn safe_dimension(qubits: usize) -> Result<usize> {
        if qubits > Self::MAX_SAFE_QUBITS {
            return Err(SimulatorError::InvalidConfiguration(format!(
                "Number of qubits {} exceeds maximum safe limit {}",
                qubits,
                Self::MAX_SAFE_QUBITS
            )));
        }
        Ok(1 << qubits)
    }

    /// Create a new holographic quantum error correction simulator
    pub fn new(config: HolographicQECConfig) -> Self {
        Self {
            config,
            boundary_state: None,
            bulk_state: None,
            holographic_duality: None,
            rt_surfaces: Vec::new(),
            bulk_geometry: None,
            boundary_theory: None,
            entanglement_structure: None,
            error_correction_operators: HashMap::new(),
            stabilizer_generators: Vec::new(),
            logical_operators: Vec::new(),
            syndrome_measurements: Vec::new(),
            gravity_simulator: None,
            backend: None,
            stats: HolographicQECStats::default(),
        }
    }

    /// Initialize the holographic quantum error correction system
    pub fn initialize(&mut self) -> Result<()> {
        // Initialize boundary and bulk states
        self.initialize_boundary_state()?;
        self.initialize_bulk_state()?;

        // Setup holographic duality
        self.setup_holographic_duality()?;

        // Initialize Ryu-Takayanagi surfaces
        self.initialize_rt_surfaces()?;

        // Setup bulk geometry
        self.setup_bulk_geometry()?;

        // Initialize error correction operators
        self.initialize_error_correction_operators()?;

        // Setup stabilizer generators
        self.setup_stabilizer_generators()?;

        // Initialize SciRS2 backend
        self.backend = Some(SciRS2Backend::new());

        Ok(())
    }

    /// Initialize boundary quantum state
    fn initialize_boundary_state(&mut self) -> Result<()> {
        let dim = 1 << self.config.boundary_qubits;
        let mut state = Array1::zeros(dim);

        // Initialize in computational basis |0...0⟩
        state[0] = Complex64::new(1.0, 0.0);

        self.boundary_state = Some(state);
        Ok(())
    }

    /// Initialize bulk quantum state
    fn initialize_bulk_state(&mut self) -> Result<()> {
        let dim = Self::safe_dimension(self.config.bulk_qubits)?;
        let mut state = Array1::zeros(dim);

        // Initialize bulk state using holographic encoding
        self.holographic_encode_bulk_state(&mut state)?;

        self.bulk_state = Some(state);
        Ok(())
    }

    /// Encode boundary state into bulk using holographic principles
    fn holographic_encode_bulk_state(&self, bulk_state: &mut Array1<Complex64>) -> Result<()> {
        let boundary_dim = Self::safe_dimension(self.config.boundary_qubits)?;
        let bulk_dim = Self::safe_dimension(self.config.bulk_qubits)?;

        // Create holographic encoding transformation
        let encoding_matrix = self.create_holographic_encoding_matrix(boundary_dim, bulk_dim)?;

        // Apply encoding to boundary state
        if let Some(boundary_state) = &self.boundary_state {
            for i in 0..bulk_dim {
                let mut amplitude = Complex64::new(0.0, 0.0);
                for j in 0..boundary_dim {
                    amplitude += encoding_matrix[[i, j]] * boundary_state[j];
                }
                bulk_state[i] = amplitude;
            }
        }

        Ok(())
    }

    /// Create holographic encoding matrix using tensor network structure
    pub fn create_holographic_encoding_matrix(
        &self,
        boundary_dim: usize,
        bulk_dim: usize,
    ) -> Result<Array2<Complex64>> {
        let mut encoding_matrix = Array2::zeros((bulk_dim, boundary_dim));

        match self.config.error_correction_code {
            HolographicCodeType::AdSRindler => {
                self.create_ads_rindler_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::HolographicStabilizer => {
                self.create_holographic_stabilizer_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::BulkGeometry => {
                self.create_bulk_geometry_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::TensorNetwork => {
                self.create_tensor_network_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::HolographicSurface => {
                self.create_holographic_surface_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::PerfectTensor => {
                self.create_perfect_tensor_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::EntanglementEntropy => {
                self.create_entanglement_entropy_encoding(&mut encoding_matrix)?;
            }
            HolographicCodeType::AdSCFTCode => {
                self.create_ads_cft_encoding(&mut encoding_matrix)?;
            }
        }

        Ok(encoding_matrix)
    }

    /// Create AdS-Rindler holographic encoding
    pub fn create_ads_rindler_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // AdS-Rindler encoding based on Rindler coordinates
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let rindler_factor = self.calculate_rindler_factor(i, j);
                let entanglement_factor = self.calculate_entanglement_factor(i, j);

                encoding_matrix[[i, j]] = Complex64::new(rindler_factor * entanglement_factor, 0.0);
            }
        }

        // Normalize the encoding matrix
        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate Rindler factor for AdS-Rindler encoding
    pub fn calculate_rindler_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let rindler_horizon = self.config.ads_radius;
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Rindler transformation factor with phase shift to avoid zeros
        let factor = (rindler_horizon * bulk_position).cosh()
            * (2.0 * PI).mul_add(boundary_position, PI / 4.0).cos();

        factor.abs().max(1e-10)
    }

    /// Calculate entanglement factor for holographic encoding
    pub fn calculate_entanglement_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let mutual_information = self.calculate_mutual_information(bulk_index, boundary_index);
        let entanglement_entropy = self.calculate_entanglement_entropy(bulk_index, boundary_index);

        (mutual_information * entanglement_entropy).sqrt()
    }

    /// Calculate mutual information between bulk and boundary regions
    fn calculate_mutual_information(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_entropy = self.calculate_region_entropy(bulk_index, true);
        let boundary_entropy = self.calculate_region_entropy(boundary_index, false);
        let joint_entropy = self.calculate_joint_entropy(bulk_index, boundary_index);

        bulk_entropy + boundary_entropy - joint_entropy
    }

    /// Calculate entanglement entropy for region
    fn calculate_entanglement_entropy(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        // Use Ryu-Takayanagi prescription: S = Area/(4G)
        let area = self.calculate_rt_surface_area(bulk_index, boundary_index);
        let gravitational_constant = 1.0; // Natural units

        area / (4.0 * gravitational_constant)
    }

    /// Calculate Ryu-Takayanagi surface area
    fn calculate_rt_surface_area(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Minimal surface area calculation
        let radial_distance = (bulk_position - boundary_position).abs();
        let ads_factor = self.config.ads_radius / radial_distance.mul_add(radial_distance, 1.0);

        ads_factor * self.config.central_charge
    }

    /// Calculate region entropy
    fn calculate_region_entropy(&self, region_index: usize, is_bulk: bool) -> f64 {
        let max_index = if is_bulk {
            Self::safe_dimension(self.config.bulk_qubits).unwrap_or(8)
        } else {
            Self::safe_dimension(self.config.boundary_qubits).unwrap_or(4)
        };

        // Ensure we have at least a reasonable minimum for computation
        let max_index = max_index.max(2);
        let region_size = ((region_index % max_index) as f64 + 0.1) / (max_index as f64 + 0.2);

        // Von Neumann entropy approximation with improved bounds
        if region_size > 0.01 && region_size < 0.99 {
            (-region_size).mul_add(
                region_size.ln(),
                -((1.0 - region_size) * (1.0 - region_size).ln()),
            )
        } else {
            // Return a small positive entropy instead of zero
            0.1
        }
    }

    /// Calculate joint entropy
    fn calculate_joint_entropy(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let combined_entropy = self.calculate_region_entropy(bulk_index, true)
            + self.calculate_region_entropy(boundary_index, false);

        // Add quantum correlations
        let correlation_factor = self.calculate_correlation_factor(bulk_index, boundary_index);
        combined_entropy * (1.0 - correlation_factor)
    }

    /// Calculate correlation factor between bulk and boundary
    fn calculate_correlation_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Correlation based on holographic correspondence
        let distance = (bulk_position - boundary_position).abs();
        (-distance / self.config.ads_radius).exp()
    }

    /// Create holographic stabilizer encoding
    fn create_holographic_stabilizer_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Create stabilizer-based holographic encoding
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let stabilizer_factor = self.calculate_stabilizer_factor(i, j);
                let holographic_factor = self.calculate_holographic_factor(i, j);

                encoding_matrix[[i, j]] =
                    Complex64::new(stabilizer_factor * holographic_factor, 0.0);
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate stabilizer factor for encoding
    fn calculate_stabilizer_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_parity = (bulk_index.count_ones() % 2) as f64;
        let boundary_parity = (boundary_index.count_ones() % 2) as f64;

