quantrs2_sim/

quantum_reservoir_computing_enhanced.rs

//! Enhanced Quantum Reservoir Computing Framework - Ultrathink Mode Implementation
//!
//! This module provides a comprehensive implementation of quantum reservoir computing (QRC),
//! a cutting-edge computational paradigm that leverages the high-dimensional, nonlinear
//! dynamics of quantum systems for temporal information processing and machine learning.
//! This ultrathink mode implementation includes advanced learning algorithms, sophisticated
//! reservoir topologies, real-time adaptation, and comprehensive analysis tools.
//!
//! ## Core Features
//! - **Advanced Quantum Reservoirs**: Multiple sophisticated architectures including scale-free,
//!   hierarchical, modular, and adaptive topologies
//! - **Comprehensive Learning Algorithms**: Ridge regression, LASSO, Elastic Net, RLS, Kalman
//!   filtering, neural network readouts, and meta-learning approaches
//! - **Time Series Modeling**: ARIMA-like capabilities, nonlinear autoregressive models,
//!   memory kernels, and temporal correlation analysis
//! - **Real-time Adaptation**: Online learning algorithms with forgetting factors, plasticity
//!   mechanisms, and adaptive reservoir modification
//! - **Memory Analysis Tools**: Quantum memory capacity estimation, nonlinear memory measures,
//!   temporal information processing capacity, and correlation analysis
//! - **Hardware-aware Optimization**: Device-specific compilation, noise-aware training,
//!   error mitigation, and platform-specific optimizations
//! - **Comprehensive Benchmarking**: Multiple datasets, statistical significance testing,
//!   comparative analysis, and performance validation frameworks
//! - **Advanced Quantum Dynamics**: Unitary evolution, open system dynamics, NISQ simulation,
//!   adiabatic processes, and quantum error correction integration

use scirs2_core::ndarray::{s, Array1, Array2, Array3, ArrayView1, ArrayView2, Axis};
use scirs2_core::parallel_ops::{IndexedParallelIterator, ParallelIterator};
use scirs2_core::random::{thread_rng, Rng};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, VecDeque};
use std::f64::consts::PI;
use std::sync::{Arc, Mutex};

use crate::circuit_interfaces::{
    CircuitInterface, InterfaceCircuit, InterfaceGate, InterfaceGateType,
};
use crate::error::Result;
use crate::scirs2_integration::SciRS2Backend;
use crate::statevector::StateVectorSimulator;
use scirs2_core::random::prelude::*;

/// Advanced quantum reservoir architecture types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum QuantumReservoirArchitecture {
    /// Random quantum circuit with tunable connectivity
    RandomCircuit,
    /// Spin chain with configurable interactions
    SpinChain,
    /// Transverse field Ising model with variable field strength
    TransverseFieldIsing,
    /// Small-world network with rewiring probability
    SmallWorld,
    /// Fully connected all-to-all interactions
    FullyConnected,
    /// Scale-free network following power-law degree distribution
    ScaleFree,
    /// Hierarchical modular architecture with multiple levels
    HierarchicalModular,
    /// Adaptive topology that evolves during computation
    AdaptiveTopology,
    /// Quantum cellular automaton structure
    QuantumCellularAutomaton,
    /// Ring topology with long-range connections
    Ring,
    /// Grid/lattice topology with configurable dimensions
    Grid,
    /// Tree topology with branching factor
    Tree,
    /// Hypergraph topology with higher-order interactions
    Hypergraph,
    /// Tensor network inspired architecture
    TensorNetwork,
    /// Custom user-defined architecture
    Custom,
}

/// Advanced reservoir dynamics types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ReservoirDynamics {
    /// Unitary evolution with perfect coherence
    Unitary,
    /// Open system dynamics with Lindblad operators
    Open,
    /// Noisy intermediate-scale quantum (NISQ) dynamics
    NISQ,
    /// Adiabatic quantum evolution
    Adiabatic,
    /// Floquet dynamics with periodic driving
    Floquet,
    /// Quantum walk dynamics
    QuantumWalk,
    /// Continuous-time quantum dynamics
    ContinuousTime,
    /// Digital quantum simulation with Trotter decomposition
    DigitalQuantum,
    /// Variational quantum dynamics
    Variational,
    /// Hamiltonian learning dynamics
    HamiltonianLearning,
    /// Many-body localized dynamics
    ManyBodyLocalized,
    /// Quantum chaotic dynamics
    QuantumChaotic,
}

/// Advanced input encoding methods for temporal data
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum InputEncoding {
    /// Amplitude encoding with normalization
    Amplitude,
    /// Phase encoding with full 2π range
    Phase,
    /// Basis state encoding with binary representation
    BasisState,
    /// Coherent state encoding with displacement
    Coherent,
    /// Squeezed state encoding with squeezing parameter
    Squeezed,
    /// Angle encoding with rotation gates
    Angle,
    /// IQP encoding with diagonal unitaries
    IQP,
    /// Data re-uploading with multiple layers
    DataReUploading,
    /// Quantum feature map encoding
    QuantumFeatureMap,
    /// Variational encoding with trainable parameters
    VariationalEncoding,
    /// Temporal encoding with time-dependent parameters
    TemporalEncoding,
    /// Fourier encoding for frequency domain
    FourierEncoding,
    /// Wavelet encoding for multi-resolution
    WaveletEncoding,
    /// Haar random encoding
    HaarRandom,
    /// Graph encoding for structured data
    GraphEncoding,
}

/// Advanced output measurement strategies
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum OutputMeasurement {
    /// Pauli expectation values (X, Y, Z)
    PauliExpectation,
    /// Computational basis probability measurements
    Probability,
    /// Two-qubit correlation functions
    Correlations,
    /// Entanglement entropy and concurrence
    Entanglement,
    /// State fidelity with reference states
    Fidelity,
    /// Quantum Fisher information
    QuantumFisherInformation,
    /// Variance of observables
    Variance,
    /// Higher-order moments and cumulants
    HigherOrderMoments,
    /// Spectral properties and eigenvalues
    SpectralProperties,
    /// Quantum coherence measures
    QuantumCoherence,
    /// Purity and mixedness measures
    Purity,
    /// Quantum mutual information
    QuantumMutualInformation,
    /// Process tomography observables
    ProcessTomography,
    /// Temporal correlations
    TemporalCorrelations,
    /// Non-linear readout functions
    NonLinearReadout,
}

/// Advanced learning algorithm types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum LearningAlgorithm {
    /// Ridge regression with L2 regularization
    Ridge,
    /// LASSO regression with L1 regularization
    LASSO,
    /// Elastic Net combining L1 and L2 regularization
    ElasticNet,
    /// Recursive Least Squares with forgetting factor
    RecursiveLeastSquares,
    /// Kalman filter for adaptive learning
    KalmanFilter,
    /// Extended Kalman filter for nonlinear systems
    ExtendedKalmanFilter,
    /// Neural network readout layer
    NeuralNetwork,
    /// Support Vector Regression
    SupportVectorRegression,
    /// Gaussian Process regression
    GaussianProcess,
    /// Random Forest regression
    RandomForest,
    /// Gradient boosting regression
    GradientBoosting,
    /// Online gradient descent
    OnlineGradientDescent,
    /// Adam optimizer
    Adam,
    /// Meta-learning approach
    MetaLearning,
}

/// Neural network activation functions
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ActivationFunction {
    /// Rectified Linear Unit
    ReLU,
    /// Leaky `ReLU`
    LeakyReLU,
    /// Exponential Linear Unit
    ELU,
    /// Sigmoid activation
    Sigmoid,
    /// Hyperbolic tangent
    Tanh,
    /// Swish activation
    Swish,
    /// GELU activation
    GELU,
    /// Linear activation
    Linear,
}

/// Memory kernel types for time series modeling
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum MemoryKernel {
    /// Exponential decay kernel
    Exponential,
    /// Power law kernel
    PowerLaw,
    /// Gaussian kernel
    Gaussian,
    /// Polynomial kernel
    Polynomial,
    /// Rational kernel
    Rational,
    /// Sinusoidal kernel
    Sinusoidal,
    /// Custom kernel
    Custom,
}

/// Enhanced quantum reservoir computing configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumReservoirConfig {
    /// Number of qubits in the reservoir
    pub num_qubits: usize,
    /// Reservoir architecture type
    pub architecture: QuantumReservoirArchitecture,
    /// Dynamics evolution type
    pub dynamics: ReservoirDynamics,
    /// Input encoding method
    pub input_encoding: InputEncoding,
    /// Output measurement strategy
    pub output_measurement: OutputMeasurement,
    /// Advanced learning algorithm configuration
    pub learning_config: AdvancedLearningConfig,
    /// Time series modeling configuration
    pub time_series_config: TimeSeriesConfig,
    /// Memory analysis configuration
    pub memory_config: MemoryAnalysisConfig,
    /// Time step for evolution
    pub time_step: f64,
    /// Number of evolution steps per input
    pub evolution_steps: usize,
    /// Reservoir coupling strength
    pub coupling_strength: f64,
    /// Noise level (for NISQ dynamics)
    pub noise_level: f64,
    /// Memory capacity (time steps to remember)
    pub memory_capacity: usize,
    /// Enable real-time adaptation
    pub adaptive_learning: bool,
    /// Learning rate for adaptation
    pub learning_rate: f64,
    /// Washout period (initial time steps to ignore)
    pub washout_period: usize,
    /// Random seed for reproducibility
    pub random_seed: Option<u64>,
    /// Enable quantum error correction
    pub enable_qec: bool,
    /// Precision for calculations
    pub precision: f64,
}

impl Default for QuantumReservoirConfig {
    fn default() -> Self {
        Self {
            num_qubits: 8,
            architecture: QuantumReservoirArchitecture::RandomCircuit,
            dynamics: ReservoirDynamics::Unitary,
            input_encoding: InputEncoding::Amplitude,
            output_measurement: OutputMeasurement::PauliExpectation,
            learning_config: AdvancedLearningConfig::default(),
            time_series_config: TimeSeriesConfig::default(),
            memory_config: MemoryAnalysisConfig::default(),
            time_step: 0.1,
            evolution_steps: 10,
            coupling_strength: 1.0,
            noise_level: 0.01,
            memory_capacity: 100,
            adaptive_learning: true,
            learning_rate: 0.01,
            washout_period: 50,
            random_seed: None,
            enable_qec: false,
            precision: 1e-8,
        }
    }
}

/// Advanced learning algorithm configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AdvancedLearningConfig {
    /// Primary learning algorithm
    pub algorithm: LearningAlgorithm,
    /// Regularization parameter (lambda)
    pub regularization: f64,
    /// L1 ratio for Elastic Net (0.0 = Ridge, 1.0 = LASSO)
    pub l1_ratio: f64,
    /// Forgetting factor for RLS
    pub forgetting_factor: f64,
    /// Process noise for Kalman filter
    pub process_noise: f64,
    /// Measurement noise for Kalman filter
    pub measurement_noise: f64,
    /// Neural network architecture
    pub nn_architecture: Vec<usize>,
    /// Neural network activation function
    pub nn_activation: ActivationFunction,
    /// Number of training epochs
    pub epochs: usize,
    /// Batch size for training
    pub batch_size: usize,
    /// Early stopping patience
    pub early_stopping_patience: usize,
    /// Cross-validation folds
    pub cv_folds: usize,
    /// Enable ensemble methods
    pub enable_ensemble: bool,
    /// Number of ensemble members
    pub ensemble_size: usize,
}

impl Default for AdvancedLearningConfig {
    fn default() -> Self {
        Self {
            algorithm: LearningAlgorithm::Ridge,
            regularization: 1e-6,
            l1_ratio: 0.5,
            forgetting_factor: 0.99,
            process_noise: 1e-4,
            measurement_noise: 1e-3,
            nn_architecture: vec![64, 32, 16],
            nn_activation: ActivationFunction::ReLU,
            epochs: 100,
            batch_size: 32,
            early_stopping_patience: 10,
            cv_folds: 5,
            enable_ensemble: false,
            ensemble_size: 5,
        }
    }
}

