quantrs2-core 0.1.3

//! Quantum Algorithm Complexity Analysis Tools
//!
//! This module provides comprehensive tools for analyzing the complexity and performance
//! characteristics of quantum algorithms, including gate count analysis, circuit depth
//! calculation, quantum volume estimation, and theoretical complexity bounds.

use pyo3::prelude::*;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;

use std::fmt::Write;
/// Comprehensive quantum algorithm complexity analyzer
#[pyclass(name = "QuantumComplexityAnalyzer")]
pub struct PyQuantumComplexityAnalyzer {
    algorithm_name: String,
    analysis_results: Vec<ComplexityAnalysisResult>,
    circuit_metrics: CircuitMetrics,
}

/// Result of a complexity analysis
#[derive(Debug, Clone, Serialize, Deserialize)]
struct ComplexityAnalysisResult {
    algorithm_type: String,
    input_size: usize,
    gate_count: HashMap<String, usize>,
    circuit_depth: usize,
    qubit_count: usize,
    classical_complexity: String,
    quantum_advantage: Option<f64>,
    fidelity_estimate: Option<f64>,
    time_complexity: String,
    space_complexity: String,
    entanglement_entropy: Option<f64>,
    quantum_volume: Option<f64>,
}

/// Detailed circuit metrics
#[derive(Debug, Clone, Serialize, Deserialize)]
struct CircuitMetrics {
    total_gates: usize,
    single_qubit_gates: usize,
    two_qubit_gates: usize,
    multi_qubit_gates: usize,
    measurement_operations: usize,
    parallel_depth: usize,
    critical_path_length: usize,
    connectivity_degree: f64,
    gate_density: f64,
}

impl Default for CircuitMetrics {
    fn default() -> Self {
        Self {
            total_gates: 0,
            single_qubit_gates: 0,
            two_qubit_gates: 0,
            multi_qubit_gates: 0,
            measurement_operations: 0,
            parallel_depth: 0,
            critical_path_length: 0,
            connectivity_degree: 0.0,
            gate_density: 0.0,
        }
    }
}

#[pymethods]
impl PyQuantumComplexityAnalyzer {
    #[new]
    fn new(algorithm_name: String) -> Self {
        Self {
            algorithm_name,
            analysis_results: Vec::new(),
            circuit_metrics: CircuitMetrics::default(),
        }
    }

    /// Analyze the complexity of a quantum circuit
    fn analyze_circuit(
        &mut self,
        gates: Vec<(String, Vec<u32>, Option<Vec<f64>>)>,
        algorithm_type: String,
        input_size: usize,
    ) -> PyResult<()> {
        let mut gate_count = HashMap::new();
        let mut qubit_usage = std::collections::HashSet::new();
        let _max_parallel_depth = 0;

        // Count gates by type
        for (gate_type, qubits, _params) in &gates {
            *gate_count.entry(gate_type.clone()).or_insert(0) += 1;
            for &qubit in qubits {
                qubit_usage.insert(qubit);
            }
        }

        let qubit_count = qubit_usage.len();
        let circuit_depth = gates.len(); // Simplified depth calculation

        // Calculate quantum volume (simplified)
        let quantum_volume = Some(Self::calculate_quantum_volume(qubit_count, circuit_depth));

        // Estimate quantum advantage based on algorithm type
        let quantum_advantage = Self::estimate_quantum_advantage(&algorithm_type, input_size);

        // Determine complexity classes
        let (time_complexity, space_complexity) =
            Self::analyze_complexity_class(&algorithm_type, input_size);

        // Estimate fidelity based on gate count and depth
        let fidelity_estimate = Self::estimate_circuit_fidelity(&gate_count, circuit_depth);