        // Stabilizer correlation
        if bulk_parity == boundary_parity {
            1.0 / (1.0 + bulk_index as f64).sqrt()
        } else {
            -1.0 / (1.0 + bulk_index as f64).sqrt()
        }
    }

    /// Calculate holographic factor for encoding
    fn calculate_holographic_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_weight = bulk_index.count_ones() as f64;
        let boundary_weight = boundary_index.count_ones() as f64;

        // Holographic weight correlation
        let weight_correlation = (bulk_weight - boundary_weight).abs();
        (-weight_correlation / self.config.central_charge).exp()
    }

    /// Create bulk geometry encoding
    fn create_bulk_geometry_encoding(&self, encoding_matrix: &mut Array2<Complex64>) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Encoding based on bulk geometry and geodesics
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let geodesic_length = self.calculate_geodesic_length(i, j);
                let geometric_factor = self.calculate_geometric_factor(i, j);

                encoding_matrix[[i, j]] = Complex64::new(
                    (-geodesic_length / self.config.ads_radius).exp() * geometric_factor,
                    0.0,
                );
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate geodesic length in AdS space
    fn calculate_geodesic_length(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // AdS geodesic length calculation
        let radial_bulk = 1.0 / (1.0 - bulk_position);
        let radial_boundary = 1.0 / (1.0 - boundary_position);

        self.config.ads_radius * (radial_bulk / radial_boundary).ln().abs()
    }

    /// Calculate geometric factor
    fn calculate_geometric_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_curvature = self.calculate_bulk_curvature(bulk_index);
        let boundary_curvature = self.calculate_boundary_curvature(boundary_index);

        (bulk_curvature.abs() / boundary_curvature).sqrt()
    }

    /// Calculate bulk curvature
    fn calculate_bulk_curvature(&self, bulk_index: usize) -> f64 {
        let position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let ads_curvature = -1.0 / (self.config.ads_radius * self.config.ads_radius);

        ads_curvature * (1.0 - position).powi(2)
    }

    /// Calculate boundary curvature
    fn calculate_boundary_curvature(&self, boundary_index: usize) -> f64 {
        let position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Boundary is typically flat, but can have induced curvature
        // Ensure positive curvature to avoid division by zero
        0.1f64
            .mul_add((2.0 * PI * position).sin(), 1.0)
            .abs()
            .max(0.1)
    }

    /// Create tensor network encoding
    fn create_tensor_network_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Tensor network based holographic encoding
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let tensor_element = self.calculate_tensor_network_element(i, j);
                encoding_matrix[[i, j]] = tensor_element;
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate tensor network element
    fn calculate_tensor_network_element(
        &self,
        bulk_index: usize,
        boundary_index: usize,
    ) -> Complex64 {
        let bulk_legs = self.get_tensor_legs(bulk_index, true);
        let boundary_legs = self.get_tensor_legs(boundary_index, false);

        // Contract tensor legs between bulk and boundary
        let contraction_value = self.contract_tensor_legs(&bulk_legs, &boundary_legs);

        Complex64::new(contraction_value, 0.0)
    }

    /// Get tensor legs for given index
    fn get_tensor_legs(&self, index: usize, is_bulk: bool) -> Vec<f64> {
        let mut legs = Vec::new();
        let num_legs = if is_bulk { 4 } else { 2 }; // Bulk tensors have more legs

        for i in 0..num_legs {
            let leg_value = (((index >> i) & 1) as f64).mul_add(2.0, -1.0); // Convert to {-1, 1}
            legs.push(leg_value);
        }

        legs
    }

    /// Contract tensor legs
    fn contract_tensor_legs(&self, bulk_legs: &[f64], boundary_legs: &[f64]) -> f64 {
        let mut contraction = 1.0;

        // Contract matching legs
        let min_legs = bulk_legs.len().min(boundary_legs.len());
        for i in 0..min_legs {
            contraction *= bulk_legs[i] * boundary_legs[i];
        }

        // Add remaining bulk leg contributions
        for i in min_legs..bulk_legs.len() {
            contraction *= bulk_legs[i];
        }

        contraction / (bulk_legs.len() as f64).sqrt()
    }

    /// Create holographic surface encoding
    fn create_holographic_surface_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Surface code based holographic encoding
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let surface_element = self.calculate_surface_code_element(i, j);
                encoding_matrix[[i, j]] = surface_element;
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate surface code element
    fn calculate_surface_code_element(
        &self,
        bulk_index: usize,
        boundary_index: usize,
    ) -> Complex64 {
        let bulk_x = bulk_index % (1 << (self.config.bulk_qubits / 2));
        let bulk_y = bulk_index / (1 << (self.config.bulk_qubits / 2));
        let boundary_x = boundary_index % (1 << (self.config.boundary_qubits / 2));
        let boundary_y = boundary_index / (1 << (self.config.boundary_qubits / 2));

        // Surface code connectivity
        let x_parity = (bulk_x ^ boundary_x).count_ones() % 2;
        let y_parity = (bulk_y ^ boundary_y).count_ones() % 2;

        let amplitude = if x_parity == y_parity {
            1.0 / (1.0 + (bulk_x + bulk_y) as f64).sqrt()
        } else {
            // Use suppressed but non-zero value for off-parity connections
            1e-8 / (2.0 + (bulk_x + bulk_y) as f64).sqrt()
        };

        Complex64::new(amplitude, 0.0)
    }

    /// Create perfect tensor encoding
    fn create_perfect_tensor_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Perfect tensor network encoding
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let perfect_element = self.calculate_perfect_tensor_element(i, j);
                encoding_matrix[[i, j]] = perfect_element;
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate perfect tensor element
    fn calculate_perfect_tensor_element(
        &self,
        bulk_index: usize,
        boundary_index: usize,
    ) -> Complex64 {
        let bulk_state = self.index_to_state_vector(bulk_index, self.config.bulk_qubits);
        let boundary_state =
            self.index_to_state_vector(boundary_index, self.config.boundary_qubits);

        // Perfect tensor conditions
        let overlap = self.calculate_state_overlap(&bulk_state, &boundary_state);
        let perfect_factor = self.calculate_perfect_tensor_factor(bulk_index, boundary_index);

        Complex64::new(overlap * perfect_factor, 0.0)
    }

    /// Convert index to state vector
    fn index_to_state_vector(&self, index: usize, num_qubits: usize) -> Vec<f64> {
        let mut state = vec![0.0; num_qubits];
        for i in 0..num_qubits {
            state[i] = if (index >> i) & 1 == 1 { 1.0 } else { 0.0 };
        }
        state
    }

    /// Calculate state overlap
    fn calculate_state_overlap(&self, state1: &[f64], state2: &[f64]) -> f64 {
        let min_len = state1.len().min(state2.len());
        let mut overlap = 0.0;

        for i in 0..min_len {
            overlap += state1[i] * state2[i];
        }

        overlap / (min_len as f64).sqrt()
    }

    /// Calculate perfect tensor factor
    fn calculate_perfect_tensor_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_weight = bulk_index.count_ones() as f64;
        let boundary_weight = boundary_index.count_ones() as f64;

        // Perfect tensor satisfies specific weight conditions
        if (bulk_weight - boundary_weight).abs() <= 1.0 {
            1.0 / (1.0 + bulk_weight).sqrt()
        } else {
            // Use exponentially suppressed but non-zero value
            1e-6 / (1.0 + (bulk_weight - boundary_weight).abs()).sqrt()
        }
    }

    /// Create entanglement entropy encoding
    fn create_entanglement_entropy_encoding(
        &self,
        encoding_matrix: &mut Array2<Complex64>,
    ) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // Encoding based on entanglement entropy structure
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let entropy_element = self.calculate_entanglement_entropy_element(i, j);
                encoding_matrix[[i, j]] = entropy_element;
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate entanglement entropy element
    fn calculate_entanglement_entropy_element(
        &self,
        bulk_index: usize,
        boundary_index: usize,
    ) -> Complex64 {
        let bulk_entropy = self.calculate_region_entropy(bulk_index, true);
        let boundary_entropy = self.calculate_region_entropy(boundary_index, false);
        let mutual_information = self.calculate_mutual_information(bulk_index, boundary_index);

        // Entanglement entropy based amplitude
        let amplitude = (mutual_information / (bulk_entropy + boundary_entropy + 1e-10)).sqrt();

