quantrs2_sim/

topological_quantum_simulation.rs

//! Topological Quantum Simulation Framework
//!
//! This module provides a comprehensive implementation of topological quantum computing,
//! including anyonic systems, surface codes, topological phases of matter, and
//! fault-tolerant quantum computation using topological protection. This framework
//! enables simulation of exotic quantum states and robust quantum computation.

use scirs2_core::ndarray::{Array1, Array2, Array3, Array4, Axis};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, HashSet, VecDeque};
use std::f64::consts::PI;
use std::sync::{Arc, RwLock};

use crate::error::{Result, SimulatorError};
use crate::statevector::StateVectorSimulator;

/// Topological quantum simulation configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TopologicalConfig {
    /// Lattice type for topological simulation
    pub lattice_type: LatticeType,
    /// System dimensions
    pub dimensions: Vec<usize>,
    /// Anyonic model type
    pub anyon_model: AnyonModel,
    /// Boundary conditions
    pub boundary_conditions: TopologicalBoundaryConditions,
    /// Temperature for thermal effects
    pub temperature: f64,
    /// Magnetic field strength
    pub magnetic_field: f64,
    /// Enable topological protection
    pub topological_protection: bool,
    /// Error correction code type
    pub error_correction_code: TopologicalErrorCode,
    /// Enable braiding operations
    pub enable_braiding: bool,
}

impl Default for TopologicalConfig {
    fn default() -> Self {
        Self {
            lattice_type: LatticeType::SquareLattice,
            dimensions: vec![8, 8],
            anyon_model: AnyonModel::Abelian,
            boundary_conditions: TopologicalBoundaryConditions::Periodic,
            temperature: 0.0,
            magnetic_field: 0.1,
            topological_protection: true,
            error_correction_code: TopologicalErrorCode::SurfaceCode,
            enable_braiding: true,
        }
    }
}

/// Lattice types for topological systems
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum LatticeType {
    /// Square lattice (for surface codes)
    SquareLattice,
    /// Triangular lattice (for color codes)
    TriangularLattice,
    /// Hexagonal lattice (for Majorana systems)
    HexagonalLattice,
    /// Kagome lattice (for spin liquids)
    KagomeLattice,
    /// Honeycomb lattice (for Kitaev model)
    HoneycombLattice,
    /// Custom lattice structure
    CustomLattice,
}

/// Anyon models for topological quantum computation
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum AnyonModel {
    /// Abelian anyons (simple topological phases)
    Abelian,
    /// Non-Abelian anyons (universal quantum computation)
    NonAbelian,
    /// Fibonacci anyons (specific non-Abelian model)
    Fibonacci,
    /// Ising anyons (Majorana fermions)
    Ising,
    /// Parafermion anyons
    Parafermion,
    /// SU(2)_k Chern-Simons anyons
    ChernSimons(u32), // Level k
}

/// Boundary conditions for topological systems
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum TopologicalBoundaryConditions {
    /// Periodic boundary conditions
    Periodic,
    /// Open boundary conditions
    Open,
    /// Twisted boundary conditions
    Twisted,
    /// Antiperiodic boundary conditions
    Antiperiodic,
}

/// Topological error correction codes
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum TopologicalErrorCode {
    /// Surface code (toric code)
    SurfaceCode,
    /// Color code
    ColorCode,
    /// Hypergraph product codes
    HypergraphProductCode,
    /// Quantum LDPC codes with topological structure
    TopologicalLDPC,
}

/// Anyon type definition
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub struct AnyonType {
    /// Anyon label/identifier
    pub label: String,
    /// Quantum dimension
    pub quantum_dimension: f64,
    /// Topological charge
    pub topological_charge: i32,
    /// Fusion rules (what this anyon fuses to with others)
    pub fusion_rules: HashMap<String, Vec<String>>,
    /// R-matrix (braiding phase)
    pub r_matrix: Complex64,
    /// Whether this is an Abelian anyon
    pub is_abelian: bool,
}

impl AnyonType {
    /// Create vacuum anyon (identity)
    #[must_use]
    pub fn vacuum() -> Self {
        let mut fusion_rules = HashMap::new();
        fusion_rules.insert("vacuum".to_string(), vec!["vacuum".to_string()]);

        Self {
            label: "vacuum".to_string(),
            quantum_dimension: 1.0,
            topological_charge: 0,
            fusion_rules,
            r_matrix: Complex64::new(1.0, 0.0),
            is_abelian: true,
        }
    }

    /// Create sigma anyon (Ising model)
    #[must_use]
    pub fn sigma() -> Self {
        let mut fusion_rules = HashMap::new();
        fusion_rules.insert(
            "sigma".to_string(),
            vec!["vacuum".to_string(), "psi".to_string()],
        );
        fusion_rules.insert("psi".to_string(), vec!["sigma".to_string()]);
        fusion_rules.insert("vacuum".to_string(), vec!["sigma".to_string()]);

        Self {
            label: "sigma".to_string(),
            quantum_dimension: 2.0_f64.sqrt(),
            topological_charge: 1,
            fusion_rules,
            r_matrix: Complex64::new(0.0, 1.0) * (PI / 8.0).exp(), // e^(iπ/8)
            is_abelian: false,
        }
    }

    /// Create tau anyon (Fibonacci model)
    #[must_use]
    pub fn tau() -> Self {
        let golden_ratio = f64::midpoint(1.0, 5.0_f64.sqrt());
        let mut fusion_rules = HashMap::new();
        fusion_rules.insert(
            "tau".to_string(),
            vec!["vacuum".to_string(), "tau".to_string()],
        );
        fusion_rules.insert("vacuum".to_string(), vec!["tau".to_string()]);

        Self {
            label: "tau".to_string(),
            quantum_dimension: golden_ratio,
            topological_charge: 1,
            fusion_rules,
            r_matrix: Complex64::new(0.0, 1.0) * (4.0 * PI / 5.0).exp(), // e^(i4π/5)
            is_abelian: false,
        }
    }
}

/// Anyon configuration on the lattice
#[derive(Debug, Clone)]
pub struct AnyonConfiguration {
    /// Anyon positions and types
    pub anyons: Vec<(Vec<usize>, AnyonType)>,
    /// Worldlines connecting anyons
    pub worldlines: Vec<AnyonWorldline>,
    /// Fusion tree structure
    pub fusion_tree: Option<FusionTree>,
    /// Total topological charge
    pub total_charge: i32,
}

/// Anyon worldline for braiding operations
#[derive(Debug, Clone)]
pub struct AnyonWorldline {
    /// Anyon type
    pub anyon_type: AnyonType,
    /// Path of positions over time
    pub path: Vec<Vec<usize>>,
    /// Time stamps
    pub time_stamps: Vec<f64>,
    /// Braiding phase accumulated
    pub accumulated_phase: Complex64,
}

/// Fusion tree for non-Abelian anyons
#[derive(Debug, Clone)]
pub struct FusionTree {
    /// Tree structure (anyon indices and fusion outcomes)
    pub tree_structure: Vec<FusionNode>,
    /// Total quantum dimension
    pub total_dimension: f64,
    /// Basis labels
    pub basis_labels: Vec<String>,
}

/// Node in fusion tree
#[derive(Debug, Clone)]
pub struct FusionNode {
    /// Input anyon types
    pub inputs: Vec<AnyonType>,
    /// Output anyon type
    pub output: AnyonType,
    /// F-matrix elements
    pub f_matrix: Array2<Complex64>,
    /// Multiplicity
    pub multiplicity: usize,
}

/// Topological quantum state
#[derive(Debug, Clone)]
pub struct TopologicalState {
    /// Anyonic configuration
    pub anyon_config: AnyonConfiguration,
    /// Quantum state amplitudes
    pub amplitudes: Array1<Complex64>,
    /// Degeneracy of ground state
    pub degeneracy: usize,
    /// Topological invariants
    pub topological_invariants: TopologicalInvariants,
    /// Energy gap
    pub energy_gap: f64,
}