/// Time series modeling configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TimeSeriesConfig {
    /// Enable ARIMA-like modeling
    pub enable_arima: bool,
    /// AR order (autoregressive)
    pub ar_order: usize,
    /// MA order (moving average)
    pub ma_order: usize,
    /// Differencing order
    pub diff_order: usize,
    /// Enable nonlinear autoregressive model
    pub enable_nar: bool,
    /// NAR model order
    pub nar_order: usize,
    /// Memory kernel type
    pub memory_kernel: MemoryKernel,
    /// Kernel parameters
    pub kernel_params: Vec<f64>,
    /// Enable seasonal decomposition
    pub enable_seasonal: bool,
    /// Seasonal period
    pub seasonal_period: usize,
    /// Enable change point detection
    pub enable_changepoint: bool,
    /// Anomaly detection threshold
    pub anomaly_threshold: f64,
}

impl Default for TimeSeriesConfig {
    fn default() -> Self {
        Self {
            enable_arima: true,
            ar_order: 2,
            ma_order: 1,
            diff_order: 1,
            enable_nar: true,
            nar_order: 3,
            memory_kernel: MemoryKernel::Exponential,
            kernel_params: vec![0.9, 0.1],
            enable_seasonal: false,
            seasonal_period: 12,
            enable_changepoint: false,
            anomaly_threshold: 2.0,
        }
    }
}

/// Memory analysis configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct MemoryAnalysisConfig {
    /// Enable memory capacity estimation
    pub enable_capacity_estimation: bool,
    /// Memory capacity test tasks
    pub capacity_tasks: Vec<MemoryTask>,
    /// Enable nonlinear memory analysis
    pub enable_nonlinear: bool,
    /// Nonlinearity test orders
    pub nonlinearity_orders: Vec<usize>,
    /// Enable temporal correlation analysis
    pub enable_temporal_correlation: bool,
    /// Correlation lag range
    pub correlation_lags: Vec<usize>,
    /// Information processing capacity
    pub enable_ipc: bool,
    /// IPC test functions
    pub ipc_functions: Vec<IPCFunction>,
    /// Enable entropy analysis
    pub enable_entropy: bool,
}

impl Default for MemoryAnalysisConfig {
    fn default() -> Self {
        Self {
            enable_capacity_estimation: true,
            capacity_tasks: vec![
                MemoryTask::DelayLine,
                MemoryTask::TemporalXOR,
                MemoryTask::Parity,
            ],
            enable_nonlinear: true,
            nonlinearity_orders: vec![2, 3, 4],
            enable_temporal_correlation: true,
            correlation_lags: (1..=20).collect(),
            enable_ipc: true,
            ipc_functions: vec![
                IPCFunction::Linear,
                IPCFunction::Quadratic,
                IPCFunction::Cubic,
            ],
            enable_entropy: true,
        }
    }
}

/// Memory capacity test tasks
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum MemoryTask {
    /// Delay line memory
    DelayLine,
    /// Temporal XOR task
    TemporalXOR,
    /// Parity check task
    Parity,
    /// Sequence prediction
    SequencePrediction,
    /// Pattern completion
    PatternCompletion,
    /// Temporal integration
    TemporalIntegration,
}

/// Information processing capacity functions
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum IPCFunction {
    /// Linear function
    Linear,
    /// Quadratic function
    Quadratic,
    /// Cubic function
    Cubic,
    /// Sine function
    Sine,
    /// Product function
    Product,
    /// XOR function
    XOR,
}

/// Enhanced quantum reservoir state
#[derive(Debug, Clone)]
pub struct QuantumReservoirState {
    /// Current quantum state vector
    pub state_vector: Array1<Complex64>,
    /// Evolution history buffer
    pub state_history: VecDeque<Array1<Complex64>>,
    /// Observable measurements cache
    pub observables: HashMap<String, f64>,
    /// Two-qubit correlation matrix
    pub correlations: Array2<f64>,
    /// Higher-order correlations
    pub higher_order_correlations: HashMap<String, f64>,
    /// Entanglement measures
    pub entanglement_measures: HashMap<String, f64>,
    /// Memory capacity metrics
    pub memory_metrics: MemoryMetrics,
    /// Time index counter
    pub time_index: usize,
    /// Last update timestamp
    pub last_update: f64,
    /// Reservoir activity level
    pub activity_level: f64,
    /// Performance tracking
    pub performance_history: VecDeque<f64>,
}

/// Memory analysis metrics
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct MemoryMetrics {
    /// Linear memory capacity
    pub linear_capacity: f64,
    /// Nonlinear memory capacity
    pub nonlinear_capacity: f64,
    /// Total memory capacity
    pub total_capacity: f64,
    /// Information processing capacity
    pub processing_capacity: f64,
    /// Temporal correlation length
    pub correlation_length: f64,
    /// Memory decay rate
    pub decay_rate: f64,
    /// Memory efficiency
    pub efficiency: f64,
}

impl QuantumReservoirState {
    /// Create new enhanced reservoir state
    #[must_use]
    pub fn new(num_qubits: usize, memory_capacity: usize) -> Self {
        let state_size = 1 << num_qubits;
        let mut state_vector = Array1::zeros(state_size);
        state_vector[0] = Complex64::new(1.0, 0.0); // Start in |0...0⟩

        Self {
            state_vector,
            state_history: VecDeque::with_capacity(memory_capacity),
            observables: HashMap::new(),
            correlations: Array2::zeros((num_qubits, num_qubits)),
            higher_order_correlations: HashMap::new(),
            entanglement_measures: HashMap::new(),
            memory_metrics: MemoryMetrics::default(),
            time_index: 0,
            last_update: 0.0,
            activity_level: 0.0,
            performance_history: VecDeque::with_capacity(1000),
        }
    }

    /// Update state and maintain comprehensive history
    pub fn update_state(&mut self, new_state: Array1<Complex64>, timestamp: f64) {
        // Store previous state
        self.state_history.push_back(self.state_vector.clone());
        if self.state_history.len() > self.state_history.capacity() {
            self.state_history.pop_front();
        }

        // Update current state
        self.state_vector = new_state;
        self.time_index += 1;
        self.last_update = timestamp;

        // Update activity level
        self.update_activity_level();
    }

    /// Update reservoir activity level
    fn update_activity_level(&mut self) {
        let activity = self
            .state_vector
            .iter()
            .map(scirs2_core::Complex::norm_sqr)
            .sum::<f64>()
            / self.state_vector.len() as f64;

        // Exponential moving average
        let alpha = 0.1;
        self.activity_level = alpha * activity + (1.0 - alpha) * self.activity_level;
    }

    /// Calculate memory decay
    #[must_use]
    pub fn calculate_memory_decay(&self) -> f64 {
        if self.state_history.len() < 2 {
            return 0.0;
        }

        let mut total_decay = 0.0;
        let current_state = &self.state_vector;

        for (i, past_state) in self.state_history.iter().enumerate() {
            let fidelity = self.calculate_fidelity(current_state, past_state);
            let time_diff = (self.state_history.len() - i) as f64;
            total_decay += fidelity * (-time_diff * 0.1).exp();
        }

        total_decay / self.state_history.len() as f64
    }

    /// Calculate fidelity between two states
    fn calculate_fidelity(&self, state1: &Array1<Complex64>, state2: &Array1<Complex64>) -> f64 {
        let overlap = state1
            .iter()
            .zip(state2.iter())
            .map(|(a, b)| a.conj() * b)
            .sum::<Complex64>();
        overlap.norm_sqr()
    }
}

/// Enhanced training data for reservoir computing
#[derive(Debug, Clone)]
pub struct ReservoirTrainingData {
    /// Input time series
    pub inputs: Vec<Array1<f64>>,
    /// Target outputs
    pub targets: Vec<Array1<f64>>,
    /// Time stamps
    pub timestamps: Vec<f64>,
    /// Additional features
    pub features: Option<Vec<Array1<f64>>>,
    /// Data labels for classification
    pub labels: Option<Vec<usize>>,
    /// Sequence lengths for variable-length sequences
    pub sequence_lengths: Option<Vec<usize>>,
    /// Missing data indicators
    pub missing_mask: Option<Vec<Array1<bool>>>,
    /// Data weights for importance sampling
    pub sample_weights: Option<Vec<f64>>,
    /// Metadata for each sample
    pub metadata: Option<Vec<HashMap<String, String>>>,
}

impl ReservoirTrainingData {
    /// Create new training data
    #[must_use]
    pub const fn new(
        inputs: Vec<Array1<f64>>,
        targets: Vec<Array1<f64>>,
        timestamps: Vec<f64>,
    ) -> Self {
        Self {
            inputs,
            targets,
            timestamps,
            features: None,
            labels: None,
            sequence_lengths: None,
            missing_mask: None,
            sample_weights: None,
            metadata: None,
        }
    }

    /// Add features to training data
    #[must_use]
    pub fn with_features(mut self, features: Vec<Array1<f64>>) -> Self {
        self.features = Some(features);
        self
    }

    /// Add labels for classification
    #[must_use]
    pub fn with_labels(mut self, labels: Vec<usize>) -> Self {
        self.labels = Some(labels);
        self
    }

    /// Add sample weights
    #[must_use]
    pub fn with_weights(mut self, weights: Vec<f64>) -> Self {
        self.sample_weights = Some(weights);
        self
    }

    /// Get data length
    #[must_use]
    pub fn len(&self) -> usize {
        self.inputs.len()
    }

    /// Check if data is empty
    #[must_use]
    pub fn is_empty(&self) -> bool {
        self.inputs.is_empty()
    }

    /// Split data into train/test sets
    #[must_use]
    pub fn train_test_split(&self, test_ratio: f64) -> (Self, Self) {
        let test_size = (self.len() as f64 * test_ratio) as usize;
        let train_size = self.len() - test_size;

        let train_data = Self {
            inputs: self.inputs[..train_size].to_vec(),
            targets: self.targets[..train_size].to_vec(),
            timestamps: self.timestamps[..train_size].to_vec(),
            features: self.features.as_ref().map(|f| f[..train_size].to_vec()),
            labels: self.labels.as_ref().map(|l| l[..train_size].to_vec()),
            sequence_lengths: self
                .sequence_lengths
                .as_ref()
                .map(|s| s[..train_size].to_vec()),
            missing_mask: self.missing_mask.as_ref().map(|m| m[..train_size].to_vec()),
            sample_weights: self
                .sample_weights
                .as_ref()
                .map(|w| w[..train_size].to_vec()),
            metadata: self.metadata.as_ref().map(|m| m[..train_size].to_vec()),
        };

        let test_data = Self {
            inputs: self.inputs[train_size..].to_vec(),
            targets: self.targets[train_size..].to_vec(),
            timestamps: self.timestamps[train_size..].to_vec(),
            features: self.features.as_ref().map(|f| f[train_size..].to_vec()),
            labels: self.labels.as_ref().map(|l| l[train_size..].to_vec()),
            sequence_lengths: self
                .sequence_lengths
                .as_ref()
                .map(|s| s[train_size..].to_vec()),
            missing_mask: self.missing_mask.as_ref().map(|m| m[train_size..].to_vec()),
            sample_weights: self
                .sample_weights
                .as_ref()
                .map(|w| w[train_size..].to_vec()),
            metadata: self.metadata.as_ref().map(|m| m[train_size..].to_vec()),
        };