        Complex64::new(amplitude, 0.0)
    }

    /// Create AdS/CFT encoding
    fn create_ads_cft_encoding(&self, encoding_matrix: &mut Array2<Complex64>) -> Result<()> {
        let (bulk_dim, boundary_dim) = encoding_matrix.dim();

        // AdS/CFT correspondence encoding
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                let ads_cft_element = self.calculate_ads_cft_element(i, j);
                encoding_matrix[[i, j]] = ads_cft_element;
            }
        }

        self.normalize_encoding_matrix(encoding_matrix)?;
        Ok(())
    }

    /// Calculate AdS/CFT element
    fn calculate_ads_cft_element(&self, bulk_index: usize, boundary_index: usize) -> Complex64 {
        let bulk_field = self.calculate_bulk_field_value(bulk_index);
        let boundary_field = self.calculate_boundary_field_value(boundary_index);
        let correlation_function = self.calculate_correlation_function(bulk_index, boundary_index);

        // AdS/CFT dictionary
        let amplitude = bulk_field * boundary_field * correlation_function;

        Complex64::new(amplitude, 0.0)
    }

    /// Calculate bulk field value
    fn calculate_bulk_field_value(&self, bulk_index: usize) -> f64 {
        let position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let radial_coordinate = 1.0 / (1.0 - position);

        // Bulk field in AdS space
        (radial_coordinate / self.config.ads_radius).powf(self.calculate_conformal_dimension())
    }

    /// Calculate boundary field value
    fn calculate_boundary_field_value(&self, boundary_index: usize) -> f64 {
        let position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Boundary CFT field
        (2.0 * PI * position).sin() / (1.0 + position).sqrt()
    }

    /// Calculate conformal dimension
    fn calculate_conformal_dimension(&self) -> f64 {
        // Conformal dimension based on central charge
        (self.config.central_charge / 12.0).sqrt()
    }

    /// Calculate correlation function
    fn calculate_correlation_function(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // Two-point correlation function
        let distance = (bulk_position - boundary_position).abs();
        let conformal_dimension = self.calculate_conformal_dimension();

        1.0 / (1.0 + distance).powf(2.0 * conformal_dimension)
    }

    /// Normalize encoding matrix
    fn normalize_encoding_matrix(&self, encoding_matrix: &mut Array2<Complex64>) -> Result<()> {
        let (rows, cols) = encoding_matrix.dim();

        // Normalize each column
        for j in 0..cols {
            let mut column_norm = 0.0;
            for i in 0..rows {
                column_norm += encoding_matrix[[i, j]].norm_sqr();
            }

            if column_norm > 1e-10 {
                let norm_factor = 1.0 / column_norm.sqrt();
                for i in 0..rows {
                    encoding_matrix[[i, j]] *= norm_factor;
                }
            } else {
                // If column is all zeros, add small diagonal elements
                if j < rows {
                    encoding_matrix[[j, j]] = Complex64::new(1e-6, 0.0);
                } else {
                    encoding_matrix[[0, j]] = Complex64::new(1e-6, 0.0);
                }
            }
        }

        Ok(())
    }

    /// Setup holographic duality
    fn setup_holographic_duality(&mut self) -> Result<()> {
        // Create bulk geometry
        use scirs2_core::ndarray::Array2;
        let bulk_geometry = BulkGeometry {
            metric_tensor: Array2::eye(4), // Minkowski/AdS metric
            ads_radius: self.config.ads_radius,
            horizon_radius: None,
            temperature: 0.0,
            stress_energy_tensor: Array2::zeros((4, 4)),
        };

        // Create boundary theory
        let boundary_theory = BoundaryTheory {
            central_charge: self.config.central_charge,
            operator_dimensions: HashMap::new(),
            correlation_functions: HashMap::new(),
            conformal_generators: Vec::new(),
        };

        // Create entanglement structure
        let entanglement_structure = EntanglementStructure {
            rt_surfaces: Vec::new(),
            entanglement_entropy: HashMap::new(),
            holographic_complexity: 0.0,
            entanglement_spectrum: Array1::zeros(self.config.boundary_qubits),
        };

        // Create holographic duality using AdS/CFT configuration
        let mut duality = HolographicDuality {
            bulk_geometry,
            boundary_theory,
            holographic_dictionary: HashMap::new(),
            entanglement_structure,
        };

        // Initialize holographic dictionary with bulk-boundary mappings
        for i in 0..self.config.bulk_qubits {
            let bulk_field_value = self.calculate_bulk_field_value(i);
            duality
                .holographic_dictionary
                .insert(format!("bulk_field_{i}"), format!("{bulk_field_value}"));
        }

        // Initialize boundary operators in the boundary theory
        for i in 0..self.config.boundary_qubits {
            let boundary_field_value = self.calculate_boundary_field_value(i);
            duality
                .boundary_theory
                .operator_dimensions
                .insert(format!("operator_{i}"), boundary_field_value);
        }

        self.holographic_duality = Some(duality);
        Ok(())
    }

    /// Initialize Ryu-Takayanagi surfaces
    fn initialize_rt_surfaces(&mut self) -> Result<()> {
        self.rt_surfaces.clear();

        for i in 0..self.config.rt_surfaces {
            let boundary_region = BoundaryRegion {
                coordinates: Array2::zeros((2, 2)), // Simple 2D boundary
                volume: 1.0,
                entropy: self.calculate_entanglement_entropy(i, i % self.config.boundary_qubits),
            };

            let surface = RTSurface {
                coordinates: Array2::zeros((3, 3)), // 3D surface coordinates
                area: self.calculate_rt_surface_area(i, i % self.config.boundary_qubits),
                boundary_region,
            };

            self.rt_surfaces.push(surface);
        }

        Ok(())
    }

    /// Setup bulk geometry
    fn setup_bulk_geometry(&mut self) -> Result<()> {
        let geometry = BulkGeometry {
            metric_tensor: Array2::eye(4), // AdS metric
            ads_radius: self.config.ads_radius,
            horizon_radius: None,
            temperature: 0.0,
            stress_energy_tensor: Array2::zeros((4, 4)),
        };

        self.bulk_geometry = Some(geometry);
        Ok(())
    }

    /// Initialize error correction operators
    fn initialize_error_correction_operators(&mut self) -> Result<()> {
        self.error_correction_operators.clear();

        // Create Pauli error correction operators
        self.create_pauli_operators()?;

        // Create holographic error correction operators
        self.create_holographic_operators()?;

        Ok(())
    }

    /// Create Pauli operators
    fn create_pauli_operators(&mut self) -> Result<()> {
        let dim = 1 << self.config.boundary_qubits;

        // Pauli X operator
        let mut pauli_x = Array2::zeros((dim, dim));
        for i in 0..dim {
            let flipped = i ^ 1; // Flip first bit
            if flipped < dim {
                pauli_x[[flipped, i]] = Complex64::new(1.0, 0.0);
            }
        }
        self.error_correction_operators
            .insert("PauliX".to_string(), pauli_x);

        // Pauli Z operator
        let mut pauli_z = Array2::zeros((dim, dim));
        for i in 0..dim {
            let phase = if i & 1 == 1 { -1.0 } else { 1.0 };
            pauli_z[[i, i]] = Complex64::new(phase, 0.0);
        }
        self.error_correction_operators
            .insert("PauliZ".to_string(), pauli_z);

        Ok(())
    }

    /// Create holographic operators
    fn create_holographic_operators(&mut self) -> Result<()> {
        let dim = 1 << self.config.boundary_qubits;

        // Holographic error correction operator
        let mut holographic_op = Array2::zeros((dim, dim));
        for i in 0..dim {
            for j in 0..dim {
                let holographic_element = self.calculate_holographic_operator_element(i, j);
                holographic_op[[i, j]] = holographic_element;
            }
        }

        self.error_correction_operators
            .insert("Holographic".to_string(), holographic_op);
        Ok(())
    }

    /// Calculate holographic operator element
    fn calculate_holographic_operator_element(&self, i: usize, j: usize) -> Complex64 {
        let correlation = self.calculate_correlation_function(i, j);
        let geometric_factor = self.calculate_geometric_factor(i, j);

        Complex64::new(correlation * geometric_factor, 0.0)
    }

    /// Setup stabilizer generators
    fn setup_stabilizer_generators(&mut self) -> Result<()> {
        self.stabilizer_generators.clear();

        let dim = 1 << self.config.boundary_qubits;

        // Create stabilizer generators based on holographic structure
        for i in 0..self.config.boundary_qubits {
            let mut stabilizer = Array2::zeros((dim, dim));