/// Topological invariants
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct TopologicalInvariants {
    /// Chern number
    pub chern_number: i32,
    /// Winding number
    pub winding_number: i32,
    /// Z2 topological invariant
    pub z2_invariant: bool,
    /// Berry phase
    pub berry_phase: f64,
    /// Quantum Hall conductivity
    pub hall_conductivity: f64,
    /// Topological entanglement entropy
    pub topological_entanglement_entropy: f64,
}

/// Braiding operation
#[derive(Debug, Clone)]
pub struct BraidingOperation {
    /// Anyons being braided
    pub anyon_indices: Vec<usize>,
    /// Braiding type (clockwise/counterclockwise)
    pub braiding_type: BraidingType,
    /// Braiding matrix
    pub braiding_matrix: Array2<Complex64>,
    /// Execution time
    pub execution_time: f64,
}

/// Type of braiding operation
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum BraidingType {
    /// Clockwise braiding
    Clockwise,
    /// Counterclockwise braiding
    Counterclockwise,
    /// Exchange operation
    Exchange,
    /// Identity (no braiding)
    Identity,
}

/// Surface code for topological error correction
#[derive(Debug, Clone)]
pub struct SurfaceCode {
    /// Code distance
    pub distance: usize,
    /// Data qubits positions
    pub data_qubits: Vec<Vec<usize>>,
    /// X-stabilizer positions
    pub x_stabilizers: Vec<Vec<usize>>,
    /// Z-stabilizer positions
    pub z_stabilizers: Vec<Vec<usize>>,
    /// Logical operators
    pub logical_operators: LogicalOperators,
    /// Error syndrome detection
    pub syndrome_detectors: Vec<SyndromeDetector>,
}

/// Logical operators for surface code
#[derive(Debug, Clone)]
pub struct LogicalOperators {
    /// Logical X operators
    pub logical_x: Vec<Array1<bool>>,
    /// Logical Z operators
    pub logical_z: Vec<Array1<bool>>,
    /// Number of logical qubits
    pub num_logical_qubits: usize,
}

/// Syndrome detector for error correction
#[derive(Debug, Clone)]
pub struct SyndromeDetector {
    /// Stabilizer type (X or Z)
    pub stabilizer_type: StabilizerType,
    /// Qubits measured by this detector
    pub measured_qubits: Vec<usize>,
    /// Detection threshold
    pub threshold: f64,
    /// Error correction suggestions
    pub correction_map: HashMap<Vec<bool>, Vec<usize>>,
}

/// Type of stabilizer measurement
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum StabilizerType {
    /// Pauli-X stabilizer
    PauliX,
    /// Pauli-Z stabilizer
    PauliZ,
    /// Combined XZ stabilizer
    XZ,
}

/// Topological quantum simulator
pub struct TopologicalQuantumSimulator {
    /// Configuration
    config: TopologicalConfig,
    /// Current topological state
    state: TopologicalState,
    /// Lattice structure
    lattice: TopologicalLattice,
    /// Anyon model implementation
    anyon_model: Box<dyn AnyonModelImplementation + Send + Sync>,
    /// Error correction system
    error_correction: Option<SurfaceCode>,
    /// Braiding history
    braiding_history: Vec<BraidingOperation>,
    /// Simulation statistics
    stats: TopologicalSimulationStats,
}

/// Lattice structure for topological systems
#[derive(Debug, Clone)]
pub struct TopologicalLattice {
    /// Lattice type
    pub lattice_type: LatticeType,
    /// Dimensions
    pub dimensions: Vec<usize>,
    /// Site positions
    pub sites: Vec<Vec<f64>>,
    /// Bonds between sites
    pub bonds: Vec<(usize, usize)>,
    /// Plaquettes (for gauge theories)
    pub plaquettes: Vec<Vec<usize>>,
    /// Coordination number
    pub coordination_number: usize,
}

/// Simulation statistics
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct TopologicalSimulationStats {
    /// Number of braiding operations performed
    pub braiding_operations: usize,
    /// Total simulation time
    pub total_simulation_time_ms: f64,
    /// Average braiding time
    pub avg_braiding_time_ms: f64,
    /// Number of error corrections
    pub error_corrections: usize,
    /// Fidelity of operations
    pub average_fidelity: f64,
    /// Topological protection effectiveness
    pub protection_effectiveness: f64,
}

/// Trait for anyon model implementations
pub trait AnyonModelImplementation {
    /// Get anyon types for this model
    fn get_anyon_types(&self) -> Vec<AnyonType>;

    /// Compute fusion coefficients
    fn fusion_coefficients(&self, a: &AnyonType, b: &AnyonType, c: &AnyonType) -> Complex64;

    /// Compute braiding matrix
    fn braiding_matrix(&self, a: &AnyonType, b: &AnyonType) -> Array2<Complex64>;

    /// Compute F-matrix
    fn f_matrix(
        &self,
        a: &AnyonType,
        b: &AnyonType,
        c: &AnyonType,
        d: &AnyonType,
    ) -> Array2<Complex64>;

    /// Check if model is Abelian
    fn is_abelian(&self) -> bool;

    /// Get model name
    fn name(&self) -> &str;
}

impl TopologicalQuantumSimulator {
    /// Create new topological quantum simulator
    pub fn new(config: TopologicalConfig) -> Result<Self> {
        let lattice = Self::create_lattice(&config)?;
        let anyon_model = Self::create_anyon_model(&config.anyon_model)?;
        let initial_state = Self::create_initial_topological_state(&config, &lattice)?;

        let error_correction = if config.topological_protection {
            Some(Self::create_surface_code(&config, &lattice)?)
        } else {
            None
        };

        Ok(Self {
            config,
            state: initial_state,
            lattice,
            anyon_model,
            error_correction,
            braiding_history: Vec::new(),
            stats: TopologicalSimulationStats::default(),
        })
    }

    /// Create lattice structure
    fn create_lattice(config: &TopologicalConfig) -> Result<TopologicalLattice> {
        match config.lattice_type {
            LatticeType::SquareLattice => Self::create_square_lattice(&config.dimensions),
            LatticeType::TriangularLattice => Self::create_triangular_lattice(&config.dimensions),
            LatticeType::HexagonalLattice => Self::create_hexagonal_lattice(&config.dimensions),
            LatticeType::HoneycombLattice => Self::create_honeycomb_lattice(&config.dimensions),
            LatticeType::KagomeLattice => Self::create_kagome_lattice(&config.dimensions),
            LatticeType::CustomLattice => Self::create_custom_lattice(&config.dimensions),
        }
    }

    /// Create square lattice
    fn create_square_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Square lattice requires 2D dimensions".to_string(),
            ));
        }

        let (width, height) = (dimensions[0], dimensions[1]);
        let mut sites = Vec::new();
        let mut bonds = Vec::new();
        let mut plaquettes = Vec::new();

        // Create sites
        for y in 0..height {
            for x in 0..width {
                sites.push(vec![x as f64, y as f64]);
            }
        }

        // Create bonds (nearest neighbors)
        for y in 0..height {
            for x in 0..width {
                let site = y * width + x;

                // Horizontal bonds
                if x < width - 1 {
                    bonds.push((site, site + 1));
                }

                // Vertical bonds
                if y < height - 1 {
                    bonds.push((site, site + width));
                }
            }
        }

        // Create plaquettes (2x2 squares)
        for y in 0..height - 1 {
            for x in 0..width - 1 {
                let plaquette = vec![
                    y * width + x,           // Bottom-left
                    y * width + x + 1,       // Bottom-right
                    (y + 1) * width + x,     // Top-left
                    (y + 1) * width + x + 1, // Top-right
                ];
                plaquettes.push(plaquette);
            }
        }

        Ok(TopologicalLattice {
            lattice_type: LatticeType::SquareLattice,
            dimensions: dimensions.to_vec(),
            sites,
            bonds,
            plaquettes,
            coordination_number: 4,
        })
    }