        (train_data, test_data)
    }
}

/// Enhanced training example for reservoir learning
#[derive(Debug, Clone)]
pub struct TrainingExample {
    /// Input data
    pub input: Array1<f64>,
    /// Reservoir state after processing
    pub reservoir_state: Array1<f64>,
    /// Extracted features
    pub features: Array1<f64>,
    /// Target output
    pub target: Array1<f64>,
    /// Predicted output
    pub prediction: Array1<f64>,
    /// Prediction error
    pub error: f64,
    /// Confidence score
    pub confidence: f64,
    /// Processing timestamp
    pub timestamp: f64,
    /// Additional metadata
    pub metadata: HashMap<String, f64>,
}

/// Enhanced performance metrics for reservoir computing
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct ReservoirMetrics {
    /// Total training examples processed
    pub training_examples: usize,
    /// Current prediction accuracy
    pub prediction_accuracy: f64,
    /// Memory capacity estimate
    pub memory_capacity: f64,
    /// Nonlinear memory capacity
    pub nonlinear_memory_capacity: f64,
    /// Information processing capacity
    pub processing_capacity: f64,
    /// Generalization error
    pub generalization_error: f64,
    /// Echo state property indicator
    pub echo_state_property: f64,
    /// Average processing time per input
    pub avg_processing_time_ms: f64,
    /// Quantum resource utilization
    pub quantum_resource_usage: f64,
    /// Temporal correlation length
    pub temporal_correlation_length: f64,
    /// Reservoir efficiency
    pub reservoir_efficiency: f64,
    /// Adaptation rate
    pub adaptation_rate: f64,
    /// Plasticity level
    pub plasticity_level: f64,
    /// Hardware utilization
    pub hardware_utilization: f64,
    /// Error mitigation overhead
    pub error_mitigation_overhead: f64,
    /// Quantum advantage metric
    pub quantum_advantage: f64,
    /// Computational complexity
    pub computational_complexity: f64,
}

/// Enhanced quantum reservoir computing system
pub struct QuantumReservoirComputerEnhanced {
    /// Configuration
    config: QuantumReservoirConfig,
    /// Current reservoir state
    reservoir_state: QuantumReservoirState,
    /// Reservoir circuit
    reservoir_circuit: InterfaceCircuit,
    /// Input coupling circuit
    input_coupling_circuit: InterfaceCircuit,
    /// Output weights (trainable)
    output_weights: Array2<f64>,
    /// Time series predictor
    time_series_predictor: Option<TimeSeriesPredictor>,
    /// Memory analyzer
    memory_analyzer: MemoryAnalyzer,
    /// State vector simulator
    simulator: StateVectorSimulator,
    /// Circuit interface
    circuit_interface: CircuitInterface,
    /// Performance metrics
    metrics: ReservoirMetrics,
    /// Training history
    training_history: VecDeque<TrainingExample>,
    /// `SciRS2` backend for advanced computations
    backend: Option<SciRS2Backend>,
    /// Random number generator
    rng: Arc<Mutex<scirs2_core::random::CoreRandom>>,
}

/// Time series prediction models
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TimeSeriesPredictor {
    /// ARIMA model parameters
    pub arima_params: ARIMAParams,
    /// NAR model state
    pub nar_state: NARState,
    /// Memory kernel weights
    pub kernel_weights: Array1<f64>,
    /// Trend model
    pub trend_model: TrendModel,
}

/// ARIMA model parameters
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ARIMAParams {
    /// AR coefficients
    pub ar_coeffs: Array1<f64>,
    /// MA coefficients
    pub ma_coeffs: Array1<f64>,
    /// Differencing order
    pub diff_order: usize,
    /// Model residuals
    pub residuals: VecDeque<f64>,
    /// Model variance
    pub variance: f64,
}

/// Nonlinear autoregressive model state
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct NARState {
    /// Model order
    pub order: usize,
    /// Nonlinear coefficients
    pub coeffs: Array2<f64>,
    /// Past values buffer
    pub history: VecDeque<f64>,
    /// Activation function
    pub activation: ActivationFunction,
}

/// Trend model
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TrendModel {
    /// Model parameters
    pub params: Vec<f64>,
    /// Trend strength
    pub strength: f64,
    /// Trend direction
    pub direction: f64,
}

/// Memory analyzer for capacity estimation
#[derive(Debug)]
pub struct MemoryAnalyzer {
    /// Analysis configuration
    pub config: MemoryAnalysisConfig,
    /// Current capacity estimates
    pub capacity_estimates: HashMap<String, f64>,
    /// Nonlinearity measures
    pub nonlinearity_measures: HashMap<usize, f64>,
    /// Temporal correlations
    pub temporal_correlations: Array2<f64>,
    /// Information processing metrics
    pub ipc_metrics: HashMap<String, f64>,
}

impl QuantumReservoirComputerEnhanced {
    /// Create new enhanced quantum reservoir computer
    pub fn new(config: QuantumReservoirConfig) -> Result<Self> {
        let circuit_interface = CircuitInterface::new(Default::default())?;
        let simulator = StateVectorSimulator::new();

        let reservoir_state = QuantumReservoirState::new(config.num_qubits, config.memory_capacity);

        // Generate reservoir circuit based on architecture
        let reservoir_circuit = Self::generate_reservoir_circuit(&config)?;

        // Generate input coupling circuit
        let input_coupling_circuit = Self::generate_input_coupling_circuit(&config)?;

        // Initialize output weights randomly
        let output_size = Self::calculate_output_size(&config);
        let feature_size = Self::calculate_feature_size(&config);
        let mut output_weights = Array2::zeros((output_size, feature_size));

        // Xavier initialization
        let scale = (2.0 / (output_size + feature_size) as f64).sqrt();
        for elem in &mut output_weights {
            *elem = (fastrand::f64() - 0.5) * 2.0 * scale;
        }

        // Initialize time series predictor if enabled
        let time_series_predictor =
            if config.time_series_config.enable_arima || config.time_series_config.enable_nar {
                Some(TimeSeriesPredictor::new(&config.time_series_config))
            } else {
                None
            };

        // Initialize memory analyzer
        let memory_analyzer = MemoryAnalyzer::new(config.memory_config.clone());

        Ok(Self {
            config,
            reservoir_state,
            reservoir_circuit,
            input_coupling_circuit,
            output_weights,
            time_series_predictor,
            memory_analyzer,
            simulator,
            circuit_interface,
            metrics: ReservoirMetrics::default(),
            training_history: VecDeque::with_capacity(10_000),
            backend: None,
            rng: Arc::new(Mutex::new(thread_rng())),
        })
    }

    /// Generate reservoir circuit based on architecture
    fn generate_reservoir_circuit(config: &QuantumReservoirConfig) -> Result<InterfaceCircuit> {
        let mut circuit = InterfaceCircuit::new(config.num_qubits, 0);

        match config.architecture {
            QuantumReservoirArchitecture::RandomCircuit => {
                Self::generate_random_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::SpinChain => {
                Self::generate_spin_chain_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::TransverseFieldIsing => {
                Self::generate_tfim_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::SmallWorld => {
                Self::generate_small_world_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::FullyConnected => {
                Self::generate_fully_connected_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::ScaleFree => {
                Self::generate_scale_free_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::HierarchicalModular => {
                Self::generate_hierarchical_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::Ring => {
                Self::generate_ring_circuit(&mut circuit, config)?;
            }
            QuantumReservoirArchitecture::Grid => {
                Self::generate_grid_circuit(&mut circuit, config)?;
            }
            _ => {
                // Default to random circuit for other architectures
                Self::generate_random_circuit(&mut circuit, config)?;
            }
        }

        Ok(circuit)
    }

    /// Generate random quantum circuit
    fn generate_random_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let depth = config.evolution_steps;

        for _ in 0..depth {
            // Add random single-qubit gates
            for qubit in 0..config.num_qubits {
                let angle = fastrand::f64() * 2.0 * PI;
                let gate_type = match fastrand::usize(0..3) {
                    0 => InterfaceGateType::RX(angle),
                    1 => InterfaceGateType::RY(angle),
                    _ => InterfaceGateType::RZ(angle),
                };
                circuit.add_gate(InterfaceGate::new(gate_type, vec![qubit]));
            }

            // Add random two-qubit gates
            for _ in 0..(config.num_qubits / 2) {
                let qubit1 = fastrand::usize(0..config.num_qubits);
                let qubit2 = fastrand::usize(0..config.num_qubits);
                if qubit1 != qubit2 {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::CNOT,
                        vec![qubit1, qubit2],
                    ));
                }
            }
        }

        Ok(())
    }

    /// Generate spin chain circuit
    fn generate_spin_chain_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;

        for _ in 0..config.evolution_steps {
            // Nearest-neighbor interactions
            for i in 0..config.num_qubits - 1 {
                // ZZ interaction
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step),
                    vec![i],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step),
                    vec![i + 1],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
            }
        }

        Ok(())
    }

    /// Generate transverse field Ising model circuit
    fn generate_tfim_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;
        let field = coupling * 0.5; // Transverse field strength

        for _ in 0..config.evolution_steps {
            // Transverse field (X rotations)
            for qubit in 0..config.num_qubits {
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RX(field * config.time_step),
                    vec![qubit],
                ));
            }

            // Nearest-neighbor ZZ interactions
            for i in 0..config.num_qubits - 1 {
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                    vec![i],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step),
                    vec![i + 1],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                    vec![i],
                ));
            }
        }

        Ok(())
    }

    /// Generate small-world network circuit
    fn generate_small_world_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;
        let rewiring_prob = 0.1; // Small-world rewiring probability

        for _ in 0..config.evolution_steps {
            // Regular lattice connections
            for i in 0..config.num_qubits {
                let next = (i + 1) % config.num_qubits;

                // Random rewiring
                let target = if fastrand::f64() < rewiring_prob {
                    fastrand::usize(0..config.num_qubits)
                } else {
                    next
                };

                if target != i {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                        vec![i],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, target]));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step),
                        vec![target],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, target]));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                        vec![i],
                    ));
                }
            }
        }

        Ok(())
    }

    /// Generate fully connected circuit
    fn generate_fully_connected_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength / config.num_qubits as f64; // Scale by system size

        for _ in 0..config.evolution_steps {
            // All-to-all interactions
            for i in 0..config.num_qubits {
                for j in i + 1..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                        vec![i],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step),
                        vec![j],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                        vec![i],
                    ));
                }
            }
        }

        Ok(())
    }

    /// Generate scale-free network circuit
    fn generate_scale_free_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        // Implement scale-free topology with preferential attachment
        let mut degree_dist = vec![1; config.num_qubits];
        let coupling = config.coupling_strength;

        for _ in 0..config.evolution_steps {
            // Scale-free connections based on degree distribution
            for i in 0..config.num_qubits {
                // Probability proportional to degree
                let total_degree: usize = degree_dist.iter().sum();
                let prob_threshold = degree_dist[i] as f64 / total_degree as f64;

                if fastrand::f64() < prob_threshold {
                    let j = fastrand::usize(0..config.num_qubits);
                    if i != j {
                        // Add interaction
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                            vec![i],
                        ));
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RZ(coupling * config.time_step),
                            vec![j],
                        ));
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));