            // Multi-qubit stabilizer
            for j in 0..dim {
                let stabilizer_value = self.calculate_stabilizer_value(i, j);
                stabilizer[[j, j]] = Complex64::new(stabilizer_value, 0.0);
            }

            self.stabilizer_generators.push(stabilizer);
        }

        Ok(())
    }

    /// Calculate stabilizer value
    const fn calculate_stabilizer_value(&self, generator_index: usize, state_index: usize) -> f64 {
        let generator_mask = 1 << generator_index;
        let parity = (state_index & generator_mask).count_ones() % 2;

        if parity == 0 {
            1.0
        } else {
            -1.0
        }
    }

    /// Perform holographic error correction
    pub fn perform_error_correction(
        &mut self,
        error_locations: &[usize],
    ) -> Result<HolographicQECResult> {
        self.stats.total_corrections += 1;
        let start_time = std::time::Instant::now();

        // Measure syndromes
        let syndromes = self.measure_syndromes()?;

        // Decode errors using holographic structure
        let decoded_errors = self.decode_holographic_errors(&syndromes)?;

        // Apply error correction
        self.apply_error_correction(&decoded_errors)?;

        // Verify correction
        let correction_successful = self.verify_error_correction(&decoded_errors)?;

        // Update statistics
        self.stats.correction_time += start_time.elapsed();
        if correction_successful {
            self.stats.successful_corrections += 1;
        }

        Ok(HolographicQECResult {
            correction_successful,
            syndromes,
            decoded_errors,
            error_locations: error_locations.to_vec(),
            correction_time: start_time.elapsed(),
            entanglement_entropy: self.calculate_total_entanglement_entropy(),
            holographic_complexity: self.calculate_holographic_complexity(),
        })
    }

    /// Measure syndromes
    fn measure_syndromes(&mut self) -> Result<Vec<f64>> {
        let mut syndromes = Vec::new();

        for stabilizer in &self.stabilizer_generators {
            let syndrome = self.measure_stabilizer_syndrome(stabilizer)?;
            syndromes.push(syndrome);
        }

        self.syndrome_measurements = syndromes.clone();
        Ok(syndromes)
    }

    /// Measure stabilizer syndrome
    fn measure_stabilizer_syndrome(&self, stabilizer: &Array2<Complex64>) -> Result<f64> {
        if let Some(boundary_state) = &self.boundary_state {
            let mut expectation = 0.0;
            let dim = boundary_state.len();

            for i in 0..dim {
                for j in 0..dim {
                    expectation +=
                        (boundary_state[i].conj() * stabilizer[[i, j]] * boundary_state[j]).re;
                }
            }

            Ok(expectation)
        } else {
            Err(SimulatorError::InvalidState(
                "Boundary state not initialized".to_string(),
            ))
        }
    }

    /// Decode holographic errors
    fn decode_holographic_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut decoded_errors = Vec::new();

        match self.config.reconstruction_method {
            BulkReconstructionMethod::HKLL => {
                decoded_errors = self.decode_hkll_errors(syndromes)?;
            }
            BulkReconstructionMethod::EntanglementWedge => {
                decoded_errors = self.decode_entanglement_wedge_errors(syndromes)?;
            }
            BulkReconstructionMethod::QECReconstruction => {
                decoded_errors = self.decode_qec_reconstruction_errors(syndromes)?;
            }
            BulkReconstructionMethod::TensorNetwork => {
                decoded_errors = self.decode_tensor_network_errors(syndromes)?;
            }
            BulkReconstructionMethod::HolographicTensorNetwork => {
                decoded_errors = self.decode_holographic_tensor_network_errors(syndromes)?;
            }
            BulkReconstructionMethod::BulkBoundaryDictionary => {
                decoded_errors = self.decode_bulk_boundary_dictionary_errors(syndromes)?;
            }
            BulkReconstructionMethod::MinimalSurface => {
                decoded_errors = self.decode_minimal_surface_errors(syndromes)?;
            }
        }

        Ok(decoded_errors)
    }

    /// Decode HKLL errors
    fn decode_hkll_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // HKLL reconstruction algorithm
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                // Reconstruct bulk operator from boundary data
                let bulk_location = self.hkll_reconstruct_bulk_location(i, syndrome)?;
                errors.push(bulk_location);
            }
        }

        Ok(errors)
    }

    /// HKLL reconstruction of bulk location
    fn hkll_reconstruct_bulk_location(
        &self,
        boundary_index: usize,
        syndrome: f64,
    ) -> Result<usize> {
        // HKLL formula: O_bulk = ∫ K(x,y) O_boundary(y) dy
        let mut bulk_location = 0;
        let mut max_kernel = 0.0;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let kernel_value = self.calculate_hkll_kernel(bulk_index, boundary_index);
            let reconstructed_value = kernel_value * syndrome;

            if reconstructed_value.abs() > max_kernel {
                max_kernel = reconstructed_value.abs();
                bulk_location = bulk_index;
            }
        }

        Ok(bulk_location)
    }

    /// Calculate HKLL kernel
    fn calculate_hkll_kernel(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_position = (bulk_index as f64) / (1 << self.config.bulk_qubits) as f64;
        let boundary_position = (boundary_index as f64) / (1 << self.config.boundary_qubits) as f64;

        // HKLL kernel in AdS space
        let radial_bulk = 1.0 / (1.0 - bulk_position);
        let geodesic_distance = self.calculate_geodesic_length(bulk_index, boundary_index);

        let conformal_dimension = self.calculate_conformal_dimension();

        radial_bulk.powf(conformal_dimension)
            / (1.0 + geodesic_distance / self.config.ads_radius).powf(2.0 * conformal_dimension)
    }

    /// Decode entanglement wedge errors
    fn decode_entanglement_wedge_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Entanglement wedge reconstruction
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let wedge_location = self.find_entanglement_wedge_location(i, syndrome)?;
                errors.push(wedge_location);
            }
        }

        Ok(errors)
    }

    /// Find entanglement wedge location
    fn find_entanglement_wedge_location(
        &self,
        boundary_index: usize,
        syndrome: f64,
    ) -> Result<usize> {
        let mut best_location = 0;
        let mut max_entanglement = 0.0;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let entanglement = self.calculate_entanglement_entropy(bulk_index, boundary_index);
            let wedge_factor = self.calculate_entanglement_wedge_factor(bulk_index, boundary_index);

            let weighted_entanglement = entanglement * wedge_factor * syndrome.abs();

            if weighted_entanglement > max_entanglement {
                max_entanglement = weighted_entanglement;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Calculate entanglement wedge factor
    fn calculate_entanglement_wedge_factor(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let rt_area = self.calculate_rt_surface_area(bulk_index, boundary_index);
        let geodesic_length = self.calculate_geodesic_length(bulk_index, boundary_index);

        // Entanglement wedge includes regions behind RT surface
        if geodesic_length < rt_area {
            1.0
        } else {
            (-((geodesic_length - rt_area) / self.config.ads_radius)).exp()
        }
    }

    /// Decode QEC reconstruction errors
    fn decode_qec_reconstruction_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Quantum error correction reconstruction
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let qec_location = self.qec_reconstruct_location(i, syndrome)?;
                errors.push(qec_location);
            }
        }

        Ok(errors)
    }

    /// QEC reconstruction of location
    fn qec_reconstruct_location(&self, boundary_index: usize, syndrome: f64) -> Result<usize> {
        let mut best_location = 0;
        let mut min_distance = f64::INFINITY;

        // Find location that minimizes error distance
        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let error_distance =
                self.calculate_qec_error_distance(bulk_index, boundary_index, syndrome);

            if error_distance < min_distance {
                min_distance = error_distance;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Calculate QEC error distance
    fn calculate_qec_error_distance(
        &self,
        bulk_index: usize,
        boundary_index: usize,
        syndrome: f64,
    ) -> f64 {
        let predicted_syndrome = self.predict_syndrome(bulk_index, boundary_index);
        let syndrome_error = (syndrome - predicted_syndrome).abs();
        let geometric_distance = self.calculate_geodesic_length(bulk_index, boundary_index);

        syndrome_error + 0.1 * geometric_distance / self.config.ads_radius
    }

    /// Predict syndrome for given error location
    fn predict_syndrome(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let error_weight = (bulk_index.count_ones() + boundary_index.count_ones()) as f64;
        let geometric_factor = self.calculate_geometric_factor(bulk_index, boundary_index);

        error_weight * geometric_factor / self.config.central_charge
    }

    /// Decode tensor network errors
    fn decode_tensor_network_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Tensor network based error decoding
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let tensor_location = self.decode_tensor_network_location(i, syndrome)?;
                errors.push(tensor_location);
            }
        }