    /// Create triangular lattice
    fn create_triangular_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Triangular lattice requires 2D dimensions".to_string(),
            ));
        }

        let (width, height) = (dimensions[0], dimensions[1]);
        let mut sites = Vec::new();
        let mut bonds = Vec::new();
        let mut plaquettes = Vec::new();

        // Create sites with triangular arrangement
        for y in 0..height {
            for x in 0..width {
                let x_pos = x as f64 + if y % 2 == 1 { 0.5 } else { 0.0 };
                let y_pos = y as f64 * 3.0_f64.sqrt() / 2.0;
                sites.push(vec![x_pos, y_pos]);
            }
        }

        // Create bonds (6 nearest neighbors for triangular lattice)
        for y in 0..height {
            for x in 0..width {
                let site = y * width + x;

                // Right neighbor
                if x < width - 1 {
                    bonds.push((site, site + 1));
                }

                // Upper neighbors
                if y < height - 1 {
                    bonds.push((site, site + width));

                    if y % 2 == 0 && x < width - 1 {
                        bonds.push((site, site + width + 1));
                    } else if y % 2 == 1 && x > 0 {
                        bonds.push((site, site + width - 1));
                    }
                }
            }
        }

        // Create triangular plaquettes
        for y in 0..height - 1 {
            for x in 0..width - 1 {
                if y % 2 == 0 {
                    // Upward triangles
                    let plaquette = vec![y * width + x, y * width + x + 1, (y + 1) * width + x];
                    plaquettes.push(plaquette);
                }
            }
        }

        Ok(TopologicalLattice {
            lattice_type: LatticeType::TriangularLattice,
            dimensions: dimensions.to_vec(),
            sites,
            bonds,
            plaquettes,
            coordination_number: 6,
        })
    }

    /// Create hexagonal lattice
    fn create_hexagonal_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Hexagonal lattice requires 2D dimensions".to_string(),
            ));
        }

        let (width, height) = (dimensions[0], dimensions[1]);
        let mut sites = Vec::new();
        let mut bonds = Vec::new();
        let mut plaquettes = Vec::new();

        // Create hexagonal arrangement
        for y in 0..height {
            for x in 0..width {
                let x_pos = x as f64 * 1.5;
                let y_pos = (y as f64).mul_add(
                    3.0_f64.sqrt(),
                    if x % 2 == 1 {
                        3.0_f64.sqrt() / 2.0
                    } else {
                        0.0
                    },
                );
                sites.push(vec![x_pos, y_pos]);
            }
        }

        // Create bonds for hexagonal coordination
        for y in 0..height {
            for x in 0..width {
                let site = y * width + x;

                // Horizontal neighbor
                if x < width - 1 {
                    bonds.push((site, site + 1));
                }

                // Vertical neighbors (depending on column parity)
                if y < height - 1 {
                    bonds.push((site, site + width));
                }

                if y > 0 {
                    bonds.push((site, site - width));
                }
            }
        }

        // Create hexagonal plaquettes
        for y in 1..height - 1 {
            for x in 1..width - 1 {
                let plaquette = vec![
                    (y - 1) * width + x,
                    (y - 1) * width + x + 1,
                    y * width + x + 1,
                    (y + 1) * width + x + 1,
                    (y + 1) * width + x,
                    y * width + x,
                ];
                plaquettes.push(plaquette);
            }
        }

        Ok(TopologicalLattice {
            lattice_type: LatticeType::HexagonalLattice,
            dimensions: dimensions.to_vec(),
            sites,
            bonds,
            plaquettes,
            coordination_number: 3,
        })
    }

    /// Create honeycomb lattice (for Kitaev model)
    fn create_honeycomb_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Honeycomb lattice requires 2D dimensions".to_string(),
            ));
        }

        let (width, height) = (dimensions[0], dimensions[1]);
        let mut sites = Vec::new();
        let mut bonds = Vec::new();
        let mut plaquettes = Vec::new();

        // Honeycomb has two sublattices A and B
        for y in 0..height {
            for x in 0..width {
                // A sublattice
                let x_a = x as f64 * 3.0 / 2.0;
                let y_a = y as f64 * 3.0_f64.sqrt();
                sites.push(vec![x_a, y_a]);

                // B sublattice
                let x_b = x as f64 * 3.0 / 2.0 + 1.0;
                let y_b = (y as f64).mul_add(3.0_f64.sqrt(), 3.0_f64.sqrt() / 3.0);
                sites.push(vec![x_b, y_b]);
            }
        }

        // Create bonds between A and B sublattices
        for y in 0..height {
            for x in 0..width {
                let a_site = 2 * (y * width + x);
                let b_site = a_site + 1;

                // Connect A to B in same unit cell
                bonds.push((a_site, b_site));

                // Connect to neighboring cells
                if x < width - 1 {
                    bonds.push((b_site, a_site + 2));
                }

                if y < height - 1 {
                    bonds.push((b_site, a_site + 2 * width));
                }
            }
        }

        // Create hexagonal plaquettes for honeycomb
        for y in 0..height - 1 {
            for x in 0..width - 1 {
                let plaquette = vec![
                    2 * (y * width + x),           // A
                    2 * (y * width + x) + 1,       // B
                    2 * (y * width + x + 1),       // A'
                    2 * (y * width + x + 1) + 1,   // B'
                    2 * ((y + 1) * width + x),     // A''
                    2 * ((y + 1) * width + x) + 1, // B''
                ];
                plaquettes.push(plaquette);
            }
        }

        Ok(TopologicalLattice {
            lattice_type: LatticeType::HoneycombLattice,
            dimensions: dimensions.to_vec(),
            sites,
            bonds,
            plaquettes,
            coordination_number: 3,
        })
    }

    /// Create Kagome lattice
    fn create_kagome_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Kagome lattice requires 2D dimensions".to_string(),
            ));
        }

        let (width, height) = (dimensions[0], dimensions[1]);
        let mut sites = Vec::new();
        let mut bonds = Vec::new();
        let mut plaquettes = Vec::new();

        // Kagome has three sites per unit cell
        for y in 0..height {
            for x in 0..width {
                let base_x = x as f64 * 2.0;
                let base_y = y as f64 * 3.0_f64.sqrt();

                // Three sites forming kagome unit
                sites.push(vec![base_x, base_y]);
                sites.push(vec![base_x + 1.0, base_y]);
                sites.push(vec![base_x + 0.5, base_y + 3.0_f64.sqrt() / 2.0]);
            }
        }

        // Create bonds for kagome structure
        for y in 0..height {
            for x in 0..width {
                let base_site = 3 * (y * width + x);

                // Internal triangle bonds
                bonds.push((base_site, base_site + 1));
                bonds.push((base_site + 1, base_site + 2));
                bonds.push((base_site + 2, base_site));

                // Inter-unit bonds
                if x < width - 1 {
                    bonds.push((base_site + 1, base_site + 3));
                }

                if y < height - 1 {
                    bonds.push((base_site + 2, base_site + 3 * width));
                }
            }
        }

        // Create triangular and hexagonal plaquettes
        for y in 0..height {
            for x in 0..width {
                let base_site = 3 * (y * width + x);

                // Triangular plaquette
                let triangle = vec![base_site, base_site + 1, base_site + 2];
                plaquettes.push(triangle);

                // Hexagonal plaquettes (if neighbors exist)
                if x < width - 1 && y < height - 1 {
                    let hexagon = vec![
                        base_site + 1,
                        base_site + 3,
                        base_site + 3 + 2,
                        base_site + 3 * width + 2,
                        base_site + 3 * width,
                        base_site + 2,
                    ];
                    plaquettes.push(hexagon);
                }
            }
        }

        Ok(TopologicalLattice {
            lattice_type: LatticeType::KagomeLattice,
            dimensions: dimensions.to_vec(),
            sites,
            bonds,
            plaquettes,
            coordination_number: 4,
        })
    }