                        // Update degrees
                        degree_dist[i] += 1;
                        degree_dist[j] += 1;
                    }
                }
            }
        }

        Ok(())
    }

    /// Generate hierarchical modular circuit
    fn generate_hierarchical_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;
        let module_size = (config.num_qubits as f64).sqrt() as usize;

        for _ in 0..config.evolution_steps {
            // Intra-module connections (stronger)
            for module in 0..(config.num_qubits / module_size) {
                let start = module * module_size;
                let end = ((module + 1) * module_size).min(config.num_qubits);

                for i in start..end {
                    for j in (i + 1)..end {
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RZ(coupling * config.time_step),
                            vec![i],
                        ));
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    }
                }
            }

            // Inter-module connections (weaker)
            for i in 0..config.num_qubits {
                let j = fastrand::usize(0..config.num_qubits);
                if i / module_size != j / module_size && i != j {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(coupling * config.time_step * 0.3),
                        vec![i],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }

        Ok(())
    }

    /// Generate ring topology circuit
    fn generate_ring_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;

        for _ in 0..config.evolution_steps {
            // Ring connections
            for i in 0..config.num_qubits {
                let j = (i + 1) % config.num_qubits;

                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                    vec![i],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                circuit.add_gate(InterfaceGate::new(
                    InterfaceGateType::RZ(coupling * config.time_step),
                    vec![j],
                ));
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
            }

            // Long-range connections (sparse)
            if fastrand::f64() < 0.1 {
                let i = fastrand::usize(0..config.num_qubits);
                let j = fastrand::usize(0..config.num_qubits);
                if i != j && (i as i32 - j as i32).abs() > 2 {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }

        Ok(())
    }

    /// Generate grid topology circuit
    fn generate_grid_circuit(
        circuit: &mut InterfaceCircuit,
        config: &QuantumReservoirConfig,
    ) -> Result<()> {
        let coupling = config.coupling_strength;
        let grid_size = (config.num_qubits as f64).sqrt() as usize;

        for _ in 0..config.evolution_steps {
            // Grid connections (nearest neighbors)
            for i in 0..grid_size {
                for j in 0..grid_size {
                    let current = i * grid_size + j;
                    if current >= config.num_qubits {
                        break;
                    }

                    // Right neighbor
                    if j + 1 < grid_size {
                        let neighbor = i * grid_size + j + 1;
                        if neighbor < config.num_qubits {
                            circuit.add_gate(InterfaceGate::new(
                                InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                                vec![current],
                            ));
                            circuit.add_gate(InterfaceGate::new(
                                InterfaceGateType::CNOT,
                                vec![current, neighbor],
                            ));
                        }
                    }

                    // Bottom neighbor
                    if i + 1 < grid_size {
                        let neighbor = (i + 1) * grid_size + j;
                        if neighbor < config.num_qubits {
                            circuit.add_gate(InterfaceGate::new(
                                InterfaceGateType::RZ(coupling * config.time_step / 2.0),
                                vec![current],
                            ));
                            circuit.add_gate(InterfaceGate::new(
                                InterfaceGateType::CNOT,
                                vec![current, neighbor],
                            ));
                        }
                    }
                }
            }
        }

        Ok(())
    }

    /// Generate input coupling circuit
    fn generate_input_coupling_circuit(
        config: &QuantumReservoirConfig,
    ) -> Result<InterfaceCircuit> {
        let mut circuit = InterfaceCircuit::new(config.num_qubits, 0);

        match config.input_encoding {
            InputEncoding::Amplitude => {
                // Amplitude encoding through controlled rotations
                for qubit in 0..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RY(0.0), // Will be set dynamically
                        vec![qubit],
                    ));
                }
            }
            InputEncoding::Phase => {
                // Phase encoding through Z rotations
                for qubit in 0..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RZ(0.0), // Will be set dynamically
                        vec![qubit],
                    ));
                }
            }
            InputEncoding::BasisState => {
                // Basis state encoding through X gates
                for qubit in 0..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::X, vec![qubit]));
                }
            }
            InputEncoding::Angle => {
                // Angle encoding with multiple rotation axes
                for qubit in 0..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RX(0.0), vec![qubit]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(0.0), vec![qubit]));
                }
            }
            _ => {
                // Default to amplitude encoding
                for qubit in 0..config.num_qubits {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(0.0), vec![qubit]));
                }
            }
        }

        Ok(circuit)
    }

    /// Calculate output size based on configuration
    const fn calculate_output_size(config: &QuantumReservoirConfig) -> usize {
        // For time series prediction, typically 1 output
        1
    }

    /// Calculate feature size based on configuration
    fn calculate_feature_size(config: &QuantumReservoirConfig) -> usize {
        match config.output_measurement {
            OutputMeasurement::PauliExpectation => config.num_qubits * 3,
            OutputMeasurement::Probability => 1 << config.num_qubits.min(10), // Limit for memory
            OutputMeasurement::Correlations => config.num_qubits * config.num_qubits,
            OutputMeasurement::Entanglement => config.num_qubits,
            OutputMeasurement::Fidelity => 1,
            OutputMeasurement::QuantumFisherInformation => config.num_qubits,
            OutputMeasurement::Variance => config.num_qubits * 3,
            OutputMeasurement::HigherOrderMoments => config.num_qubits * 6, // Up to 3rd moments
            OutputMeasurement::SpectralProperties => config.num_qubits,
            OutputMeasurement::QuantumCoherence => config.num_qubits,
            OutputMeasurement::Purity => 1,
            OutputMeasurement::QuantumMutualInformation => config.num_qubits * config.num_qubits,
            OutputMeasurement::ProcessTomography => config.num_qubits * config.num_qubits * 4,
            OutputMeasurement::TemporalCorrelations => config.memory_capacity,
            OutputMeasurement::NonLinearReadout => config.num_qubits * 2,
        }
    }

    /// Process input through quantum reservoir
    pub fn process_input(&mut self, input: &Array1<f64>) -> Result<Array1<f64>> {
        let start_time = std::time::Instant::now();

        // Encode input into quantum state
        self.encode_input(input)?;

        // Evolve through reservoir dynamics
        self.evolve_reservoir()?;

        // Extract features from reservoir state
        let features = self.extract_features()?;

        // Update reservoir state with timestamp
        let timestamp = start_time.elapsed().as_secs_f64();
        self.reservoir_state
            .update_state(self.reservoir_state.state_vector.clone(), timestamp);

        // Update metrics
        let processing_time = start_time.elapsed().as_secs_f64() * 1000.0;
        self.update_processing_time(processing_time);

        Ok(features)
    }

    /// Encode input data into quantum state
    fn encode_input(&mut self, input: &Array1<f64>) -> Result<()> {
        match self.config.input_encoding {
            InputEncoding::Amplitude => {
                self.encode_amplitude(input)?;
            }
            InputEncoding::Phase => {
                self.encode_phase(input)?;
            }
            InputEncoding::BasisState => {
                self.encode_basis_state(input)?;
            }
            InputEncoding::Angle => {
                self.encode_angle(input)?;
            }
            _ => {
                self.encode_amplitude(input)?;
            }
        }
        Ok(())
    }

    /// Amplitude encoding
    fn encode_amplitude(&mut self, input: &Array1<f64>) -> Result<()> {
        let num_inputs = input.len().min(self.config.num_qubits);

        for i in 0..num_inputs {
            let angle = input[i] * PI; // Scale to [0, π]
            self.apply_single_qubit_rotation(i, InterfaceGateType::RY(angle))?;
        }

        Ok(())
    }

    /// Phase encoding
    fn encode_phase(&mut self, input: &Array1<f64>) -> Result<()> {
        let num_inputs = input.len().min(self.config.num_qubits);

        for i in 0..num_inputs {
            let angle = input[i] * 2.0 * PI; // Full phase range
            self.apply_single_qubit_rotation(i, InterfaceGateType::RZ(angle))?;
        }

        Ok(())
    }

    /// Basis state encoding
    fn encode_basis_state(&mut self, input: &Array1<f64>) -> Result<()> {
        let num_inputs = input.len().min(self.config.num_qubits);

        for i in 0..num_inputs {
            if input[i] > 0.5 {
                self.apply_single_qubit_gate(i, InterfaceGateType::X)?;
            }
        }

        Ok(())
    }

    /// Angle encoding with multiple rotation axes
    fn encode_angle(&mut self, input: &Array1<f64>) -> Result<()> {
        let num_inputs = input.len().min(self.config.num_qubits);

        for i in 0..num_inputs {
            let angle_x = input[i] * PI;
            let angle_y = if i + 1 < input.len() {
                input[i + 1] * PI
            } else {
                0.0
            };

            self.apply_single_qubit_rotation(i, InterfaceGateType::RX(angle_x))?;
            self.apply_single_qubit_rotation(i, InterfaceGateType::RY(angle_y))?;
        }

        Ok(())
    }

    /// Apply single qubit rotation
    fn apply_single_qubit_rotation(
        &mut self,
        qubit: usize,
        gate_type: InterfaceGateType,
    ) -> Result<()> {
        let mut temp_circuit = InterfaceCircuit::new(self.config.num_qubits, 0);
        temp_circuit.add_gate(InterfaceGate::new(gate_type, vec![qubit]));

        self.simulator.apply_interface_circuit(&temp_circuit)?;

        Ok(())
    }

    /// Apply single qubit gate
    fn apply_single_qubit_gate(
        &mut self,
        qubit: usize,
        gate_type: InterfaceGateType,
    ) -> Result<()> {
        let mut temp_circuit = InterfaceCircuit::new(self.config.num_qubits, 0);
        temp_circuit.add_gate(InterfaceGate::new(gate_type, vec![qubit]));

        self.simulator.apply_interface_circuit(&temp_circuit)?;

        Ok(())
    }

    /// Evolve quantum reservoir through dynamics
    fn evolve_reservoir(&mut self) -> Result<()> {
        match self.config.dynamics {
            ReservoirDynamics::Unitary => {
                self.evolve_unitary()?;
            }
            ReservoirDynamics::Open => {
                self.evolve_open_system()?;
            }
            ReservoirDynamics::NISQ => {
                self.evolve_nisq()?;
            }
            ReservoirDynamics::Adiabatic => {
                self.evolve_adiabatic()?;
            }
            ReservoirDynamics::Floquet => {
                self.evolve_floquet()?;
            }
            _ => {
                // Default to unitary evolution
                self.evolve_unitary()?;
            }
        }
        Ok(())
    }

    /// Unitary evolution
    fn evolve_unitary(&mut self) -> Result<()> {
        self.simulator
            .apply_interface_circuit(&self.reservoir_circuit)?;
        Ok(())
    }

    /// Open system evolution with noise
    fn evolve_open_system(&mut self) -> Result<()> {
        // Apply unitary evolution first
        self.evolve_unitary()?;

        // Apply decoherence
        self.apply_decoherence()?;

        Ok(())
    }

    /// NISQ evolution with realistic noise
    fn evolve_nisq(&mut self) -> Result<()> {
        // Apply unitary evolution
        self.evolve_unitary()?;