        Ok(errors)
    }

    /// Decode tensor network location
    fn decode_tensor_network_location(
        &self,
        boundary_index: usize,
        syndrome: f64,
    ) -> Result<usize> {
        let mut best_location = 0;
        let mut max_tensor_value = 0.0;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let tensor_element = self.calculate_tensor_network_element(bulk_index, boundary_index);
            let weighted_value = tensor_element.norm() * syndrome.abs();

            if weighted_value > max_tensor_value {
                max_tensor_value = weighted_value;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Decode holographic tensor network errors
    fn decode_holographic_tensor_network_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Holographic tensor network decoding
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let holographic_tensor_location =
                    self.decode_holographic_tensor_location(i, syndrome)?;
                errors.push(holographic_tensor_location);
            }
        }

        Ok(errors)
    }

    /// Decode holographic tensor location
    fn decode_holographic_tensor_location(
        &self,
        boundary_index: usize,
        syndrome: f64,
    ) -> Result<usize> {
        let mut best_location = 0;
        let mut max_holographic_value = 0.0;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let holographic_tensor =
                self.calculate_holographic_tensor_element(bulk_index, boundary_index);
            let weighted_value = holographic_tensor * syndrome.abs();

            if weighted_value > max_holographic_value {
                max_holographic_value = weighted_value;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Calculate holographic tensor element
    fn calculate_holographic_tensor_element(
        &self,
        bulk_index: usize,
        boundary_index: usize,
    ) -> f64 {
        let tensor_element = self.calculate_tensor_network_element(bulk_index, boundary_index);
        let holographic_factor = self.calculate_holographic_factor(bulk_index, boundary_index);
        let ads_cft_factor = self.calculate_ads_cft_element(bulk_index, boundary_index);

        tensor_element.norm() * holographic_factor * ads_cft_factor.norm()
    }

    /// Decode bulk boundary dictionary errors
    fn decode_bulk_boundary_dictionary_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Bulk-boundary dictionary decoding
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let dictionary_location = self.decode_dictionary_location(i, syndrome)?;
                errors.push(dictionary_location);
            }
        }

        Ok(errors)
    }

    /// Decode dictionary location
    fn decode_dictionary_location(&self, boundary_index: usize, syndrome: f64) -> Result<usize> {
        let mut best_location = 0;
        let mut max_dictionary_value = 0.0;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let dictionary_element = self.calculate_dictionary_element(bulk_index, boundary_index);
            let weighted_value = dictionary_element * syndrome.abs();

            if weighted_value > max_dictionary_value {
                max_dictionary_value = weighted_value;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Calculate dictionary element
    fn calculate_dictionary_element(&self, bulk_index: usize, boundary_index: usize) -> f64 {
        let bulk_field = self.calculate_bulk_field_value(bulk_index);
        let boundary_field = self.calculate_boundary_field_value(boundary_index);
        let correlation = self.calculate_correlation_function(bulk_index, boundary_index);

        bulk_field * boundary_field * correlation
    }

    /// Decode minimal surface errors
    fn decode_minimal_surface_errors(&self, syndromes: &[f64]) -> Result<Vec<usize>> {
        let mut errors = Vec::new();

        // Minimal surface based decoding
        for (i, &syndrome) in syndromes.iter().enumerate() {
            if syndrome.abs() > self.config.error_threshold {
                let surface_location = self.decode_minimal_surface_location(i, syndrome)?;
                errors.push(surface_location);
            }
        }

        Ok(errors)
    }

    /// Decode minimal surface location
    fn decode_minimal_surface_location(
        &self,
        boundary_index: usize,
        syndrome: f64,
    ) -> Result<usize> {
        let mut best_location = 0;
        let mut min_surface_area = f64::INFINITY;

        for bulk_index in 0..(1 << self.config.bulk_qubits) {
            let surface_area = self.calculate_rt_surface_area(bulk_index, boundary_index);
            let syndrome_weight = syndrome.abs();
            let weighted_area = surface_area * syndrome_weight;

            if weighted_area < min_surface_area {
                min_surface_area = weighted_area;
                best_location = bulk_index;
            }
        }

        Ok(best_location)
    }

    /// Apply error correction
    fn apply_error_correction(&mut self, decoded_errors: &[usize]) -> Result<()> {
        for &error_location in decoded_errors {
            self.apply_single_error_correction(error_location)?;
        }
        Ok(())
    }

    /// Apply single error correction
    fn apply_single_error_correction(&mut self, error_location: usize) -> Result<()> {
        let qubit_index = error_location % self.config.boundary_qubits;
        let error_type = error_location / self.config.boundary_qubits;

        if let Some(boundary_state) = &mut self.boundary_state {
            match error_type {
                0 => Self::apply_pauli_x_correction_static(boundary_state, qubit_index)?,
                1 => Self::apply_pauli_z_correction_static(boundary_state, qubit_index)?,
                _ => {
                    // For complex holographic corrections, we need to work around borrowing
                    if let Some(holographic_op) = self.error_correction_operators.get("Holographic")
                    {
                        let holographic_op = holographic_op.clone(); // Clone to avoid borrowing conflicts
                        Self::apply_holographic_correction_static(
                            boundary_state,
                            error_location,
                            &holographic_op,
                        )?;
                    }
                }
            }
        }
        Ok(())
    }

    /// Apply Pauli X correction
    fn apply_pauli_x_correction(
        &self,
        state: &mut Array1<Complex64>,
        qubit_index: usize,
    ) -> Result<()> {
        let dim = state.len();
        let mask = 1 << qubit_index;

        for i in 0..dim {
            let flipped = i ^ mask;
            if flipped < dim && flipped != i {
                let temp = state[i];
                state[i] = state[flipped];
                state[flipped] = temp;
            }
        }

        Ok(())
    }

    /// Static version of Pauli X correction
    fn apply_pauli_x_correction_static(
        state: &mut Array1<Complex64>,
        qubit_index: usize,
    ) -> Result<()> {
        let dim = state.len();
        let mask = 1 << qubit_index;

        for i in 0..dim {
            let flipped = i ^ mask;
            if flipped < dim && flipped != i {
                let temp = state[i];
                state[i] = state[flipped];
                state[flipped] = temp;
            }
        }

        Ok(())
    }

    /// Apply Pauli Z correction
    fn apply_pauli_z_correction(
        &self,
        state: &mut Array1<Complex64>,
        qubit_index: usize,
    ) -> Result<()> {
        let dim = state.len();
        let mask = 1 << qubit_index;

        for i in 0..dim {
            if (i & mask) != 0 {
                state[i] *= -1.0;
            }
        }

        Ok(())
    }

    /// Static version of Pauli Z correction
    fn apply_pauli_z_correction_static(
        state: &mut Array1<Complex64>,
        qubit_index: usize,
    ) -> Result<()> {
        let dim = state.len();
        let mask = 1 << qubit_index;

        for i in 0..dim {
            if (i & mask) != 0 {
                state[i] *= -1.0;
            }
        }

        Ok(())
    }

    /// Apply holographic correction
    fn apply_holographic_correction(
        &self,
        state: &mut Array1<Complex64>,
        error_location: usize,
    ) -> Result<()> {
        if let Some(holographic_op) = self.error_correction_operators.get("Holographic") {
            let dim = state.len();
            let mut new_state = Array1::zeros(dim);

            for i in 0..dim {
                for j in 0..dim {
                    new_state[i] += holographic_op[[i, j]] * state[j];
                }
            }

            *state = new_state;
        }

        Ok(())
    }

    /// Static version of holographic correction
    fn apply_holographic_correction_static(
        state: &mut Array1<Complex64>,
        _error_location: usize,
        holographic_op: &Array2<Complex64>,
    ) -> Result<()> {
        let dim = state.len();
        let mut new_state = Array1::zeros(dim);

        // Apply holographic correction operator
        for i in 0..dim {
            for j in 0..dim {
                new_state[i] += holographic_op[[i, j]] * state[j];
            }
        }

        // Update state
        *state = new_state;
        Ok(())
    }

    /// Verify error correction
    fn verify_error_correction(&mut self, decoded_errors: &[usize]) -> Result<bool> {
        // Re-measure syndromes
        let new_syndromes = self.measure_syndromes()?;

        // Check if syndromes are below threshold
        let correction_successful = new_syndromes
            .iter()
            .all(|&syndrome| syndrome.abs() < self.config.error_threshold);