    /// Create custom lattice
    fn create_custom_lattice(dimensions: &[usize]) -> Result<TopologicalLattice> {
        // For now, default to square lattice for custom
        Self::create_square_lattice(dimensions)
    }

    /// Create anyon model implementation
    fn create_anyon_model(
        model: &AnyonModel,
    ) -> Result<Box<dyn AnyonModelImplementation + Send + Sync>> {
        match model {
            AnyonModel::Abelian => Ok(Box::new(AbelianAnyons::new())),
            AnyonModel::NonAbelian => Ok(Box::new(NonAbelianAnyons::new())),
            AnyonModel::Fibonacci => Ok(Box::new(FibonacciAnyons::new())),
            AnyonModel::Ising => Ok(Box::new(IsingAnyons::new())),
            AnyonModel::Parafermion => Ok(Box::new(ParafermionAnyons::new())),
            AnyonModel::ChernSimons(k) => Ok(Box::new(ChernSimonsAnyons::new(*k))),
        }
    }

    /// Create initial topological state
    fn create_initial_topological_state(
        config: &TopologicalConfig,
        lattice: &TopologicalLattice,
    ) -> Result<TopologicalState> {
        // Create vacuum state with no anyons
        let anyon_config = AnyonConfiguration {
            anyons: Vec::new(),
            worldlines: Vec::new(),
            fusion_tree: None,
            total_charge: 0,
        };

        // Initialize ground state (typically degenerate for topological phases)
        let degeneracy = Self::calculate_ground_state_degeneracy(config, lattice);
        let amplitudes = Array1::zeros(degeneracy);

        let topological_invariants = TopologicalInvariants::default();

        Ok(TopologicalState {
            anyon_config,
            amplitudes,
            degeneracy,
            topological_invariants,
            energy_gap: config.magnetic_field, // Simplification
        })
    }

    /// Calculate ground state degeneracy
    fn calculate_ground_state_degeneracy(
        config: &TopologicalConfig,
        lattice: &TopologicalLattice,
    ) -> usize {
        match config.anyon_model {
            AnyonModel::Abelian => {
                // For Abelian anyons, degeneracy depends on genus
                let genus = Self::calculate_genus(lattice);
                2_usize.pow(genus as u32)
            }
            AnyonModel::Fibonacci => {
                // Fibonacci anyons: exponential degeneracy
                let num_qubits = lattice.sites.len() / 2;
                let golden_ratio = f64::midpoint(1.0, 5.0_f64.sqrt());
                (golden_ratio.powi(num_qubits as i32) / 5.0_f64.sqrt()).round() as usize
            }
            AnyonModel::Ising => {
                // Ising anyons: 2^(n/2) for n Majorana modes
                let num_majoranas = lattice.sites.len();
                2_usize.pow((num_majoranas / 2) as u32)
            }
            _ => 1, // Default to non-degenerate
        }
    }

    /// Calculate topological genus
    fn calculate_genus(lattice: &TopologicalLattice) -> usize {
        // Simplified genus calculation: V - E + F = 2 - 2g
        let vertices = lattice.sites.len();
        let edges = lattice.bonds.len();
        let faces = lattice.plaquettes.len() + 1; // +1 for outer face

        let euler_characteristic = vertices as i32 - edges as i32 + faces as i32;
        let genus = (2 - euler_characteristic) / 2;
        genus.max(0) as usize
    }

    /// Create surface code for error correction
    fn create_surface_code(
        config: &TopologicalConfig,
        lattice: &TopologicalLattice,
    ) -> Result<SurfaceCode> {
        match config.error_correction_code {
            TopologicalErrorCode::SurfaceCode => {
                Self::create_toric_surface_code(&config.dimensions)
            }
            TopologicalErrorCode::ColorCode => Self::create_color_code(&config.dimensions),
            _ => {
                // Default to surface code
                Self::create_toric_surface_code(&config.dimensions)
            }
        }
    }

    /// Create toric surface code
    fn create_toric_surface_code(dimensions: &[usize]) -> Result<SurfaceCode> {
        if dimensions.len() != 2 {
            return Err(SimulatorError::InvalidInput(
                "Surface code requires 2D lattice".to_string(),
            ));
        }

        let distance = dimensions[0].min(dimensions[1]);
        let mut data_qubits = Vec::new();
        let mut x_stabilizers = Vec::new();
        let mut z_stabilizers = Vec::new();

        // Create data qubits on edges of square lattice
        for y in 0..distance {
            for x in 0..distance {
                // Horizontal edges
                data_qubits.push(vec![x, y, 0]); // 0 = horizontal
                                                 // Vertical edges
                data_qubits.push(vec![x, y, 1]); // 1 = vertical
            }
        }

        // Create X-stabilizers (star operators) on vertices
        for y in 0..distance {
            for x in 0..distance {
                let stabilizer_pos = vec![x, y];
                x_stabilizers.push(stabilizer_pos);
            }
        }

        // Create Z-stabilizers (plaquette operators) on faces
        for y in 0..distance - 1 {
            for x in 0..distance - 1 {
                let stabilizer_pos = vec![x, y];
                z_stabilizers.push(stabilizer_pos);
            }
        }

        // Create logical operators
        let logical_x = vec![Array1::from_elem(distance, true)];
        let logical_z = vec![Array1::from_elem(distance, true)];

        let logical_operators = LogicalOperators {
            logical_x,
            logical_z,
            num_logical_qubits: 1,
        };

        // Create syndrome detectors
        let mut syndrome_detectors = Vec::new();

        for stabilizer in &x_stabilizers {
            let detector = SyndromeDetector {
                stabilizer_type: StabilizerType::PauliX,
                measured_qubits: vec![0, 1, 2, 3], // Simplified
                threshold: 0.5,
                correction_map: HashMap::new(),
            };
            syndrome_detectors.push(detector);
        }

        for stabilizer in &z_stabilizers {
            let detector = SyndromeDetector {
                stabilizer_type: StabilizerType::PauliZ,
                measured_qubits: vec![0, 1, 2, 3], // Simplified
                threshold: 0.5,
                correction_map: HashMap::new(),
            };
            syndrome_detectors.push(detector);
        }

        Ok(SurfaceCode {
            distance,
            data_qubits,
            x_stabilizers,
            z_stabilizers,
            logical_operators,
            syndrome_detectors,
        })
    }

    /// Create color code
    fn create_color_code(dimensions: &[usize]) -> Result<SurfaceCode> {
        // For now, create a simplified version that falls back to surface code
        Self::create_toric_surface_code(dimensions)
    }

    /// Place anyon on the lattice
    pub fn place_anyon(&mut self, anyon_type: AnyonType, position: Vec<usize>) -> Result<usize> {
        // Validate position
        if position.len() != self.config.dimensions.len() {
            return Err(SimulatorError::InvalidInput(
                "Position dimension mismatch".to_string(),
            ));
        }

        for (i, &pos) in position.iter().enumerate() {
            if pos >= self.config.dimensions[i] {
                return Err(SimulatorError::InvalidInput(
                    "Position out of bounds".to_string(),
                ));
            }
        }

        // Add anyon to configuration
        let anyon_id = self.state.anyon_config.anyons.len();
        self.state
            .anyon_config
            .anyons
            .push((position.clone(), anyon_type.clone()));

        // Update total charge
        self.state.anyon_config.total_charge += anyon_type.topological_charge;

        // Create worldline for tracking
        let worldline = AnyonWorldline {
            anyon_type,
            path: vec![position],
            time_stamps: vec![0.0],
            accumulated_phase: Complex64::new(1.0, 0.0),
        };
        self.state.anyon_config.worldlines.push(worldline);