        // Apply gate errors
        self.apply_gate_errors()?;

        // Apply measurement errors
        self.apply_measurement_errors()?;

        Ok(())
    }

    /// Adiabatic evolution
    fn evolve_adiabatic(&mut self) -> Result<()> {
        // Simplified adiabatic evolution
        // In practice, this would implement proper adiabatic dynamics
        self.evolve_unitary()?;
        Ok(())
    }

    /// Floquet evolution with periodic driving
    fn evolve_floquet(&mut self) -> Result<()> {
        // Apply time-dependent Hamiltonian
        let drive_frequency = 1.0;
        let time = self.reservoir_state.time_index as f64 * self.config.time_step;
        let drive_strength = (drive_frequency * time).sin();

        // Apply driving field
        for qubit in 0..self.config.num_qubits {
            let angle = drive_strength * self.config.time_step;
            self.apply_single_qubit_rotation(qubit, InterfaceGateType::RX(angle))?;
        }

        // Apply base evolution
        self.evolve_unitary()?;

        Ok(())
    }

    /// Apply decoherence to the reservoir state
    fn apply_decoherence(&mut self) -> Result<()> {
        let decoherence_rate = self.config.noise_level;

        for amplitude in &mut self.reservoir_state.state_vector {
            // Apply phase decoherence
            let phase_noise = (fastrand::f64() - 0.5) * decoherence_rate * 2.0 * PI;
            *amplitude *= Complex64::new(0.0, phase_noise).exp();

            // Apply amplitude damping
            let damping = (1.0 - decoherence_rate).sqrt();
            *amplitude *= damping;
        }

        // Renormalize
        let norm: f64 = self
            .reservoir_state
            .state_vector
            .iter()
            .map(scirs2_core::Complex::norm_sqr)
            .sum::<f64>()
            .sqrt();

        if norm > 1e-15 {
            self.reservoir_state.state_vector.mapv_inplace(|x| x / norm);
        }

        Ok(())
    }

    /// Apply gate errors
    fn apply_gate_errors(&mut self) -> Result<()> {
        let error_rate = self.config.noise_level;

        for qubit in 0..self.config.num_qubits {
            if fastrand::f64() < error_rate {
                let error_type = fastrand::usize(0..3);
                let gate_type = match error_type {
                    0 => InterfaceGateType::X,
                    1 => InterfaceGateType::PauliY,
                    _ => InterfaceGateType::PauliZ,
                };
                self.apply_single_qubit_gate(qubit, gate_type)?;
            }
        }

        Ok(())
    }

    /// Apply measurement errors
    fn apply_measurement_errors(&mut self) -> Result<()> {
        let error_rate = self.config.noise_level * 0.1; // Lower rate for measurement errors

        if fastrand::f64() < error_rate {
            let qubit = fastrand::usize(0..self.config.num_qubits);
            self.apply_single_qubit_gate(qubit, InterfaceGateType::X)?;
        }

        Ok(())
    }

    /// Extract features from reservoir state
    fn extract_features(&mut self) -> Result<Array1<f64>> {
        match self.config.output_measurement {
            OutputMeasurement::PauliExpectation => self.measure_pauli_expectations(),
            OutputMeasurement::Probability => self.measure_probabilities(),
            OutputMeasurement::Correlations => self.measure_correlations(),
            OutputMeasurement::Entanglement => self.measure_entanglement(),
            OutputMeasurement::Fidelity => self.measure_fidelity(),
            OutputMeasurement::QuantumFisherInformation => {
                self.measure_quantum_fisher_information()
            }
            OutputMeasurement::Variance => self.measure_variance(),
            OutputMeasurement::HigherOrderMoments => self.measure_higher_order_moments(),
            OutputMeasurement::QuantumCoherence => self.measure_quantum_coherence(),
            OutputMeasurement::Purity => self.measure_purity(),
            OutputMeasurement::TemporalCorrelations => self.measure_temporal_correlations(),
            _ => {
                // Default to Pauli expectations
                self.measure_pauli_expectations()
            }
        }
    }

    /// Measure Pauli expectation values
    fn measure_pauli_expectations(&self) -> Result<Array1<f64>> {
        let mut expectations = Vec::new();

        for qubit in 0..self.config.num_qubits {
            // X expectation
            let x_exp = self.calculate_single_qubit_expectation(
                qubit,
                &[
                    Complex64::new(0.0, 0.0),
                    Complex64::new(1.0, 0.0),
                    Complex64::new(1.0, 0.0),
                    Complex64::new(0.0, 0.0),
                ],
            )?;
            expectations.push(x_exp);

            // Y expectation
            let y_exp = self.calculate_single_qubit_expectation(
                qubit,
                &[
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, -1.0),
                    Complex64::new(0.0, 1.0),
                    Complex64::new(0.0, 0.0),
                ],
            )?;
            expectations.push(y_exp);

            // Z expectation
            let z_exp = self.calculate_single_qubit_expectation(
                qubit,
                &[
                    Complex64::new(1.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(-1.0, 0.0),
                ],
            )?;
            expectations.push(z_exp);
        }

        Ok(Array1::from_vec(expectations))
    }

    /// Calculate single qubit expectation value
    fn calculate_single_qubit_expectation(
        &self,
        qubit: usize,
        pauli_matrix: &[Complex64; 4],
    ) -> Result<f64> {
        let state = &self.reservoir_state.state_vector;
        let mut expectation = 0.0;

        for i in 0..state.len() {
            for j in 0..state.len() {
                let i_bit = (i >> qubit) & 1;
                let j_bit = (j >> qubit) & 1;
                let matrix_element = pauli_matrix[i_bit * 2 + j_bit];

                expectation += (state[i].conj() * matrix_element * state[j]).re;
            }
        }

        Ok(expectation)
    }

    /// Measure probability distribution
    fn measure_probabilities(&self) -> Result<Array1<f64>> {
        let probabilities: Vec<f64> = self
            .reservoir_state
            .state_vector
            .iter()
            .map(scirs2_core::Complex::norm_sqr)
            .collect();

        // Limit size for large systems
        let max_size = 1 << 10; // 2^10 = 1024
        if probabilities.len() > max_size {
            // Sample random subset
            let mut sampled = Vec::with_capacity(max_size);
            for _ in 0..max_size {
                let idx = fastrand::usize(0..probabilities.len());
                sampled.push(probabilities[idx]);
            }
            Ok(Array1::from_vec(sampled))
        } else {
            Ok(Array1::from_vec(probabilities))
        }
    }

    /// Measure two-qubit correlations
    fn measure_correlations(&mut self) -> Result<Array1<f64>> {
        let mut correlations = Vec::new();

        for i in 0..self.config.num_qubits {
            for j in 0..self.config.num_qubits {
                if i == j {
                    correlations.push(1.0); // Self-correlation
                    self.reservoir_state.correlations[[i, j]] = 1.0;
                } else {
                    // ZZ correlation
                    let corr = self.calculate_two_qubit_correlation(i, j)?;
                    correlations.push(corr);
                    self.reservoir_state.correlations[[i, j]] = corr;
                }
            }
        }

        Ok(Array1::from_vec(correlations))
    }

    /// Calculate two-qubit correlation
    fn calculate_two_qubit_correlation(&self, qubit1: usize, qubit2: usize) -> Result<f64> {
        let state = &self.reservoir_state.state_vector;
        let mut correlation = 0.0;

        for i in 0..state.len() {
            let bit1 = (i >> qubit1) & 1;
            let bit2 = (i >> qubit2) & 1;
            let sign = if bit1 == bit2 { 1.0 } else { -1.0 };
            correlation += sign * state[i].norm_sqr();
        }

        Ok(correlation)
    }

    /// Measure entanglement metrics
    fn measure_entanglement(&self) -> Result<Array1<f64>> {
        let mut entanglement_measures = Vec::new();

        // Simplified entanglement measures
        for qubit in 0..self.config.num_qubits {
            // Von Neumann entropy of reduced state (approximation)
            let entropy = self.calculate_von_neumann_entropy(qubit)?;
            entanglement_measures.push(entropy);
        }

        Ok(Array1::from_vec(entanglement_measures))
    }

    /// Calculate von Neumann entropy (simplified)
    fn calculate_von_neumann_entropy(&self, _qubit: usize) -> Result<f64> {
        let state = &self.reservoir_state.state_vector;
        let mut entropy = 0.0;

        for amplitude in state {
            let prob = amplitude.norm_sqr();
            if prob > 1e-15 {
                entropy -= prob * prob.ln();
            }
        }

        Ok(entropy / (state.len() as f64).ln()) // Normalized entropy
    }

    /// Measure fidelity with reference state
    fn measure_fidelity(&self) -> Result<Array1<f64>> {
        // Fidelity with initial state |0...0⟩
        let fidelity = self.reservoir_state.state_vector[0].norm_sqr();
        Ok(Array1::from_vec(vec![fidelity]))
    }

    /// Measure quantum Fisher information
    fn measure_quantum_fisher_information(&self) -> Result<Array1<f64>> {
        let mut qfi_values = Vec::new();

        for qubit in 0..self.config.num_qubits {
            // Simplified QFI calculation for single qubit observables
            let z_exp = self.calculate_single_qubit_expectation(
                qubit,
                &[
                    Complex64::new(1.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(-1.0, 0.0),
                ],
            )?;

            // QFI ≈ 4 * Var(Z) for single qubit
            let qfi = 4.0 * (1.0 - z_exp * z_exp);
            qfi_values.push(qfi);
        }

        Ok(Array1::from_vec(qfi_values))
    }

    /// Measure variance of observables
    fn measure_variance(&self) -> Result<Array1<f64>> {
        let mut variances = Vec::new();

        for qubit in 0..self.config.num_qubits {
            // X, Y, Z variances
            for pauli_idx in 0..3 {
                let pauli_matrix = match pauli_idx {
                    0 => [
                        Complex64::new(0.0, 0.0),
                        Complex64::new(1.0, 0.0),
                        Complex64::new(1.0, 0.0),
                        Complex64::new(0.0, 0.0),
                    ],
                    1 => [
                        Complex64::new(0.0, 0.0),
                        Complex64::new(0.0, -1.0),
                        Complex64::new(0.0, 1.0),
                        Complex64::new(0.0, 0.0),
                    ],
                    _ => [
                        Complex64::new(1.0, 0.0),
                        Complex64::new(0.0, 0.0),
                        Complex64::new(0.0, 0.0),
                        Complex64::new(-1.0, 0.0),
                    ],
                };

                let expectation = self.calculate_single_qubit_expectation(qubit, &pauli_matrix)?;
                let variance = 1.0 - expectation * expectation; // For Pauli operators
                variances.push(variance);
            }
        }

        Ok(Array1::from_vec(variances))
    }

    /// Measure higher-order moments
    fn measure_higher_order_moments(&self) -> Result<Array1<f64>> {
        let mut moments = Vec::new();

        for qubit in 0..self.config.num_qubits {
            // Calculate moments up to 3rd order for Z observable
            let z_exp = self.calculate_single_qubit_expectation(
                qubit,
                &[
                    Complex64::new(1.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(0.0, 0.0),
                    Complex64::new(-1.0, 0.0),
                ],
            )?;

            // First moment (mean)
            moments.push(z_exp);

            // Second central moment (variance)
            let variance = 1.0 - z_exp * z_exp;
            moments.push(variance);

            // Third central moment (skewness measure)
            // For Pauli-Z, this is typically zero due to symmetry
            moments.push(0.0);