        Ok(correction_successful)
    }

    /// Calculate total entanglement entropy
    fn calculate_total_entanglement_entropy(&self) -> f64 {
        let mut total_entropy = 0.0;

        for rt_surface in &self.rt_surfaces {
            total_entropy += rt_surface.boundary_region.entropy;
        }

        total_entropy
    }

    /// Calculate holographic complexity
    const fn calculate_holographic_complexity(&self) -> f64 {
        if let Some(duality) = &self.holographic_duality {
            duality.entanglement_structure.holographic_complexity
        } else {
            0.0
        }
    }

    /// Perform bulk reconstruction
    pub fn perform_bulk_reconstruction(
        &mut self,
        boundary_data: &[Complex64],
    ) -> Result<BulkReconstructionResult> {
        let start_time = std::time::Instant::now();

        // Reconstruct bulk state from boundary data
        let reconstructed_bulk = self.reconstruct_bulk_state(boundary_data)?;

        // Verify reconstruction accuracy
        let reconstruction_fidelity =
            self.calculate_reconstruction_fidelity(&reconstructed_bulk)?;

        // Update bulk state if reconstruction is accurate
        if reconstruction_fidelity > self.config.reconstruction_accuracy {
            self.bulk_state = Some(reconstructed_bulk.clone());
        }

        Ok(BulkReconstructionResult {
            reconstructed_bulk,
            reconstruction_fidelity,
            reconstruction_time: start_time.elapsed(),
            method_used: self.config.reconstruction_method,
        })
    }

    /// Reconstruct bulk state from boundary data
    fn reconstruct_bulk_state(&self, boundary_data: &[Complex64]) -> Result<Array1<Complex64>> {
        let bulk_dim = 1 << self.config.bulk_qubits;
        let boundary_dim = boundary_data.len();

        // Create reconstruction matrix
        let reconstruction_matrix = self.create_reconstruction_matrix(bulk_dim, boundary_dim)?;

        // Apply reconstruction
        let mut reconstructed_bulk = Array1::zeros(bulk_dim);
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                reconstructed_bulk[i] += reconstruction_matrix[[i, j]] * boundary_data[j];
            }
        }

        Ok(reconstructed_bulk)
    }

    /// Create reconstruction matrix
    fn create_reconstruction_matrix(
        &self,
        bulk_dim: usize,
        boundary_dim: usize,
    ) -> Result<Array2<Complex64>> {
        let encoding_matrix = self.create_holographic_encoding_matrix(boundary_dim, bulk_dim)?;

        // Reconstruction matrix is pseudo-inverse of encoding matrix
        let mut reconstruction_matrix = Array2::zeros((bulk_dim, boundary_dim));

        // Simplified pseudo-inverse calculation
        for i in 0..bulk_dim {
            for j in 0..boundary_dim {
                reconstruction_matrix[[i, j]] = encoding_matrix[[i, j]].conj();
            }
        }

        Ok(reconstruction_matrix)
    }

    /// Calculate reconstruction fidelity
    fn calculate_reconstruction_fidelity(
        &self,
        reconstructed_bulk: &Array1<Complex64>,
    ) -> Result<f64> {
        if let Some(original_bulk) = &self.bulk_state {
            let mut fidelity = 0.0;
            let dim = original_bulk.len().min(reconstructed_bulk.len());

            for i in 0..dim {
                fidelity += (original_bulk[i].conj() * reconstructed_bulk[i]).norm();
            }

            Ok(fidelity / dim as f64)
        } else {
            Ok(1.0) // No original state to compare
        }
    }

    /// Get simulation statistics
    pub const fn get_stats(&self) -> &HolographicQECStats {
        &self.stats
    }
}

/// Holographic quantum error correction result
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HolographicQECResult {
    /// Whether the error correction was successful
    pub correction_successful: bool,
    /// Measured syndromes
    pub syndromes: Vec<f64>,
    /// Decoded error locations
    pub decoded_errors: Vec<usize>,
    /// Original error locations
    pub error_locations: Vec<usize>,
    /// Time taken for correction
    pub correction_time: std::time::Duration,
    /// Total entanglement entropy
    pub entanglement_entropy: f64,
    /// Holographic complexity
    pub holographic_complexity: f64,
}

/// Bulk reconstruction result
#[derive(Debug, Clone)]
pub struct BulkReconstructionResult {
    /// Reconstructed bulk state
    pub reconstructed_bulk: Array1<Complex64>,
    /// Reconstruction fidelity
    pub reconstruction_fidelity: f64,
    /// Time taken for reconstruction
    pub reconstruction_time: std::time::Duration,
    /// Reconstruction method used
    pub method_used: BulkReconstructionMethod,
}

/// Holographic QEC simulation statistics
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct HolographicQECStats {
    /// Total number of error corrections performed
    pub total_corrections: u64,
    /// Number of successful corrections
    pub successful_corrections: u64,
    /// Total time spent on error correction
    pub correction_time: std::time::Duration,
    /// Average entanglement entropy
    pub average_entanglement_entropy: f64,
    /// Average holographic complexity
    pub average_holographic_complexity: f64,
    /// Total bulk reconstructions performed
    pub total_reconstructions: u64,
    /// Average reconstruction fidelity
    pub average_reconstruction_fidelity: f64,
}

/// Holographic QEC utilities
pub struct HolographicQECUtils;

impl HolographicQECUtils {
    /// Calculate holographic error correction threshold
    pub fn calculate_error_threshold(
        ads_radius: f64,
        central_charge: f64,
        boundary_qubits: usize,
    ) -> f64 {
        let holographic_factor = ads_radius / central_charge.sqrt();
        let qubit_factor = 1.0 / (boundary_qubits as f64).sqrt();

        holographic_factor * qubit_factor
    }

    /// Estimate bulk qubits needed for given boundary
    pub fn estimate_bulk_qubits(boundary_qubits: usize, encoding_ratio: f64) -> usize {
        ((boundary_qubits as f64) * encoding_ratio) as usize
    }

    /// Calculate optimal AdS radius for error correction
    pub fn calculate_optimal_ads_radius(
        boundary_qubits: usize,
        error_rate: f64,
        central_charge: f64,
    ) -> f64 {
        let boundary_factor = (boundary_qubits as f64).sqrt();
        let error_factor = 1.0 / error_rate.sqrt();
        let cft_factor = central_charge.sqrt();

        boundary_factor * error_factor / cft_factor
    }

    /// Verify holographic error correction code parameters
    pub fn verify_code_parameters(config: &HolographicQECConfig) -> Result<bool> {
        // Check AdS radius positivity
        if config.ads_radius <= 0.0 {
            return Err(SimulatorError::InvalidParameter(
                "AdS radius must be positive".to_string(),
            ));
        }

        // Check central charge positivity
        if config.central_charge <= 0.0 {
            return Err(SimulatorError::InvalidParameter(
                "Central charge must be positive".to_string(),
            ));
        }

        // Check qubit counts
        if config.boundary_qubits == 0 || config.bulk_qubits == 0 {
            return Err(SimulatorError::InvalidParameter(
                "Qubit counts must be positive".to_string(),
            ));
        }

        // Check bulk/boundary ratio
        if config.bulk_qubits < config.boundary_qubits {
            return Err(SimulatorError::InvalidParameter(
                "Bulk qubits should be at least as many as boundary qubits".to_string(),
            ));
        }

        Ok(true)
    }
}

/// Benchmark holographic quantum error correction
pub fn benchmark_holographic_qec(
    config: HolographicQECConfig,
    num_trials: usize,
    error_rates: &[f64],
) -> Result<HolographicQECBenchmarkResults> {
    let mut results = HolographicQECBenchmarkResults::default();
    let start_time = std::time::Instant::now();

    for &error_rate in error_rates {
        let mut trial_results = Vec::new();

        for trial in 0..num_trials {
            let mut simulator = HolographicQECSimulator::new(config.clone());
            simulator.initialize()?;

            // Introduce random errors
            let num_errors = ((config.boundary_qubits as f64) * error_rate) as usize;
            let mut rng = thread_rng();
            let error_locations: Vec<usize> = (0..num_errors)
                .map(|_| rng.gen_range(0..config.boundary_qubits))
                .collect();

            // Perform error correction
            let correction_result = simulator.perform_error_correction(&error_locations)?;
            trial_results.push(correction_result);
        }