        Ok(anyon_id)
    }

    /// Perform braiding operation between two anyons
    pub fn braid_anyons(
        &mut self,
        anyon_a: usize,
        anyon_b: usize,
        braiding_type: BraidingType,
    ) -> Result<Complex64> {
        let start_time = std::time::Instant::now();

        if anyon_a >= self.state.anyon_config.anyons.len()
            || anyon_b >= self.state.anyon_config.anyons.len()
        {
            return Err(SimulatorError::InvalidInput(
                "Invalid anyon indices".to_string(),
            ));
        }

        let (_, ref type_a) = &self.state.anyon_config.anyons[anyon_a];
        let (_, ref type_b) = &self.state.anyon_config.anyons[anyon_b];

        // Compute braiding matrix
        let braiding_matrix = self.anyon_model.braiding_matrix(type_a, type_b);

        // Compute braiding phase
        let braiding_phase = match braiding_type {
            BraidingType::Clockwise => type_a.r_matrix * type_b.r_matrix.conj(),
            BraidingType::Counterclockwise => type_a.r_matrix.conj() * type_b.r_matrix,
            BraidingType::Exchange => type_a.r_matrix * type_b.r_matrix,
            BraidingType::Identity => Complex64::new(1.0, 0.0),
        };

        // Update worldlines
        let current_time = self.braiding_history.len() as f64;
        if anyon_a < self.state.anyon_config.worldlines.len() {
            self.state.anyon_config.worldlines[anyon_a]
                .time_stamps
                .push(current_time);
            self.state.anyon_config.worldlines[anyon_a].accumulated_phase *= braiding_phase;
        }
        if anyon_b < self.state.anyon_config.worldlines.len() {
            self.state.anyon_config.worldlines[anyon_b]
                .time_stamps
                .push(current_time);
            self.state.anyon_config.worldlines[anyon_b].accumulated_phase *= braiding_phase.conj();
        }

        // Apply braiding to quantum state
        for amplitude in &mut self.state.amplitudes {
            *amplitude *= braiding_phase;
        }

        let execution_time = start_time.elapsed().as_secs_f64() * 1000.0;

        // Record braiding operation
        let braiding_op = BraidingOperation {
            anyon_indices: vec![anyon_a, anyon_b],
            braiding_type,
            braiding_matrix,
            execution_time,
        };
        self.braiding_history.push(braiding_op);

        // Update statistics
        self.stats.braiding_operations += 1;
        self.stats.avg_braiding_time_ms = self
            .stats
            .avg_braiding_time_ms
            .mul_add((self.stats.braiding_operations - 1) as f64, execution_time)
            / self.stats.braiding_operations as f64;

        Ok(braiding_phase)
    }

    /// Move anyon to new position
    pub fn move_anyon(&mut self, anyon_id: usize, new_position: Vec<usize>) -> Result<()> {
        if anyon_id >= self.state.anyon_config.anyons.len() {
            return Err(SimulatorError::InvalidInput("Invalid anyon ID".to_string()));
        }

        // Validate new position
        for (i, &pos) in new_position.iter().enumerate() {
            if pos >= self.config.dimensions[i] {
                return Err(SimulatorError::InvalidInput(
                    "New position out of bounds".to_string(),
                ));
            }
        }

        // Update anyon position
        self.state.anyon_config.anyons[anyon_id].0 = new_position.clone();

        // Update worldline
        if anyon_id < self.state.anyon_config.worldlines.len() {
            self.state.anyon_config.worldlines[anyon_id]
                .path
                .push(new_position);
            let current_time = self.braiding_history.len() as f64;
            self.state.anyon_config.worldlines[anyon_id]
                .time_stamps
                .push(current_time);
        }

        Ok(())
    }

    /// Fuse two anyons
    pub fn fuse_anyons(&mut self, anyon_a: usize, anyon_b: usize) -> Result<Vec<AnyonType>> {
        if anyon_a >= self.state.anyon_config.anyons.len()
            || anyon_b >= self.state.anyon_config.anyons.len()
        {
            return Err(SimulatorError::InvalidInput(
                "Invalid anyon indices".to_string(),
            ));
        }

        let type_a = &self.state.anyon_config.anyons[anyon_a].1;
        let type_b = &self.state.anyon_config.anyons[anyon_b].1;

        // Get fusion outcomes from fusion rules
        let fusion_outcomes = if let Some(outcomes) = type_a.fusion_rules.get(&type_b.label) {
            outcomes.clone()
        } else {
            vec!["vacuum".to_string()] // Default to vacuum
        };

        // Convert outcome labels to anyon types
        let outcome_types: Vec<AnyonType> = fusion_outcomes
            .iter()
            .map(|label| self.create_anyon_from_label(label))
            .collect::<Result<Vec<_>>>()?;

        // Remove the original anyons
        // Note: This is simplified - in a full implementation, we'd need to handle
        // the quantum superposition of fusion outcomes
        let mut indices_to_remove = vec![anyon_a, anyon_b];
        indices_to_remove.sort_by(|a, b| b.cmp(a)); // Remove in reverse order

        for &index in &indices_to_remove {
            if index < self.state.anyon_config.anyons.len() {
                self.state.anyon_config.anyons.remove(index);
            }
            if index < self.state.anyon_config.worldlines.len() {
                self.state.anyon_config.worldlines.remove(index);
            }
        }

        Ok(outcome_types)
    }

    /// Create anyon from label
    fn create_anyon_from_label(&self, label: &str) -> Result<AnyonType> {
        match label {
            "vacuum" => Ok(AnyonType::vacuum()),
            "sigma" => Ok(AnyonType::sigma()),
            "tau" => Ok(AnyonType::tau()),
            _ => {
                // Create a generic anyon
                Ok(AnyonType {
                    label: label.to_string(),
                    quantum_dimension: 1.0,
                    topological_charge: 0,
                    fusion_rules: HashMap::new(),
                    r_matrix: Complex64::new(1.0, 0.0),
                    is_abelian: true,
                })
            }
        }
    }

    /// Calculate topological invariants
    pub fn calculate_topological_invariants(&mut self) -> Result<TopologicalInvariants> {
        let mut invariants = TopologicalInvariants::default();

        // Calculate Chern number (simplified)
        invariants.chern_number = self.calculate_chern_number()?;

        // Calculate winding number
        invariants.winding_number = self.calculate_winding_number()?;

        // Calculate Z2 invariant
        invariants.z2_invariant = self.calculate_z2_invariant()?;

        // Calculate Berry phase
        invariants.berry_phase = self.calculate_berry_phase()?;

        // Calculate quantum Hall conductivity
        invariants.hall_conductivity = f64::from(invariants.chern_number) * 2.0 * PI / 137.0; // e²/h units

        // Calculate topological entanglement entropy
        invariants.topological_entanglement_entropy =
            self.calculate_topological_entanglement_entropy()?;

        self.state.topological_invariants = invariants.clone();
        Ok(invariants)
    }

    /// Calculate Chern number
    fn calculate_chern_number(&self) -> Result<i32> {
        // Simplified Chern number calculation
        // In a full implementation, this would involve Berry curvature integration
        let magnetic_flux = self.config.magnetic_field * self.lattice.sites.len() as f64;
        let flux_quanta = (magnetic_flux / (2.0 * PI)).round() as i32;
        Ok(flux_quanta)
    }

    /// Calculate winding number
    fn calculate_winding_number(&self) -> Result<i32> {
        // Simplified winding number for 1D systems
        match self.config.dimensions.len() {
            1 => Ok(1), // Assume non-trivial winding
            _ => Ok(0), // No winding in higher dimensions for this simple model
        }
    }

    /// Calculate Z2 invariant
    fn calculate_z2_invariant(&self) -> Result<bool> {
        // Simplified Z2 calculation based on time-reversal symmetry
        let time_reversal_broken = self.config.magnetic_field.abs() > 1e-10;
        Ok(!time_reversal_broken)
    }

    /// Calculate Berry phase
    fn calculate_berry_phase(&self) -> Result<f64> {
        // Simplified Berry phase calculation
        let total_braiding_phase: Complex64 = self
            .state
            .anyon_config
            .worldlines
            .iter()
            .map(|wl| wl.accumulated_phase)
            .fold(Complex64::new(1.0, 0.0), |acc, phase| acc * phase);