            // Kurtosis measure
            moments.push(variance * variance);

            // Fifth moment (for more complex characterization)
            moments.push(z_exp * variance);

            // Sixth moment
            moments.push(variance * variance * variance);
        }

        Ok(Array1::from_vec(moments))
    }

    /// Measure quantum coherence
    fn measure_quantum_coherence(&self) -> Result<Array1<f64>> {
        let mut coherence_measures = Vec::new();

        for qubit in 0..self.config.num_qubits {
            // L1 norm of coherence (off-diagonal elements in computational basis)
            let mut coherence = 0.0;
            let state = &self.reservoir_state.state_vector;

            for i in 0..state.len() {
                for j in 0..state.len() {
                    if i != j {
                        let i_bit = (i >> qubit) & 1;
                        let j_bit = (j >> qubit) & 1;
                        if i_bit != j_bit {
                            coherence += (state[i].conj() * state[j]).norm();
                        }
                    }
                }
            }

            coherence_measures.push(coherence);
        }

        Ok(Array1::from_vec(coherence_measures))
    }

    /// Measure purity
    fn measure_purity(&self) -> Result<Array1<f64>> {
        // Purity = Tr(ρ²) for the full state
        let state = &self.reservoir_state.state_vector;
        let purity = state.iter().map(|x| x.norm_sqr().powi(2)).sum::<f64>();

        Ok(Array1::from_vec(vec![purity]))
    }

    /// Measure temporal correlations
    fn measure_temporal_correlations(&self) -> Result<Array1<f64>> {
        let mut correlations = Vec::new();

        // Calculate autocorrelation with past states
        let current_state = &self.reservoir_state.state_vector;

        for past_state in &self.reservoir_state.state_history {
            let correlation = current_state
                .iter()
                .zip(past_state.iter())
                .map(|(a, b)| (a.conj() * b).re)
                .sum::<f64>();
            correlations.push(correlation);
        }

        // Pad with zeros if not enough history
        while correlations.len() < self.config.memory_capacity {
            correlations.push(0.0);
        }

        Ok(Array1::from_vec(correlations))
    }

    /// Train the enhanced reservoir computer
    pub fn train(&mut self, training_data: &ReservoirTrainingData) -> Result<TrainingResult> {
        let start_time = std::time::Instant::now();

        let mut all_features = Vec::new();
        let mut all_targets = Vec::new();

        // Washout period
        for i in 0..self.config.washout_period.min(training_data.inputs.len()) {
            let _ = self.process_input(&training_data.inputs[i])?;
        }

        // Collect training data after washout
        for i in self.config.washout_period..training_data.inputs.len() {
            let features = self.process_input(&training_data.inputs[i])?;
            all_features.push(features);

            if i < training_data.targets.len() {
                all_targets.push(training_data.targets[i].clone());
            }
        }

        // Train output weights using the specified learning algorithm
        self.train_with_learning_algorithm(&all_features, &all_targets)?;

        // Analyze memory capacity if enabled
        if self.config.memory_config.enable_capacity_estimation {
            self.analyze_memory_capacity(&all_features)?;
        }

        // Evaluate performance
        let (training_error, test_error) =
            self.evaluate_performance(&all_features, &all_targets)?;

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

        // Update metrics
        self.metrics.training_examples += all_features.len();
        self.metrics.generalization_error = test_error;
        self.metrics.memory_capacity = self.reservoir_state.memory_metrics.total_capacity;

        Ok(TrainingResult {
            training_error,
            test_error,
            training_time_ms: training_time,
            num_examples: all_features.len(),
            echo_state_property: self.estimate_echo_state_property()?,
            memory_capacity: self.reservoir_state.memory_metrics.total_capacity,
            nonlinear_capacity: self.reservoir_state.memory_metrics.nonlinear_capacity,
            processing_capacity: self.reservoir_state.memory_metrics.processing_capacity,
        })
    }

    /// Train using advanced learning algorithms
    fn train_with_learning_algorithm(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        match self.config.learning_config.algorithm {
            LearningAlgorithm::Ridge => {
                self.train_ridge_regression(features, targets)?;
            }
            LearningAlgorithm::LASSO => {
                self.train_lasso_regression(features, targets)?;
            }
            LearningAlgorithm::ElasticNet => {
                self.train_elastic_net(features, targets)?;
            }
            LearningAlgorithm::RecursiveLeastSquares => {
                self.train_recursive_least_squares(features, targets)?;
            }
            LearningAlgorithm::KalmanFilter => {
                self.train_kalman_filter(features, targets)?;
            }
            _ => {
                // Default to ridge regression
                self.train_ridge_regression(features, targets)?;
            }
        }

        Ok(())
    }

    /// Train ridge regression
    fn train_ridge_regression(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        if features.is_empty() || targets.is_empty() {
            return Ok(());
        }

        let n_samples = features.len().min(targets.len());
        let n_features = features[0].len();
        let n_outputs = targets[0].len().min(self.output_weights.nrows());

        // Create feature matrix
        let mut feature_matrix = Array2::zeros((n_samples, n_features));
        for (i, feature_vec) in features.iter().enumerate().take(n_samples) {
            for (j, &val) in feature_vec.iter().enumerate().take(n_features) {
                feature_matrix[[i, j]] = val;
            }
        }

        // Create target matrix
        let mut target_matrix = Array2::zeros((n_samples, n_outputs));
        for (i, target_vec) in targets.iter().enumerate().take(n_samples) {
            for (j, &val) in target_vec.iter().enumerate().take(n_outputs) {
                target_matrix[[i, j]] = val;
            }
        }

        // Ridge regression: W = (X^T X + λI)^(-1) X^T Y
        let lambda = self.config.learning_config.regularization;

        // X^T X
        let xtx = feature_matrix.t().dot(&feature_matrix);

        // Add regularization
        let mut xtx_reg = xtx;
        for i in 0..xtx_reg.nrows().min(xtx_reg.ncols()) {
            xtx_reg[[i, i]] += lambda;
        }

        // X^T Y
        let xty = feature_matrix.t().dot(&target_matrix);

        // Solve using simplified approach (in practice would use proper linear solver)
        self.solve_linear_system(&xtx_reg, &xty)?;

        Ok(())
    }

    /// Train LASSO regression (simplified)
    fn train_lasso_regression(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        // Simplified LASSO using coordinate descent
        let lambda = self.config.learning_config.regularization;
        let max_iter = 100;

        for _ in 0..max_iter {
            // Coordinate descent updates
            for j in 0..self.output_weights.ncols().min(features[0].len()) {
                for i in 0..self.output_weights.nrows().min(targets[0].len()) {
                    // Soft thresholding update
                    let old_weight = self.output_weights[[i, j]];
                    let gradient = self.compute_lasso_gradient(features, targets, i, j)?;
                    let update = 0.01f64.mul_add(-gradient, old_weight);

                    // Soft thresholding
                    self.output_weights[[i, j]] = if update > lambda {
                        update - lambda
                    } else if update < -lambda {
                        update + lambda
                    } else {
                        0.0
                    };
                }
            }
        }

        Ok(())
    }

    /// Compute LASSO gradient (simplified)
    fn compute_lasso_gradient(
        &self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
        output_idx: usize,
        feature_idx: usize,
    ) -> Result<f64> {
        let mut gradient = 0.0;

        for (feature_vec, target_vec) in features.iter().zip(targets.iter()) {
            if feature_idx < feature_vec.len() && output_idx < target_vec.len() {
                let prediction = self.predict_single_output(feature_vec, output_idx)?;
                let error = prediction - target_vec[output_idx];
                gradient += error * feature_vec[feature_idx];
            }
        }

        gradient /= features.len() as f64;
        Ok(gradient)
    }

    /// Train Elastic Net regression
    fn train_elastic_net(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        let l1_ratio = self.config.learning_config.l1_ratio;

        // Combine Ridge and LASSO with L1 ratio
        if l1_ratio > 0.5 {
            // More L1 regularization
            self.train_lasso_regression(features, targets)?;
        } else {
            // More L2 regularization
            self.train_ridge_regression(features, targets)?;
        }

        Ok(())
    }

    /// Train Recursive Least Squares
    fn train_recursive_least_squares(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        let forgetting_factor = self.config.learning_config.forgetting_factor;
        let n_features = features[0].len().min(self.output_weights.ncols());
        let n_outputs = targets[0].len().min(self.output_weights.nrows());

        // Initialize covariance matrix
        let mut p_matrix = Array2::eye(n_features) * 1000.0; // Large initial covariance

        // Online RLS updates
        for (feature_vec, target_vec) in features.iter().zip(targets.iter()) {
            let x = feature_vec.slice(s![..n_features]).to_owned();
            let y = target_vec.slice(s![..n_outputs]).to_owned();

            // Update covariance matrix
            let px = p_matrix.dot(&x);
            let denominator = forgetting_factor + x.dot(&px);

            if denominator > 1e-15 {
                let k = &px / denominator;

                // Update weights for each output
                for output_idx in 0..n_outputs {
                    let prediction = self.predict_single_output(feature_vec, output_idx)?;
                    let error = y[output_idx] - prediction;

                    // RLS weight update
                    for feature_idx in 0..n_features {
                        self.output_weights[[output_idx, feature_idx]] += k[feature_idx] * error;
                    }
                }

                // Update covariance matrix
                let outer_product = k
                    .view()
                    .insert_axis(Axis(1))
                    .dot(&x.view().insert_axis(Axis(0)));
                p_matrix = (p_matrix - outer_product) / forgetting_factor;
            }
        }

        Ok(())
    }

    /// Train Kalman filter
    fn train_kalman_filter(
        &mut self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<()> {
        let process_noise = self.config.learning_config.process_noise;
        let measurement_noise = self.config.learning_config.measurement_noise;

        let n_features = features[0].len().min(self.output_weights.ncols());
        let n_outputs = targets[0].len().min(self.output_weights.nrows());

        // Initialize Kalman filter matrices
        let mut state_covariance = Array2::eye(n_features) * 1.0;
        let process_noise_matrix: Array2<f64> = Array2::eye(n_features) * process_noise;
        let measurement_noise_scalar = measurement_noise;

        // Kalman filter updates
        for (feature_vec, target_vec) in features.iter().zip(targets.iter()) {
            let x = feature_vec.slice(s![..n_features]).to_owned();
            let y = target_vec.slice(s![..n_outputs]).to_owned();

            // Prediction step
            let predicted_covariance = &state_covariance + &process_noise_matrix;

            // Update step for each output
            for output_idx in 0..n_outputs {
                let measurement = y[output_idx];
                let prediction = self.predict_single_output(feature_vec, output_idx)?;

                // Kalman gain
                let s = x.dot(&predicted_covariance.dot(&x)) + measurement_noise_scalar;
                if s > 1e-15 {
                    let k = predicted_covariance.dot(&x) / s;

                    // Update weights
                    let innovation = measurement - prediction;
                    for feature_idx in 0..n_features {
                        self.output_weights[[output_idx, feature_idx]] +=
                            k[feature_idx] * innovation;
                    }

                    // Update covariance
                    let kh = k
                        .view()
                        .insert_axis(Axis(1))
                        .dot(&x.view().insert_axis(Axis(0)));
                    state_covariance = &predicted_covariance - &kh.dot(&predicted_covariance);
                }
            }
        }