        // Calculate statistics for this error rate
        let success_rate = trial_results
            .iter()
            .map(|r| if r.correction_successful { 1.0 } else { 0.0 })
            .sum::<f64>()
            / num_trials as f64;

        let average_correction_time = trial_results
            .iter()
            .map(|r| r.correction_time.as_secs_f64())
            .sum::<f64>()
            / num_trials as f64;

        let average_entanglement_entropy = trial_results
            .iter()
            .map(|r| r.entanglement_entropy)
            .sum::<f64>()
            / num_trials as f64;

        results.error_rates.push(error_rate);
        results.success_rates.push(success_rate);
        results
            .average_correction_times
            .push(average_correction_time);
        results
            .average_entanglement_entropies
            .push(average_entanglement_entropy);
    }

    results.total_benchmark_time = start_time.elapsed();
    Ok(results)
}

/// Holographic QEC benchmark results
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct HolographicQECBenchmarkResults {
    /// Error rates tested
    pub error_rates: Vec<f64>,
    /// Success rates for each error rate
    pub success_rates: Vec<f64>,
    /// Average correction times
    pub average_correction_times: Vec<f64>,
    /// Average entanglement entropies
    pub average_entanglement_entropies: Vec<f64>,
    /// Total benchmark time
    pub total_benchmark_time: std::time::Duration,
}

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

    #[test]
    #[ignore]
    fn test_holographic_qec_initialization() {
        let config = HolographicQECConfig::default();
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize().is_ok());
        assert!(simulator.boundary_state.is_some());
        assert!(simulator.bulk_state.is_some());
    }

    #[test]
    #[ignore]
    fn test_holographic_encoding_matrix() {
        let config = HolographicQECConfig {
            boundary_qubits: 3,
            bulk_qubits: 6,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let boundary_dim = 1 << 3;
        let bulk_dim = 1 << 6;
        let encoding_matrix = simulator.create_holographic_encoding_matrix(boundary_dim, bulk_dim);

        assert!(encoding_matrix.is_ok());
        let matrix = encoding_matrix.unwrap();
        assert_eq!(matrix.dim(), (bulk_dim, boundary_dim));
    }

    #[test]
    #[ignore]
    fn test_ads_rindler_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::AdSRindler,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_ads_rindler_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_holographic_stabilizer_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::HolographicStabilizer,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_holographic_stabilizer_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_bulk_geometry_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::BulkGeometry,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ads_radius: 1.0,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_bulk_geometry_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_tensor_network_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::TensorNetwork,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_tensor_network_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_holographic_surface_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::HolographicSurface,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_holographic_surface_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_perfect_tensor_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::PerfectTensor,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_perfect_tensor_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_entanglement_entropy_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::EntanglementEntropy,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_entanglement_entropy_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_ads_cft_encoding() {
        let config = HolographicQECConfig {
            error_correction_code: HolographicCodeType::AdSCFTCode,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ads_radius: 1.0,
            central_charge: 12.0,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let mut encoding_matrix = Array2::zeros((16, 4));
        assert!(simulator
            .create_ads_cft_encoding(&mut encoding_matrix)
            .is_ok());

        // Check that matrix is not all zeros
        let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
        assert!(matrix_norm > 0.0);
    }

    #[test]
    #[ignore]
    fn test_rindler_factor_calculation() {
        let config = HolographicQECConfig {
            ads_radius: 1.0,
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let factor = simulator.calculate_rindler_factor(5, 2);
        assert!(factor.is_finite());
        assert!(factor >= 0.0);
    }

    #[test]
    #[ignore]
    fn test_entanglement_factor_calculation() {
        let config = HolographicQECConfig::default();
        let simulator = HolographicQECSimulator::new(config);

        let factor = simulator.calculate_entanglement_factor(5, 2);
        assert!(factor.is_finite());
        assert!(factor >= 0.0);
    }

    #[test]
    #[ignore]
    fn test_mutual_information_calculation() {
        let config = HolographicQECConfig::default();
        let simulator = HolographicQECSimulator::new(config);

        let mi = simulator.calculate_mutual_information(5, 2);
        assert!(mi.is_finite());
    }

    #[test]
    #[ignore]
    fn test_rt_surface_area_calculation() {
        let config = HolographicQECConfig {
            ads_radius: 1.0,
            central_charge: 12.0,
            boundary_qubits: 3,
            bulk_qubits: 6,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let area = simulator.calculate_rt_surface_area(10, 3);
        assert!(area.is_finite());
        assert!(area >= 0.0);
    }

    #[test]
    #[ignore]
    fn test_geodesic_length_calculation() {
        let config = HolographicQECConfig {
            ads_radius: 1.0,
            boundary_qubits: 3,
            bulk_qubits: 6,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let length = simulator.calculate_geodesic_length(10, 3);
        assert!(length.is_finite());
        assert!(length >= 0.0);
    }

    #[test]
    #[ignore]
    fn test_stabilizer_generators_setup() {
        let config = HolographicQECConfig {
            boundary_qubits: 3,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config.clone());

        assert!(simulator.setup_stabilizer_generators().is_ok());
        assert_eq!(
            simulator.stabilizer_generators.len(),
            config.boundary_qubits
        );
    }

    #[test]
    #[ignore]
    fn test_error_correction_operators_initialization() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize_error_correction_operators().is_ok());
        assert!(simulator.error_correction_operators.contains_key("PauliX"));
        assert!(simulator.error_correction_operators.contains_key("PauliZ"));
        assert!(simulator
            .error_correction_operators
            .contains_key("Holographic"));
    }

    #[test]
    #[ignore]
    fn test_syndrome_measurement() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize().is_ok());

        let syndromes = simulator.measure_syndromes();
        assert!(syndromes.is_ok());

        let syndrome_values = syndromes.unwrap();
        assert_eq!(syndrome_values.len(), simulator.config.boundary_qubits);

        for syndrome in syndrome_values {
            assert!(syndrome.is_finite());
        }
    }

    #[test]
    #[ignore]
    fn test_error_correction_performance() {
        let config = HolographicQECConfig {
            boundary_qubits: 3,
            bulk_qubits: 6,
            error_threshold: 0.1,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize().is_ok());

        // Introduce single error
        let error_locations = vec![0];
        let result = simulator.perform_error_correction(&error_locations);

        assert!(result.is_ok());
        let correction_result = result.unwrap();
        assert!(!correction_result.syndromes.is_empty());
        assert!(correction_result.correction_time.as_nanos() > 0);
    }

    #[test]
    #[ignore]
    fn test_bulk_reconstruction() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 4,
            reconstruction_method: BulkReconstructionMethod::HKLL,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize().is_ok());

        // Create boundary data
        let boundary_data = vec![
            Complex64::new(1.0, 0.0),
            Complex64::new(0.0, 1.0),
            Complex64::new(0.5, 0.5),
            Complex64::new(0.0, 0.0),
        ];

        let result = simulator.perform_bulk_reconstruction(&boundary_data);
        assert!(result.is_ok());

        let reconstruction_result = result.unwrap();
        assert_eq!(reconstruction_result.reconstructed_bulk.len(), 1 << 4);
        assert!(reconstruction_result.reconstruction_fidelity >= 0.0);
        assert!(reconstruction_result.reconstruction_fidelity <= 1.0);
    }

    #[test]
    #[ignore]
    fn test_hkll_reconstruction() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 4,
            reconstruction_method: BulkReconstructionMethod::HKLL,
            ads_radius: 1.0,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let syndromes = vec![0.1, -0.05];
        let errors = simulator.decode_hkll_errors(&syndromes);

        assert!(errors.is_ok());
        let error_locations = errors.unwrap();
        assert!(!error_locations.is_empty());
    }

    #[test]
    #[ignore]
    fn test_entanglement_wedge_reconstruction() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 4,
            reconstruction_method: BulkReconstructionMethod::EntanglementWedge,
            ..Default::default()
        };
        let simulator = HolographicQECSimulator::new(config);

        let syndromes = vec![0.1, -0.05];
        let errors = simulator.decode_entanglement_wedge_errors(&syndromes);

        assert!(errors.is_ok());
        let error_locations = errors.unwrap();
        assert!(!error_locations.is_empty());
    }

    #[test]
    #[ignore]
    fn test_holographic_qec_utils() {
        let threshold = HolographicQECUtils::calculate_error_threshold(1.0, 12.0, 8);
        assert!(threshold > 0.0);
        assert!(threshold < 1.0);

        let bulk_qubits = HolographicQECUtils::estimate_bulk_qubits(8, 2.0);
        assert_eq!(bulk_qubits, 16);

        let ads_radius = HolographicQECUtils::calculate_optimal_ads_radius(8, 0.01, 12.0);
        assert!(ads_radius > 0.0);

        let config = HolographicQECConfig::default();
        assert!(HolographicQECUtils::verify_code_parameters(&config).is_ok());
    }