        Ok(total_braiding_phase.arg())
    }

    /// Calculate topological entanglement entropy
    fn calculate_topological_entanglement_entropy(&self) -> Result<f64> {
        // For topological phases, S_topo = -γ log(D) where D is total quantum dimension
        let total_quantum_dimension: f64 = self
            .anyon_model
            .get_anyon_types()
            .iter()
            .map(|anyon| anyon.quantum_dimension * anyon.quantum_dimension)
            .sum();

        let gamma = match self.config.anyon_model {
            AnyonModel::Abelian => 0.0,
            AnyonModel::Fibonacci => 0.5 * (5.0_f64.sqrt() - 1.0) / 2.0, // φ - 1
            AnyonModel::Ising => 0.5,
            _ => 0.5, // Default value
        };

        Ok(-gamma * total_quantum_dimension.ln())
    }

    /// Detect and correct topological errors
    pub fn detect_and_correct_errors(&mut self) -> Result<Vec<bool>> {
        if let Some(ref surface_code) = self.error_correction {
            let mut syndrome = Vec::new();

            // Measure stabilizers
            for detector in &surface_code.syndrome_detectors {
                let measurement = self.measure_stabilizer(detector)?;
                syndrome.push(measurement);
            }

            // Apply corrections based on syndrome
            let corrections = self.decode_syndrome(&syndrome)?;
            self.apply_corrections(&corrections)?;

            self.stats.error_corrections += 1;
            Ok(syndrome)
        } else {
            Ok(Vec::new())
        }
    }

    /// Measure stabilizer
    fn measure_stabilizer(&self, detector: &SyndromeDetector) -> Result<bool> {
        // Simplified stabilizer measurement
        // In a real implementation, this would measure Pauli operators
        let probability = match detector.stabilizer_type {
            StabilizerType::PauliX => 0.1, // Low error probability
            StabilizerType::PauliZ => 0.1,
            StabilizerType::XZ => 0.05,
        };

        Ok(fastrand::f64() < probability)
    }

    /// Decode error syndrome
    fn decode_syndrome(&self, syndrome: &[bool]) -> Result<Vec<usize>> {
        // Simplified syndrome decoding
        // In practice, this would use sophisticated decoders like MWPM
        let mut corrections = Vec::new();

        for (i, &error) in syndrome.iter().enumerate() {
            if error {
                corrections.push(i);
            }
        }

        Ok(corrections)
    }

    /// Apply error corrections
    fn apply_corrections(&mut self, corrections: &[usize]) -> Result<()> {
        // Apply Pauli corrections to the quantum state
        for &correction_site in corrections {
            if correction_site < self.state.amplitudes.len() {
                // Apply bit flip or phase flip correction
                // This is simplified - real implementation would apply proper Pauli operators
                self.state.amplitudes[correction_site] *= Complex64::new(-1.0, 0.0);
            }
        }

        Ok(())
    }

    /// Get current topological state
    #[must_use]
    pub const fn get_state(&self) -> &TopologicalState {
        &self.state
    }

    /// Get braiding history
    #[must_use]
    pub fn get_braiding_history(&self) -> &[BraidingOperation] {
        &self.braiding_history
    }

    /// Get simulation statistics
    #[must_use]
    pub const fn get_stats(&self) -> &TopologicalSimulationStats {
        &self.stats
    }

    /// Reset simulation
    pub fn reset(&mut self) -> Result<()> {
        self.state = Self::create_initial_topological_state(&self.config, &self.lattice)?;
        self.braiding_history.clear();
        self.stats = TopologicalSimulationStats::default();
        Ok(())
    }
}

// Anyon model implementations

/// Abelian anyon model
pub struct AbelianAnyons {
    anyon_types: Vec<AnyonType>,
}

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

impl AbelianAnyons {
    #[must_use]
    pub fn new() -> Self {
        let anyon_types = vec![AnyonType::vacuum()];
        Self { anyon_types }
    }
}

impl AnyonModelImplementation for AbelianAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }

    fn fusion_coefficients(&self, a: &AnyonType, b: &AnyonType, c: &AnyonType) -> Complex64 {
        // Abelian fusion: always 0 or 1
        if a.topological_charge + b.topological_charge == c.topological_charge {
            Complex64::new(1.0, 0.0)
        } else {
            Complex64::new(0.0, 0.0)
        }
    }

    fn braiding_matrix(&self, a: &AnyonType, b: &AnyonType) -> Array2<Complex64> {
        let phase = a.r_matrix * b.r_matrix.conj();
        Array2::from_shape_vec((1, 1), vec![phase])
            .expect("AbelianAnyons::braiding_matrix: 1x1 matrix shape is always valid")
    }

    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        // Trivial F-matrix for Abelian anyons
        Array2::eye(1)
    }

    fn is_abelian(&self) -> bool {
        true
    }

    fn name(&self) -> &'static str {
        "Abelian Anyons"
    }
}

/// Non-Abelian anyon model (generic)
pub struct NonAbelianAnyons {
    anyon_types: Vec<AnyonType>,
}

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

impl NonAbelianAnyons {
    #[must_use]
    pub fn new() -> Self {
        let anyon_types = vec![AnyonType::vacuum(), AnyonType::sigma()];
        Self { anyon_types }
    }
}

impl AnyonModelImplementation for NonAbelianAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }

    fn fusion_coefficients(&self, a: &AnyonType, b: &AnyonType, c: &AnyonType) -> Complex64 {
        // Non-Abelian fusion coefficients
        if let Some(outcomes) = a.fusion_rules.get(&b.label) {
            if outcomes.contains(&c.label) {
                Complex64::new(1.0, 0.0)
            } else {
                Complex64::new(0.0, 0.0)
            }
        } else {
            Complex64::new(0.0, 0.0)
        }
    }

    fn braiding_matrix(&self, a: &AnyonType, b: &AnyonType) -> Array2<Complex64> {
        let dim = (a.quantum_dimension * b.quantum_dimension) as usize;
        let mut matrix = Array2::eye(dim);

        // Non-trivial braiding for non-Abelian anyons
        if !a.is_abelian || !b.is_abelian {
            let phase = a.r_matrix * b.r_matrix.conj();
            matrix[[0, 0]] = phase;
            if dim > 1 {
                matrix[[1, 1]] = phase.conj();
            }
        }

        matrix
    }

    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        // Simplified F-matrix
        Array2::eye(2)
    }

    fn is_abelian(&self) -> bool {
        false
    }

    fn name(&self) -> &'static str {
        "Non-Abelian Anyons"
    }
}

/// Fibonacci anyon model
pub struct FibonacciAnyons {
    anyon_types: Vec<AnyonType>,
}

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

impl FibonacciAnyons {
    #[must_use]
    pub fn new() -> Self {
        let anyon_types = vec![AnyonType::vacuum(), AnyonType::tau()];
        Self { anyon_types }
    }
}

impl AnyonModelImplementation for FibonacciAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }

    fn fusion_coefficients(&self, a: &AnyonType, b: &AnyonType, c: &AnyonType) -> Complex64 {
        // Fibonacci fusion rules: τ × τ = 1 + τ
        match (a.label.as_str(), b.label.as_str(), c.label.as_str()) {
            ("tau", "tau", "vacuum" | "tau") => Complex64::new(1.0, 0.0),
            ("vacuum", _, label) | (_, "vacuum", label) if label == a.label || label == b.label => {
                Complex64::new(1.0, 0.0)
            }
            _ => Complex64::new(0.0, 0.0),
        }
    }

    fn braiding_matrix(&self, a: &AnyonType, b: &AnyonType) -> Array2<Complex64> {
        if a.label == "tau" && b.label == "tau" {
            let phi = f64::midpoint(1.0, 5.0_f64.sqrt()); // Golden ratio
            let phase = Complex64::new(0.0, 1.0) * (4.0 * PI / 5.0).exp();