        // Calculate entanglement entropy (placeholder)
        let entanglement_entropy = Some(Self::estimate_entanglement_entropy(
            qubit_count,
            &gate_count,
        ));

        let result = ComplexityAnalysisResult {
            algorithm_type: algorithm_type.clone(),
            input_size,
            gate_count: gate_count.clone(),
            circuit_depth,
            qubit_count,
            classical_complexity: Self::get_classical_complexity(&algorithm_type, input_size),
            quantum_advantage,
            fidelity_estimate,
            time_complexity,
            space_complexity,
            entanglement_entropy,
            quantum_volume,
        };

        self.analysis_results.push(result);
        self.update_circuit_metrics(&gates);

        Ok(())
    }

    /// Get detailed complexity analysis report
    fn get_analysis_report(&self) -> String {
        if self.analysis_results.is_empty() {
            return "No analysis results available.".to_string();
        }

        let mut report = "# Quantum Algorithm Complexity Analysis Report\n".to_string();
        writeln!(report, "**Algorithm:** {}\n", self.algorithm_name)
            .expect("Writing to String cannot fail");

        for (i, result) in self.analysis_results.iter().enumerate() {
            writeln!(
                report,
                "## Analysis {} - {} Algorithm",
                i + 1,
                result.algorithm_type
            )
            .expect("Writing to String cannot fail");
            writeln!(report, "- **Input Size:** {}", result.input_size)
                .expect("Writing to String cannot fail");
            writeln!(report, "- **Qubit Count:** {}", result.qubit_count)
                .expect("Writing to String cannot fail");
            writeln!(report, "- **Circuit Depth:** {}", result.circuit_depth)
                .expect("Writing to String cannot fail");
            writeln!(report, "- **Time Complexity:** {}", result.time_complexity)
                .expect("Writing to String cannot fail");
            writeln!(
                report,
                "- **Space Complexity:** {}",
                result.space_complexity
            )
            .expect("Writing to String cannot fail");
            writeln!(
                report,
                "- **Classical Complexity:** {}",
                result.classical_complexity
            )
            .expect("Writing to String cannot fail");

            if let Some(advantage) = result.quantum_advantage {
                writeln!(report, "- **Quantum Advantage:** {advantage:.2e}x speedup")
                    .expect("Writing to String cannot fail");
            }

            if let Some(fidelity) = result.fidelity_estimate {
                writeln!(report, "- **Estimated Fidelity:** {fidelity:.4}")
                    .expect("Writing to String cannot fail");
            }

            if let Some(entropy) = result.entanglement_entropy {
                writeln!(report, "- **Entanglement Entropy:** {entropy:.3} bits")
                    .expect("Writing to String cannot fail");
            }

            if let Some(qv) = result.quantum_volume {
                writeln!(report, "- **Quantum Volume:** {qv:.0}")
                    .expect("Writing to String cannot fail");
            }

            report.push_str("\n### Gate Count Distribution:\n");
            for (gate_type, count) in &result.gate_count {
                writeln!(report, "- **{gate_type}:** {count}")
                    .expect("Writing to String cannot fail");
            }
            report.push('\n');
        }

        // Add circuit metrics summary
        report.push_str("## Circuit Metrics Summary\n");
        writeln!(
            report,
            "- **Total Gates:** {}",
            self.circuit_metrics.total_gates
        )
        .expect("Writing to String cannot fail");
        writeln!(
            report,
            "- **Single-Qubit Gates:** {}",
            self.circuit_metrics.single_qubit_gates
        )
        .expect("Writing to String cannot fail");
        writeln!(
            report,
            "- **Two-Qubit Gates:** {}",
            self.circuit_metrics.two_qubit_gates
        )
        .expect("Writing to String cannot fail");
        writeln!(
            report,
            "- **Parallel Depth:** {}",
            self.circuit_metrics.parallel_depth
        )
        .expect("Writing to String cannot fail");
        writeln!(
            report,
            "- **Gate Density:** {:.3}",
            self.circuit_metrics.gate_density
        )
        .expect("Writing to String cannot fail");