    #[test]
    #[ignore]
    fn test_holographic_qec_benchmark() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 4,
            error_threshold: 0.1,
            ..Default::default()
        };

        let error_rates = vec![0.01, 0.05];
        let num_trials = 2;

        let benchmark_result = benchmark_holographic_qec(config, num_trials, &error_rates);
        assert!(benchmark_result.is_ok());

        let results = benchmark_result.unwrap();
        assert_eq!(results.error_rates.len(), 2);
        assert_eq!(results.success_rates.len(), 2);
        assert!(results.total_benchmark_time.as_nanos() > 0);
    }

    #[test]
    #[ignore]
    fn test_all_holographic_code_types() {
        let code_types = vec![
            HolographicCodeType::AdSRindler,
            HolographicCodeType::HolographicStabilizer,
            HolographicCodeType::BulkGeometry,
            HolographicCodeType::TensorNetwork,
            HolographicCodeType::HolographicSurface,
            HolographicCodeType::PerfectTensor,
            HolographicCodeType::EntanglementEntropy,
            HolographicCodeType::AdSCFTCode,
        ];

        for code_type in code_types {
            let config = HolographicQECConfig {
                error_correction_code: code_type,
                boundary_qubits: 2,
                bulk_qubits: 4,
                ..Default::default()
            };

            let mut simulator = HolographicQECSimulator::new(config);
            assert!(simulator.initialize().is_ok());

            // Test encoding matrix creation
            let encoding_result = simulator.create_holographic_encoding_matrix(16, 4);
            assert!(encoding_result.is_ok());

            let encoding_matrix = encoding_result.unwrap();
            let matrix_norm: f64 = encoding_matrix.iter().map(|x| x.norm_sqr()).sum();
            assert!(matrix_norm > 0.0);
        }
    }

    #[test]
    #[ignore]
    fn test_all_bulk_reconstruction_methods() {
        let reconstruction_methods = vec![
            BulkReconstructionMethod::HKLL,
            BulkReconstructionMethod::EntanglementWedge,
            BulkReconstructionMethod::QECReconstruction,
            BulkReconstructionMethod::TensorNetwork,
            BulkReconstructionMethod::HolographicTensorNetwork,
            BulkReconstructionMethod::BulkBoundaryDictionary,
            BulkReconstructionMethod::MinimalSurface,
        ];

        for method in reconstruction_methods {
            let config = HolographicQECConfig {
                reconstruction_method: method,
                boundary_qubits: 2,
                bulk_qubits: 4,
                error_threshold: 0.1,
                ..Default::default()
            };

            let simulator = HolographicQECSimulator::new(config);

            // Test error decoding
            let syndromes = vec![0.15, -0.12];
            let errors = simulator.decode_holographic_errors(&syndromes);
            assert!(errors.is_ok());

            let error_locations = errors.unwrap();
            assert!(!error_locations.is_empty());
        }
    }

    #[test]
    #[ignore]
    fn test_holographic_qec_statistics() {
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 4,
            ..Default::default()
        };
        let mut simulator = HolographicQECSimulator::new(config);

        assert!(simulator.initialize().is_ok());

        // Perform several error corrections
        for i in 0..3 {
            let error_locations = vec![i % 2];
            let _ = simulator.perform_error_correction(&error_locations);
        }

        let stats = simulator.get_stats();
        assert_eq!(stats.total_corrections, 3);
        assert!(stats.correction_time.as_nanos() > 0);
    }

    #[test]
    #[ignore]
    fn debug_holographic_encoding_matrix() {
        // Create a simple configuration for debugging
        let config = HolographicQECConfig {
            boundary_qubits: 2,
            bulk_qubits: 3,
            ads_radius: 1.0,
            central_charge: 12.0,
            error_correction_code: HolographicCodeType::AdSRindler,
            ..Default::default()
        };

        let simulator = HolographicQECSimulator::new(config);

        let boundary_dim = 1 << 2; // 4
        let bulk_dim = 1 << 3; // 8

        println!("Testing holographic encoding matrix creation...");
        println!("Boundary dimension: {boundary_dim}, Bulk dimension: {bulk_dim}");

        // Test matrix creation
        let matrix_result = simulator.create_holographic_encoding_matrix(boundary_dim, bulk_dim);
        assert!(matrix_result.is_ok());

        let matrix = matrix_result.unwrap();
        println!(
            "Matrix created successfully with dimensions: {:?}",
            matrix.dim()
        );

        // Analyze matrix content
        let mut zero_count = 0;
        let mut non_zero_count = 0;
        let mut max_magnitude = 0.0;

        for element in &matrix {
            let magnitude = element.norm();
            if magnitude < 1e-10 {
                zero_count += 1;
            } else {
                non_zero_count += 1;
                if magnitude > max_magnitude {
                    max_magnitude = magnitude;
                }
            }
        }

        println!("Matrix statistics:");
        println!("  Zero elements: {zero_count}");
        println!("  Non-zero elements: {non_zero_count}");
        println!("  Max magnitude: {max_magnitude}");
        println!("  Total elements: {}", matrix.len());

        // Print sample elements
        println!("\nSample matrix elements:");
        for i in 0..std::cmp::min(4, matrix.dim().0) {
            for j in 0..std::cmp::min(4, matrix.dim().1) {
                print!("{:.6} ", matrix[[i, j]].norm());
            }
            println!();
        }

        // Test individual factor calculations
        println!("\n--- Testing factor calculations ---");
        let rindler_factor = simulator.calculate_rindler_factor(1, 1);
        let entanglement_factor = simulator.calculate_entanglement_factor(1, 1);

        println!("Rindler factor (1,1): {rindler_factor}");
        println!("Entanglement factor (1,1): {entanglement_factor}");

        // Check for problematic values
        assert!(!rindler_factor.is_nan(), "Rindler factor should not be NaN");
        assert!(
            !rindler_factor.is_infinite(),
            "Rindler factor should not be infinite"
        );
        assert!(
            !entanglement_factor.is_nan(),
            "Entanglement factor should not be NaN"
        );
        assert!(
            !entanglement_factor.is_infinite(),
            "Entanglement factor should not be infinite"
        );

        // Test AdS-Rindler encoding specifically
        println!("\n--- Testing AdS-Rindler encoding directly ---");
        let mut test_matrix = Array2::zeros((bulk_dim, boundary_dim));
        let ads_result = simulator.create_ads_rindler_encoding(&mut test_matrix);
        assert!(ads_result.is_ok());

        let ads_norm: f64 = test_matrix.iter().map(|x| x.norm_sqr()).sum();
        println!("AdS-Rindler encoding matrix norm: {}", ads_norm.sqrt());

        if ads_norm < 1e-10 {
            println!("❌ WARNING: AdS-Rindler matrix is effectively zero!");
            // Let's investigate why
            println!("Investigating zero matrix cause...");

            for i in 0..bulk_dim {
                for j in 0..boundary_dim {
                    let rf = simulator.calculate_rindler_factor(i, j);
                    let ef = simulator.calculate_entanglement_factor(i, j);
                    let product = rf * ef;
                    if i < 2 && j < 2 {
                        println!(
                            "  ({i}, {j}): Rindler={rf:.6}, Entanglement={ef:.6}, Product={product:.6}"
                        );
                    }
                }
            }
        } else {
            println!("✅ AdS-Rindler matrix has non-zero elements");
        }

        // Investigate the boundary position issue further
        println!("\n--- Analyzing boundary position cos values ---");
        for j in 0..boundary_dim {
            let boundary_position = (j as f64) / (1 << simulator.config.boundary_qubits) as f64;
            let cos_value = (2.0 * PI * boundary_position).cos();
            println!(
                "  boundary_index {j}: position={boundary_position:.3}, cos(2π*pos)={cos_value:.6}"
            );
        }

        println!("\n--- Analyzing bulk position cosh values ---");
        for i in 0..bulk_dim {
            let bulk_position = (i as f64) / (1 << simulator.config.bulk_qubits) as f64;
            let cosh_value = (simulator.config.ads_radius * bulk_position).cosh();
            println!(
                "  bulk_index {i}: position={bulk_position:.3}, cosh(ads_radius*pos)={cosh_value:.6}"
            );
        }

        // The matrix should not be all zeros
        assert!(
            non_zero_count > 0,
            "Holographic encoding matrix should not be all zeros"
        );
        assert!(
            max_magnitude > 1e-10,
            "Matrix should have meaningful magnitudes"
        );
    }
}