            Array2::from_shape_vec(
                (2, 2),
                vec![
                    phase,
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    phase * Complex64::new(-1.0 / phi, 0.0),
                ],
            )
            .expect("FibonacciAnyons::braiding_matrix: 2x2 matrix shape is always valid")
        } else {
            Array2::eye(1)
        }
    }

    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        // Fibonacci F-matrix
        let phi = f64::midpoint(1.0, 5.0_f64.sqrt());
        let inv_phi = 1.0 / phi;

        Array2::from_shape_vec(
            (2, 2),
            vec![
                Complex64::new(inv_phi, 0.0),
                Complex64::new(inv_phi.sqrt(), 0.0),
                Complex64::new(inv_phi.sqrt(), 0.0),
                Complex64::new(-inv_phi, 0.0),
            ],
        )
        .expect("FibonacciAnyons::f_matrix: 2x2 matrix shape is always valid")
    }

    fn is_abelian(&self) -> bool {
        false
    }

    fn name(&self) -> &'static str {
        "Fibonacci Anyons"
    }
}

/// Ising anyon model (Majorana fermions)
pub struct IsingAnyons {
    anyon_types: Vec<AnyonType>,
}

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

impl IsingAnyons {
    #[must_use]
    pub fn new() -> Self {
        let mut psi = AnyonType {
            label: "psi".to_string(),
            quantum_dimension: 1.0,
            topological_charge: 1,
            fusion_rules: HashMap::new(),
            r_matrix: Complex64::new(-1.0, 0.0),
            is_abelian: true,
        };
        psi.fusion_rules
            .insert("psi".to_string(), vec!["vacuum".to_string()]);

        let anyon_types = vec![AnyonType::vacuum(), AnyonType::sigma(), psi];
        Self { anyon_types }
    }
}

impl AnyonModelImplementation for IsingAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }

    fn fusion_coefficients(&self, a: &AnyonType, b: &AnyonType, c: &AnyonType) -> Complex64 {
        // Ising fusion rules
        match (a.label.as_str(), b.label.as_str(), c.label.as_str()) {
            ("sigma", "sigma", "vacuum" | "psi") => Complex64::new(1.0, 0.0),
            ("psi", "psi", "vacuum") => Complex64::new(1.0, 0.0),
            ("sigma", "psi", "sigma") | ("psi", "sigma", "sigma") => Complex64::new(1.0, 0.0),
            ("vacuum", _, label) | (_, "vacuum", label) if label == a.label || label == b.label => {
                Complex64::new(1.0, 0.0)
            }
            _ => Complex64::new(0.0, 0.0),
        }
    }

    fn braiding_matrix(&self, a: &AnyonType, b: &AnyonType) -> Array2<Complex64> {
        let phase = a.r_matrix * b.r_matrix.conj();

        if a.label == "sigma" && b.label == "sigma" {
            // Non-trivial braiding for sigma anyons
            Array2::from_shape_vec(
                (2, 2),
                vec![
                    Complex64::new(0.0, 1.0) * (PI / 8.0).exp(),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, -1.0) * (PI / 8.0).exp(),
                ],
            )
            .expect("IsingAnyons::braiding_matrix: 2x2 matrix shape is always valid")
        } else {
            Array2::from_shape_vec((1, 1), vec![phase])
                .expect("IsingAnyons::braiding_matrix: 1x1 matrix shape is always valid")
        }
    }

    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        // Ising F-matrix
        let sqrt_2_inv = 1.0 / 2.0_f64.sqrt();
        Array2::from_shape_vec(
            (2, 2),
            vec![
                Complex64::new(sqrt_2_inv, 0.0),
                Complex64::new(sqrt_2_inv, 0.0),
                Complex64::new(sqrt_2_inv, 0.0),
                Complex64::new(-sqrt_2_inv, 0.0),
            ],
        )
        .expect("IsingAnyons::f_matrix: 2x2 matrix shape is always valid")
    }

    fn is_abelian(&self) -> bool {
        false
    }

    fn name(&self) -> &'static str {
        "Ising Anyons"
    }
}

// Placeholder implementations for other anyon models
pub struct ParafermionAnyons {
    anyon_types: Vec<AnyonType>,
}

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

impl ParafermionAnyons {
    #[must_use]
    pub fn new() -> Self {
        Self {
            anyon_types: vec![AnyonType::vacuum()],
        }
    }
}

impl AnyonModelImplementation for ParafermionAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }
    fn fusion_coefficients(&self, _a: &AnyonType, _b: &AnyonType, _c: &AnyonType) -> Complex64 {
        Complex64::new(1.0, 0.0)
    }
    fn braiding_matrix(&self, _a: &AnyonType, _b: &AnyonType) -> Array2<Complex64> {
        Array2::eye(1)
    }
    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        Array2::eye(1)
    }
    fn is_abelian(&self) -> bool {
        false
    }
    fn name(&self) -> &'static str {
        "Parafermion Anyons"
    }
}

pub struct ChernSimonsAnyons {
    level: u32,
    anyon_types: Vec<AnyonType>,
}

impl ChernSimonsAnyons {
    #[must_use]
    pub fn new(level: u32) -> Self {
        Self {
            level,
            anyon_types: vec![AnyonType::vacuum()],
        }
    }
}

impl AnyonModelImplementation for ChernSimonsAnyons {
    fn get_anyon_types(&self) -> Vec<AnyonType> {
        self.anyon_types.clone()
    }
    fn fusion_coefficients(&self, _a: &AnyonType, _b: &AnyonType, _c: &AnyonType) -> Complex64 {
        Complex64::new(1.0, 0.0)
    }
    fn braiding_matrix(&self, _a: &AnyonType, _b: &AnyonType) -> Array2<Complex64> {
        Array2::eye(1)
    }
    fn f_matrix(
        &self,
        _a: &AnyonType,
        _b: &AnyonType,
        _c: &AnyonType,
        _d: &AnyonType,
    ) -> Array2<Complex64> {
        Array2::eye(1)
    }
    fn is_abelian(&self) -> bool {
        self.level <= 2
    }
    fn name(&self) -> &'static str {
        "Chern-Simons Anyons"
    }
}

/// Topological utilities
pub struct TopologicalUtils;

impl TopologicalUtils {
    /// Create predefined topological configuration
    #[must_use]
    pub fn create_predefined_config(config_type: &str, size: usize) -> TopologicalConfig {
        match config_type {
            "toric_code" => TopologicalConfig {
                lattice_type: LatticeType::SquareLattice,
                dimensions: vec![size, size],
                anyon_model: AnyonModel::Abelian,
                boundary_conditions: TopologicalBoundaryConditions::Periodic,
                error_correction_code: TopologicalErrorCode::SurfaceCode,
                topological_protection: true,
                enable_braiding: false,
                ..Default::default()
            },
            "fibonacci_system" => TopologicalConfig {
                lattice_type: LatticeType::TriangularLattice,
                dimensions: vec![size, size],
                anyon_model: AnyonModel::Fibonacci,
                boundary_conditions: TopologicalBoundaryConditions::Open,
                topological_protection: true,
                enable_braiding: true,
                ..Default::default()
            },
            "majorana_system" => TopologicalConfig {
                lattice_type: LatticeType::HoneycombLattice,
                dimensions: vec![size, size],
                anyon_model: AnyonModel::Ising,
                boundary_conditions: TopologicalBoundaryConditions::Open,
                topological_protection: true,
                enable_braiding: true,
                ..Default::default()
            },
            _ => TopologicalConfig::default(),
        }
    }

    /// Benchmark topological simulation performance
    pub fn benchmark_topological_simulation() -> Result<TopologicalBenchmarkResults> {
        let mut results = TopologicalBenchmarkResults::default();

        let configs = vec![
            (
                "toric_code",
                Self::create_predefined_config("toric_code", 4),
            ),
            (
                "fibonacci",
                Self::create_predefined_config("fibonacci_system", 3),
            ),
            (
                "majorana",
                Self::create_predefined_config("majorana_system", 3),
            ),
        ];

        for (name, config) in configs {
            let mut simulator = TopologicalQuantumSimulator::new(config)?;