        Ok(())
    }

    /// Predict single output value
    fn predict_single_output(&self, features: &Array1<f64>, output_idx: usize) -> Result<f64> {
        let feature_size = features.len().min(self.output_weights.ncols());
        let mut output = 0.0;

        for j in 0..feature_size {
            output += self.output_weights[[output_idx, j]] * features[j];
        }

        Ok(output)
    }

    /// Analyze memory capacity
    fn analyze_memory_capacity(&mut self, features: &[Array1<f64>]) -> Result<()> {
        // Linear memory capacity
        let linear_capacity = self.estimate_linear_memory_capacity(features)?;
        self.reservoir_state.memory_metrics.linear_capacity = linear_capacity;

        // Nonlinear memory capacity
        if self.config.memory_config.enable_nonlinear {
            let nonlinear_capacity = self.estimate_nonlinear_memory_capacity(features)?;
            self.reservoir_state.memory_metrics.nonlinear_capacity = nonlinear_capacity;
        }

        // Total capacity
        self.reservoir_state.memory_metrics.total_capacity =
            self.reservoir_state.memory_metrics.linear_capacity
                + self.reservoir_state.memory_metrics.nonlinear_capacity;

        // Information processing capacity
        if self.config.memory_config.enable_ipc {
            let ipc = self.estimate_information_processing_capacity(features)?;
            self.reservoir_state.memory_metrics.processing_capacity = ipc;
        }

        // Update memory analyzer
        self.memory_analyzer.capacity_estimates.insert(
            "linear".to_string(),
            self.reservoir_state.memory_metrics.linear_capacity,
        );
        self.memory_analyzer.capacity_estimates.insert(
            "nonlinear".to_string(),
            self.reservoir_state.memory_metrics.nonlinear_capacity,
        );
        self.memory_analyzer.capacity_estimates.insert(
            "total".to_string(),
            self.reservoir_state.memory_metrics.total_capacity,
        );

        Ok(())
    }

    /// Estimate linear memory capacity
    fn estimate_linear_memory_capacity(&self, features: &[Array1<f64>]) -> Result<f64> {
        // Use correlation analysis to estimate linear memory
        let mut capacity = 0.0;

        for lag in 1..=20 {
            if lag < features.len() {
                let mut correlation = 0.0;
                let mut count = 0;

                for i in lag..features.len() {
                    for j in 0..features[i].len().min(features[i - lag].len()) {
                        correlation += features[i][j] * features[i - lag][j];
                        count += 1;
                    }
                }

                if count > 0 {
                    correlation /= f64::from(count);
                    capacity += correlation.abs();
                }
            }
        }

        Ok(capacity)
    }

    /// Estimate nonlinear memory capacity
    fn estimate_nonlinear_memory_capacity(&self, features: &[Array1<f64>]) -> Result<f64> {
        let mut nonlinear_capacity = 0.0;

        // Test various nonlinear functions
        for order in &self.config.memory_config.nonlinearity_orders {
            let capacity_order = self.test_nonlinear_order(*order, features)?;
            nonlinear_capacity += capacity_order;
        }

        Ok(nonlinear_capacity)
    }

    /// Test specific nonlinear order
    fn test_nonlinear_order(&self, order: usize, features: &[Array1<f64>]) -> Result<f64> {
        let mut capacity = 0.0;

        // Generate nonlinear target function
        for lag in 1..=10 {
            if lag < features.len() {
                let mut correlation = 0.0;
                let mut count = 0;

                for i in lag..features.len() {
                    for j in 0..features[i].len().min(features[i - lag].len()) {
                        // Nonlinear transformation
                        let current = features[i][j];
                        let past = features[i - lag][j];
                        let nonlinear_target = past.powi(order as i32);

                        correlation += current * nonlinear_target;
                        count += 1;
                    }
                }

                if count > 0 {
                    correlation /= f64::from(count);
                    capacity += correlation.abs() / order as f64; // Normalize by order
                }
            }
        }

        Ok(capacity)
    }

    /// Estimate information processing capacity
    fn estimate_information_processing_capacity(&self, features: &[Array1<f64>]) -> Result<f64> {
        let mut ipc = 0.0;

        for ipc_function in &self.config.memory_config.ipc_functions {
            let capacity_func = self.test_ipc_function(*ipc_function, features)?;
            ipc += capacity_func;
        }

        Ok(ipc)
    }

    /// Test specific IPC function
    fn test_ipc_function(&self, function: IPCFunction, features: &[Array1<f64>]) -> Result<f64> {
        let mut capacity = 0.0;

        for lag in 1..=10 {
            if lag < features.len() {
                let mut correlation = 0.0;
                let mut count = 0;

                for i in lag..features.len() {
                    for j in 0..features[i].len().min(features[i - lag].len()) {
                        let current = features[i][j];
                        let past = features[i - lag][j];

                        let target = match function {
                            IPCFunction::Linear => past,
                            IPCFunction::Quadratic => past * past,
                            IPCFunction::Cubic => past * past * past,
                            IPCFunction::Sine => past.sin(),
                            IPCFunction::Product => {
                                if j > 0 && j - 1 < features[i - lag].len() {
                                    past * features[i - lag][j - 1]
                                } else {
                                    past
                                }
                            }
                            IPCFunction::XOR => {
                                if past > 0.0 {
                                    1.0
                                } else {
                                    -1.0
                                }
                            }
                        };

                        correlation += current * target;
                        count += 1;
                    }
                }

                if count > 0 {
                    correlation /= f64::from(count);
                    capacity += correlation.abs();
                }
            }
        }

        Ok(capacity)
    }

    /// Solve linear system (simplified implementation)
    fn solve_linear_system(&mut self, a: &Array2<f64>, b: &Array2<f64>) -> Result<()> {
        let min_dim = a.nrows().min(a.ncols()).min(b.nrows());

        for i in 0..min_dim.min(self.output_weights.nrows()) {
            for j in 0..b.ncols().min(self.output_weights.ncols()) {
                if a[[i, i]].abs() > 1e-15 {
                    self.output_weights[[i, j]] = b[[i, j]] / a[[i, i]];
                }
            }
        }

        Ok(())
    }

    /// Evaluate performance on training data
    fn evaluate_performance(
        &self,
        features: &[Array1<f64>],
        targets: &[Array1<f64>],
    ) -> Result<(f64, f64)> {
        if features.is_empty() || targets.is_empty() {
            return Ok((0.0, 0.0));
        }

        let mut total_error = 0.0;
        let n_samples = features.len().min(targets.len());

        for i in 0..n_samples {
            let prediction = self.predict_output(&features[i])?;
            let error = self.calculate_prediction_error(&prediction, &targets[i]);
            total_error += error;
        }

        let training_error = total_error / n_samples as f64;

        // Use same error for test (in practice, would use separate test set)
        let test_error = training_error;

        Ok((training_error, test_error))
    }

    /// Predict output for given features
    fn predict_output(&self, features: &Array1<f64>) -> Result<Array1<f64>> {
        let feature_size = features.len().min(self.output_weights.ncols());
        let output_size = self.output_weights.nrows();

        let mut output = Array1::zeros(output_size);

        for i in 0..output_size {
            for j in 0..feature_size {
                output[i] += self.output_weights[[i, j]] * features[j];
            }
        }

        Ok(output)
    }

    /// Calculate prediction error
    fn calculate_prediction_error(&self, prediction: &Array1<f64>, target: &Array1<f64>) -> f64 {
        let min_len = prediction.len().min(target.len());
        let mut error = 0.0;

        for i in 0..min_len {
            let diff = prediction[i] - target[i];
            error += diff * diff;
        }

        (error / min_len as f64).sqrt() // RMSE
    }

    /// Estimate echo state property
    fn estimate_echo_state_property(&self) -> Result<f64> {
        let coupling = self.config.coupling_strength;
        let estimated_spectral_radius = coupling.tanh(); // Heuristic estimate

        // Echo state property requires spectral radius < 1
        Ok(if estimated_spectral_radius < 1.0 {
            1.0
        } else {
            1.0 / estimated_spectral_radius
        })
    }

    /// Update processing time metrics
    fn update_processing_time(&mut self, time_ms: f64) {
        let count = self.metrics.training_examples as f64;
        self.metrics.avg_processing_time_ms =
            self.metrics.avg_processing_time_ms.mul_add(count, time_ms) / (count + 1.0);
    }

    /// Get current metrics
    pub const fn get_metrics(&self) -> &ReservoirMetrics {
        &self.metrics
    }

    /// Get memory analysis results
    pub const fn get_memory_analysis(&self) -> &MemoryAnalyzer {
        &self.memory_analyzer
    }

    /// Reset reservoir computer
    pub fn reset(&mut self) -> Result<()> {
        self.reservoir_state =
            QuantumReservoirState::new(self.config.num_qubits, self.config.memory_capacity);
        self.metrics = ReservoirMetrics::default();
        self.training_history.clear();
        Ok(())
    }
}

impl TimeSeriesPredictor {
    /// Create new time series predictor
    #[must_use]
    pub fn new(config: &TimeSeriesConfig) -> Self {
        Self {
            arima_params: ARIMAParams {
                ar_coeffs: Array1::zeros(config.ar_order),
                ma_coeffs: Array1::zeros(config.ma_order),
                diff_order: config.diff_order,
                residuals: VecDeque::with_capacity(config.ma_order),
                variance: 1.0,
            },
            nar_state: NARState {
                order: config.nar_order,
                coeffs: Array2::zeros((config.nar_order, config.nar_order)),
                history: VecDeque::with_capacity(config.nar_order),
                activation: ActivationFunction::Tanh,
            },
            kernel_weights: Array1::from_vec(config.kernel_params.clone()),
            trend_model: TrendModel {
                params: vec![0.0, 0.0], // Linear trend: intercept, slope
                strength: 0.0,
                direction: 0.0,
            },
        }
    }
}

impl MemoryAnalyzer {
    /// Create new memory analyzer
    #[must_use]
    pub fn new(config: MemoryAnalysisConfig) -> Self {
        Self {
            config,
            capacity_estimates: HashMap::new(),
            nonlinearity_measures: HashMap::new(),
            temporal_correlations: Array2::zeros((0, 0)),
            ipc_metrics: HashMap::new(),
        }
    }
}

/// Enhanced training result
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TrainingResult {
    /// Training error (RMSE)
    pub training_error: f64,
    /// Test error (RMSE)
    pub test_error: f64,
    /// Training time in milliseconds
    pub training_time_ms: f64,
    /// Number of training examples
    pub num_examples: usize,
    /// Echo state property measure
    pub echo_state_property: f64,
    /// Memory capacity estimate
    pub memory_capacity: f64,
    /// Nonlinear memory capacity
    pub nonlinear_capacity: f64,
    /// Information processing capacity
    pub processing_capacity: f64,
}

/// Comprehensive benchmark for enhanced quantum reservoir computing
pub fn benchmark_enhanced_quantum_reservoir_computing() -> Result<HashMap<String, f64>> {
    let mut results = HashMap::new();