        report
    }

    /// Get complexity scaling predictions
    fn predict_scaling(
        &self,
        target_input_sizes: Vec<usize>,
    ) -> HashMap<String, Vec<(usize, f64)>> {
        let mut predictions = HashMap::new();

        if let Some(latest_result) = self.analysis_results.last() {
            let base_size = latest_result.input_size;
            let base_qubits = latest_result.qubit_count;
            let base_depth = latest_result.circuit_depth;

            let mut gate_predictions = Vec::new();
            let mut depth_predictions = Vec::new();
            let mut qubit_predictions = Vec::new();

            for &target_size in &target_input_sizes {
                let scaling_factor = target_size as f64 / base_size as f64;

                // Predict based on algorithm type
                let (gate_scaling, depth_scaling, qubit_scaling) =
                    match latest_result.algorithm_type.as_str() {
                        "Shor" => (
                            scaling_factor.powi(3),
                            scaling_factor.powi(2),
                            scaling_factor.log2(),
                        ),
                        "Grover" => (
                            scaling_factor.sqrt(),
                            scaling_factor.sqrt(),
                            scaling_factor.log2(),
                        ),
                        "VQE" => (scaling_factor.powf(1.5), scaling_factor, scaling_factor),
                        "QAOA" => (scaling_factor.powi(2), scaling_factor, scaling_factor),
                        _ => (scaling_factor, scaling_factor, scaling_factor.log2()),
                    };

                gate_predictions.push((
                    target_size,
                    self.circuit_metrics.total_gates as f64 * gate_scaling,
                ));
                depth_predictions.push((target_size, base_depth as f64 * depth_scaling));
                qubit_predictions.push((target_size, base_qubits as f64 * qubit_scaling));
            }

            predictions.insert("gate_count".to_string(), gate_predictions);
            predictions.insert("circuit_depth".to_string(), depth_predictions);
            predictions.insert("qubit_count".to_string(), qubit_predictions);
        }

        predictions
    }

    /// Analyze resource requirements for quantum error correction
    fn analyze_error_correction_overhead(
        &self,
        target_logical_error_rate: f64,
    ) -> HashMap<String, f64> {
        let mut overhead = HashMap::new();

        if let Some(latest_result) = self.analysis_results.last() {
            // Simplified error correction analysis
            let physical_error_rate: f64 = 1e-3; // Typical for current hardware
            let threshold: f64 = 1e-2; // Surface code threshold

            if physical_error_rate < threshold {
                let code_distance = target_logical_error_rate.log(physical_error_rate).ceil();
                let physical_qubits_per_logical = code_distance * code_distance * 2.0; // Surface code

                overhead.insert("code_distance".to_string(), code_distance);
                overhead.insert(
                    "physical_qubits_per_logical".to_string(),
                    physical_qubits_per_logical,
                );
                overhead.insert(
                    "total_physical_qubits".to_string(),
                    latest_result.qubit_count as f64 * physical_qubits_per_logical,
                );
                overhead.insert("overhead_factor".to_string(), physical_qubits_per_logical);

                // Time overhead from error correction
                let syndrome_cycle_time = 1e-6; // 1 microsecond
                let logical_gate_time = syndrome_cycle_time * code_distance;
                overhead.insert(
                    "logical_gate_time_overhead".to_string(),
                    logical_gate_time / syndrome_cycle_time,
                );
            }
        }

        overhead
    }

    /// Get quantum advantage analysis
    fn quantum_advantage_analysis(&self) -> HashMap<String, String> {
        let mut analysis = HashMap::new();

        if let Some(latest_result) = self.analysis_results.last() {
            // Analyze different types of quantum advantage
            analysis.insert(
                "computational_advantage".to_string(),
                Self::analyze_computational_advantage(
                    &latest_result.algorithm_type,
                    latest_result.input_size,
                ),
            );

            analysis.insert("communication_advantage".to_string(),
                          "Quantum communication protocols may offer exponential advantages in certain scenarios.".to_string());

            analysis.insert(
                "sampling_advantage".to_string(),
                Self::analyze_sampling_advantage(&latest_result.algorithm_type),
            );

            analysis.insert(
                "optimization_advantage".to_string(),
                Self::analyze_optimization_advantage(&latest_result.algorithm_type),
            );
        }

        analysis
    }

    fn __repr__(&self) -> String {
        format!(
            "QuantumComplexityAnalyzer(algorithm='{}', analyses={})",
            self.algorithm_name,
            self.analysis_results.len()
        )
    }
}