            // Place some anyons
            if simulator.config.enable_braiding {
                let vacuum = AnyonType::vacuum();
                simulator.place_anyon(vacuum.clone(), vec![0, 0])?;
                simulator.place_anyon(vacuum, vec![1, 1])?;
            }

            let start = std::time::Instant::now();

            // Perform some operations
            if simulator.config.enable_braiding && simulator.state.anyon_config.anyons.len() >= 2 {
                simulator.braid_anyons(0, 1, BraidingType::Clockwise)?;
            }

            simulator.calculate_topological_invariants()?;

            let time = start.elapsed().as_secs_f64() * 1000.0;

            results.benchmark_times.push((name.to_string(), time));
            results
                .simulation_stats
                .insert(name.to_string(), simulator.get_stats().clone());
        }

        Ok(results)
    }
}

/// Benchmark results for topological simulation
#[derive(Debug, Clone, Default)]
pub struct TopologicalBenchmarkResults {
    /// Benchmark times by configuration
    pub benchmark_times: Vec<(String, f64)>,
    /// Simulation statistics by configuration
    pub simulation_stats: HashMap<String, TopologicalSimulationStats>,
}

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

    #[test]
    fn test_topological_config_default() {
        let config = TopologicalConfig::default();
        assert_eq!(config.lattice_type, LatticeType::SquareLattice);
        assert_eq!(config.dimensions, vec![8, 8]);
        assert!(config.topological_protection);
    }

    #[test]
    fn test_anyon_type_creation() {
        let vacuum = AnyonType::vacuum();
        assert_eq!(vacuum.label, "vacuum");
        assert_eq!(vacuum.quantum_dimension, 1.0);
        assert!(vacuum.is_abelian);

        let sigma = AnyonType::sigma();
        assert_eq!(sigma.label, "sigma");
        assert_abs_diff_eq!(sigma.quantum_dimension, 2.0_f64.sqrt(), epsilon = 1e-10);
        assert!(!sigma.is_abelian);
    }

    #[test]
    fn test_topological_simulator_creation() {
        let config = TopologicalConfig::default();
        let simulator = TopologicalQuantumSimulator::new(config);
        assert!(simulator.is_ok());
    }

    #[test]
    fn test_square_lattice_creation() {
        let dimensions = vec![3, 3];
        let lattice = TopologicalQuantumSimulator::create_square_lattice(&dimensions)
            .expect("failed to create square lattice");

        assert_eq!(lattice.sites.len(), 9); // 3x3 = 9 sites
        assert_eq!(lattice.coordination_number, 4);
        assert!(!lattice.bonds.is_empty());
        assert!(!lattice.plaquettes.is_empty());
    }

    #[test]
    fn test_anyon_placement() {
        let config = TopologicalConfig::default();
        let mut simulator =
            TopologicalQuantumSimulator::new(config).expect("failed to create simulator");

        let vacuum = AnyonType::vacuum();
        let anyon_id = simulator
            .place_anyon(vacuum, vec![2, 3])
            .expect("failed to place anyon");

        assert_eq!(anyon_id, 0);
        assert_eq!(simulator.state.anyon_config.anyons.len(), 1);
        assert_eq!(simulator.state.anyon_config.anyons[0].0, vec![2, 3]);
    }

    #[test]
    fn test_braiding_operation() {
        let mut config = TopologicalConfig::default();
        config.enable_braiding = true;
        let mut simulator =
            TopologicalQuantumSimulator::new(config).expect("failed to create simulator");

        let sigma = AnyonType::sigma();
        let anyon_a = simulator
            .place_anyon(sigma.clone(), vec![1, 1])
            .expect("failed to place anyon A");
        let anyon_b = simulator
            .place_anyon(sigma, vec![2, 2])
            .expect("failed to place anyon B");

        let braiding_phase = simulator.braid_anyons(anyon_a, anyon_b, BraidingType::Clockwise);
        assert!(braiding_phase.is_ok());
        assert_eq!(simulator.braiding_history.len(), 1);
        assert_eq!(simulator.stats.braiding_operations, 1);
    }

    #[test]
    fn test_anyon_fusion() {
        let config = TopologicalConfig::default();
        let mut simulator =
            TopologicalQuantumSimulator::new(config).expect("failed to create simulator");

        let sigma = AnyonType::sigma();
        let anyon_a = simulator
            .place_anyon(sigma.clone(), vec![1, 1])
            .expect("failed to place anyon A");
        let anyon_b = simulator
            .place_anyon(sigma, vec![1, 2])
            .expect("failed to place anyon B");

        let fusion_outcomes = simulator.fuse_anyons(anyon_a, anyon_b);
        assert!(fusion_outcomes.is_ok());
    }

    #[test]
    fn test_fibonacci_anyons() {
        let fibonacci_model = FibonacciAnyons::new();
        let anyon_types = fibonacci_model.get_anyon_types();

        assert_eq!(anyon_types.len(), 2); // vacuum and tau
        assert!(!fibonacci_model.is_abelian());
        assert_eq!(fibonacci_model.name(), "Fibonacci Anyons");
    }

    #[test]
    fn test_ising_anyons() {
        let ising_model = IsingAnyons::new();
        let anyon_types = ising_model.get_anyon_types();

        assert_eq!(anyon_types.len(), 3); // vacuum, sigma, psi
        assert!(!ising_model.is_abelian());
        assert_eq!(ising_model.name(), "Ising Anyons");
    }

    #[test]
    fn test_surface_code_creation() {
        let dimensions = vec![4, 4];
        let surface_code = TopologicalQuantumSimulator::create_toric_surface_code(&dimensions)
            .expect("failed to create surface code");

        assert_eq!(surface_code.distance, 4);
        assert!(!surface_code.data_qubits.is_empty());
        assert!(!surface_code.x_stabilizers.is_empty());
        assert!(!surface_code.z_stabilizers.is_empty());
    }

    #[test]
    fn test_topological_invariants() {
        let config = TopologicalConfig::default();
        let mut simulator =
            TopologicalQuantumSimulator::new(config).expect("failed to create simulator");

        let invariants = simulator.calculate_topological_invariants();
        assert!(invariants.is_ok());

        let inv = invariants.expect("failed to calculate invariants");
        assert!(inv.chern_number.abs() >= 0);
        assert!(inv.hall_conductivity.is_finite());
    }

    #[test]
    fn test_triangular_lattice() {
        let dimensions = vec![3, 3];
        let lattice = TopologicalQuantumSimulator::create_triangular_lattice(&dimensions)
            .expect("failed to create triangular lattice");

        assert_eq!(lattice.lattice_type, LatticeType::TriangularLattice);
        assert_eq!(lattice.sites.len(), 9);
        assert_eq!(lattice.coordination_number, 6);
    }

    #[test]
    fn test_honeycomb_lattice() {
        let dimensions = vec![2, 2];
        let lattice = TopologicalQuantumSimulator::create_honeycomb_lattice(&dimensions)
            .expect("failed to create honeycomb lattice");

        assert_eq!(lattice.lattice_type, LatticeType::HoneycombLattice);
        assert_eq!(lattice.coordination_number, 3);
        assert!(!lattice.bonds.is_empty());
    }

    #[test]
    fn test_error_detection_and_correction() {
        let mut config = TopologicalConfig::default();
        config.topological_protection = true;
        let mut simulator =
            TopologicalQuantumSimulator::new(config).expect("failed to create simulator");

        let syndrome = simulator.detect_and_correct_errors();
        assert!(syndrome.is_ok());
    }

    #[test]
    fn test_predefined_configs() {
        let configs = vec!["toric_code", "fibonacci_system", "majorana_system"];

        for config_type in configs {
            let config = TopologicalUtils::create_predefined_config(config_type, 4);
            let simulator = TopologicalQuantumSimulator::new(config);
            assert!(simulator.is_ok());
        }
    }
}