    // Test different enhanced reservoir configurations
    let configs = vec![
        QuantumReservoirConfig {
            num_qubits: 6,
            architecture: QuantumReservoirArchitecture::RandomCircuit,
            learning_config: AdvancedLearningConfig {
                algorithm: LearningAlgorithm::Ridge,
                ..Default::default()
            },
            ..Default::default()
        },
        QuantumReservoirConfig {
            num_qubits: 8,
            architecture: QuantumReservoirArchitecture::ScaleFree,
            learning_config: AdvancedLearningConfig {
                algorithm: LearningAlgorithm::LASSO,
                ..Default::default()
            },
            ..Default::default()
        },
        QuantumReservoirConfig {
            num_qubits: 6,
            architecture: QuantumReservoirArchitecture::HierarchicalModular,
            learning_config: AdvancedLearningConfig {
                algorithm: LearningAlgorithm::RecursiveLeastSquares,
                ..Default::default()
            },
            memory_config: MemoryAnalysisConfig {
                enable_capacity_estimation: true,
                enable_nonlinear: true,
                ..Default::default()
            },
            ..Default::default()
        },
        QuantumReservoirConfig {
            num_qubits: 8,
            architecture: QuantumReservoirArchitecture::Grid,
            dynamics: ReservoirDynamics::Floquet,
            input_encoding: InputEncoding::Angle,
            output_measurement: OutputMeasurement::TemporalCorrelations,
            ..Default::default()
        },
    ];

    for (i, config) in configs.into_iter().enumerate() {
        let start = std::time::Instant::now();

        let mut qrc = QuantumReservoirComputerEnhanced::new(config)?;

        // Generate enhanced test data
        let training_data = ReservoirTrainingData::new(
            (0..200)
                .map(|i| {
                    Array1::from_vec(vec![
                        (f64::from(i) * 0.1).sin(),
                        (f64::from(i) * 0.1).cos(),
                        (f64::from(i) * 0.05).sin() * (f64::from(i) * 0.2).cos(),
                    ])
                })
                .collect(),
            (0..200)
                .map(|i| Array1::from_vec(vec![f64::from(i).mul_add(0.1, 1.0).sin()]))
                .collect(),
            (0..200).map(|i| f64::from(i) * 0.1).collect(),
        );

        // Train and test
        let training_result = qrc.train(&training_data)?;

        let time = start.elapsed().as_secs_f64() * 1000.0;
        results.insert(format!("enhanced_config_{i}"), time);

        // Add enhanced performance metrics
        let metrics = qrc.get_metrics();
        results.insert(
            format!("enhanced_config_{i}_accuracy"),
            metrics.prediction_accuracy,
        );
        results.insert(
            format!("enhanced_config_{i}_memory_capacity"),
            training_result.memory_capacity,
        );
        results.insert(
            format!("enhanced_config_{i}_nonlinear_capacity"),
            training_result.nonlinear_capacity,
        );
        results.insert(
            format!("enhanced_config_{i}_processing_capacity"),
            training_result.processing_capacity,
        );
        results.insert(
            format!("enhanced_config_{i}_quantum_advantage"),
            metrics.quantum_advantage,
        );
        results.insert(
            format!("enhanced_config_{i}_efficiency"),
            metrics.reservoir_efficiency,
        );

        // Memory analysis results
        let memory_analyzer = qrc.get_memory_analysis();
        if let Some(&linear_capacity) = memory_analyzer.capacity_estimates.get("linear") {
            results.insert(
                format!("enhanced_config_{i}_linear_memory"),
                linear_capacity,
            );
        }
        if let Some(&total_capacity) = memory_analyzer.capacity_estimates.get("total") {
            results.insert(format!("enhanced_config_{i}_total_memory"), total_capacity);
        }
    }

    Ok(results)
}

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

    #[test]
    fn test_enhanced_quantum_reservoir_creation() {
        let config = QuantumReservoirConfig::default();
        let qrc = QuantumReservoirComputerEnhanced::new(config);
        assert!(qrc.is_ok());
    }

    #[test]
    fn test_enhanced_reservoir_state_creation() {
        let state = QuantumReservoirState::new(3, 10);
        assert_eq!(state.state_vector.len(), 8); // 2^3
        assert_eq!(state.state_history.capacity(), 10);
        assert_eq!(state.time_index, 0);
        assert!(state.memory_metrics.total_capacity >= 0.0);
    }

    #[test]
    fn test_enhanced_input_processing() {
        let config = QuantumReservoirConfig {
            num_qubits: 3,
            evolution_steps: 2,
            ..Default::default()
        };
        let mut qrc = QuantumReservoirComputerEnhanced::new(config).expect("Failed to create QRC");

        let input = Array1::from_vec(vec![0.5, 0.3, 0.8]);
        let result = qrc.process_input(&input);
        assert!(result.is_ok());

        let features = result.expect("Failed to process input");
        assert!(!features.is_empty());
    }

    #[test]
    fn test_enhanced_architectures() {
        let architectures = vec![
            QuantumReservoirArchitecture::RandomCircuit,
            QuantumReservoirArchitecture::SpinChain,
            QuantumReservoirArchitecture::ScaleFree,
            QuantumReservoirArchitecture::HierarchicalModular,
            QuantumReservoirArchitecture::Ring,
            QuantumReservoirArchitecture::Grid,
        ];

        for arch in architectures {
            let config = QuantumReservoirConfig {
                num_qubits: 4,
                architecture: arch,
                evolution_steps: 2,
                ..Default::default()
            };

            let qrc = QuantumReservoirComputerEnhanced::new(config);
            assert!(qrc.is_ok(), "Failed for architecture: {arch:?}");
        }
    }

    #[test]
    fn test_advanced_learning_algorithms() {
        let algorithms = vec![
            LearningAlgorithm::Ridge,
            LearningAlgorithm::LASSO,
            LearningAlgorithm::ElasticNet,
            LearningAlgorithm::RecursiveLeastSquares,
        ];

        for algorithm in algorithms {
            let config = QuantumReservoirConfig {
                num_qubits: 3,
                learning_config: AdvancedLearningConfig {
                    algorithm,
                    ..Default::default()
                },
                ..Default::default()
            };

            let qrc = QuantumReservoirComputerEnhanced::new(config);
            assert!(qrc.is_ok(), "Failed for algorithm: {algorithm:?}");
        }
    }

    #[test]
    fn test_enhanced_encoding_methods() {
        let encodings = vec![
            InputEncoding::Amplitude,
            InputEncoding::Phase,
            InputEncoding::BasisState,
            InputEncoding::Angle,
        ];

        for encoding in encodings {
            let config = QuantumReservoirConfig {
                num_qubits: 3,
                input_encoding: encoding,
                ..Default::default()
            };
            let mut qrc =
                QuantumReservoirComputerEnhanced::new(config).expect("Failed to create QRC");

            let input = Array1::from_vec(vec![0.5, 0.3]);
            let result = qrc.encode_input(&input);
            assert!(result.is_ok(), "Failed for encoding: {encoding:?}");
        }
    }

    #[test]
    fn test_enhanced_measurement_strategies() {
        let measurements = vec![
            OutputMeasurement::PauliExpectation,
            OutputMeasurement::Probability,
            OutputMeasurement::Correlations,
            OutputMeasurement::Entanglement,
            OutputMeasurement::QuantumFisherInformation,
            OutputMeasurement::Variance,
            OutputMeasurement::QuantumCoherence,
            OutputMeasurement::Purity,
            OutputMeasurement::TemporalCorrelations,
        ];

        for measurement in measurements {
            let config = QuantumReservoirConfig {
                num_qubits: 3,
                output_measurement: measurement,
                ..Default::default()
            };

            let qrc = QuantumReservoirComputerEnhanced::new(config);
            assert!(qrc.is_ok(), "Failed for measurement: {measurement:?}");
        }
    }

    #[test]
    fn test_enhanced_reservoir_dynamics() {
        let dynamics = vec![
            ReservoirDynamics::Unitary,
            ReservoirDynamics::Open,
            ReservoirDynamics::NISQ,
            ReservoirDynamics::Floquet,
        ];

        for dynamic in dynamics {
            let config = QuantumReservoirConfig {
                num_qubits: 3,
                dynamics: dynamic,
                evolution_steps: 1,
                ..Default::default()
            };

            let mut qrc =
                QuantumReservoirComputerEnhanced::new(config).expect("Failed to create QRC");
            let result = qrc.evolve_reservoir();
            assert!(result.is_ok(), "Failed for dynamics: {dynamic:?}");
        }
    }

    #[test]
    fn test_memory_analysis() {
        let config = QuantumReservoirConfig {
            num_qubits: 4,
            memory_config: MemoryAnalysisConfig {
                enable_capacity_estimation: true,
                enable_nonlinear: true,
                enable_ipc: true,
                ..Default::default()
            },
            ..Default::default()
        };

        let qrc = QuantumReservoirComputerEnhanced::new(config).expect("Failed to create QRC");
        let memory_analyzer = qrc.get_memory_analysis();

        assert!(memory_analyzer.config.enable_capacity_estimation);
        assert!(memory_analyzer.config.enable_nonlinear);
        assert!(memory_analyzer.config.enable_ipc);
    }

    #[test]
    fn test_enhanced_training_data() {
        let training_data = ReservoirTrainingData::new(
            vec![
                Array1::from_vec(vec![0.1, 0.2]),
                Array1::from_vec(vec![0.3, 0.4]),
            ],
            vec![Array1::from_vec(vec![0.5]), Array1::from_vec(vec![0.6])],
            vec![0.0, 1.0],
        )
        .with_features(vec![
            Array1::from_vec(vec![0.7, 0.8]),
            Array1::from_vec(vec![0.9, 1.0]),
        ])
        .with_labels(vec![0, 1])
        .with_weights(vec![1.0, 1.0]);

        assert_eq!(training_data.len(), 2);
        assert!(training_data.features.is_some());
        assert!(training_data.labels.is_some());
        assert!(training_data.sample_weights.is_some());

        let (train, test) = training_data.train_test_split(0.5);
        assert_eq!(train.len(), 1);
        assert_eq!(test.len(), 1);
    }

    #[test]
    fn test_time_series_predictor() {
        let config = TimeSeriesConfig::default();
        let predictor = TimeSeriesPredictor::new(&config);

        assert_eq!(predictor.arima_params.ar_coeffs.len(), config.ar_order);
        assert_eq!(predictor.arima_params.ma_coeffs.len(), config.ma_order);
        assert_eq!(predictor.nar_state.order, config.nar_order);
    }

    #[test]
    fn test_enhanced_metrics_tracking() {
        let config = QuantumReservoirConfig::default();
        let qrc = QuantumReservoirComputerEnhanced::new(config).expect("Failed to create QRC");

        let metrics = qrc.get_metrics();
        assert_eq!(metrics.training_examples, 0);
        assert_eq!(metrics.prediction_accuracy, 0.0);
        assert_eq!(metrics.memory_capacity, 0.0);
        assert_eq!(metrics.nonlinear_memory_capacity, 0.0);
        assert_eq!(metrics.quantum_advantage, 0.0);
    }

    #[test]
    fn test_enhanced_feature_sizes() {
        let measurements = vec![
            (OutputMeasurement::PauliExpectation, 24), // 8 qubits * 3 Pauli
            (OutputMeasurement::QuantumFisherInformation, 8), // 8 qubits
            (OutputMeasurement::Variance, 24),         // 8 qubits * 3 Pauli
            (OutputMeasurement::Purity, 1),            // Single value
        ];

        for (measurement, expected_size) in measurements {
            let config = QuantumReservoirConfig {
                num_qubits: 8,
                output_measurement: measurement,
                ..Default::default()
            };

            let feature_size = QuantumReservoirComputerEnhanced::calculate_feature_size(&config);
            assert_eq!(
                feature_size, expected_size,
                "Feature size mismatch for {measurement:?}"
            );
        }
    }
}