// Helper methods implementation
impl PyQuantumComplexityAnalyzer {
    fn calculate_quantum_volume(qubit_count: usize, circuit_depth: usize) -> f64 {
        let min_dimension = qubit_count.min(circuit_depth);
        (min_dimension as f64).exp2()
    }

    fn estimate_quantum_advantage(algorithm_type: &str, input_size: usize) -> Option<f64> {
        match algorithm_type {
            "Shor" => {
                // Exponential advantage over classical factoring
                let classical_complexity = ((input_size as f64).cbrt()
                    * (input_size as f64).log2().powf(2.0 / 3.0))
                .exp2();
                let quantum_complexity = (input_size as f64).powi(3);
                Some(classical_complexity / quantum_complexity)
            }
            "Grover" => {
                // Quadratic advantage over classical search
                let classical_complexity = input_size as f64;
                let quantum_complexity = (input_size as f64).sqrt();
                Some(classical_complexity / quantum_complexity)
            }
            "HHL" => {
                // Exponential advantage for certain linear systems
                Some((input_size as f64).powi(2) / (input_size as f64).log2())
            }
            _ => None,
        }
    }

    fn analyze_complexity_class(algorithm_type: &str, _input_size: usize) -> (String, String) {
        match algorithm_type {
            "Shor" => ("O(n³ log n)".to_string(), "O(n)".to_string()),
            "Grover" => ("O(√N)".to_string(), "O(log N)".to_string()),
            "VQE" => ("O(n⁴)".to_string(), "O(n)".to_string()),
            "QAOA" => ("O(n² p)".to_string(), "O(n)".to_string()),
            "HHL" => ("O(log N s κ / ε)".to_string(), "O(log N)".to_string()),
            _ => ("O(poly(n))".to_string(), "O(n)".to_string()),
        }
    }

    fn estimate_circuit_fidelity(
        gate_count: &HashMap<String, usize>,
        _circuit_depth: usize,
    ) -> Option<f64> {
        // Simplified fidelity estimation based on gate errors
        let single_qubit_error: f64 = 1e-4;
        let two_qubit_error: f64 = 1e-3;

        let total_single_qubit = *gate_count.get("H").unwrap_or(&0)
            + *gate_count.get("X").unwrap_or(&0)
            + *gate_count.get("Y").unwrap_or(&0)
            + *gate_count.get("Z").unwrap_or(&0);

        let total_two_qubit =
            *gate_count.get("CNOT").unwrap_or(&0) + *gate_count.get("CZ").unwrap_or(&0);

        let error_probability = (total_single_qubit as f64).mul_add(
            single_qubit_error,
            (total_two_qubit as f64) * two_qubit_error,
        );

        Some(f64::max(1.0 - error_probability, 0.0))
    }

    fn estimate_entanglement_entropy(
        qubit_count: usize,
        gate_count: &HashMap<String, usize>,
    ) -> f64 {
        // Simplified entanglement entropy estimation
        let entangling_gates =
            *gate_count.get("CNOT").unwrap_or(&0) + *gate_count.get("CZ").unwrap_or(&0);

        let max_entropy = qubit_count as f64 / 2.0;
        let entanglement_factor = (entangling_gates as f64) / f64::max(qubit_count as f64, 1.0);

        f64::min(max_entropy * entanglement_factor.tanh(), max_entropy)
    }

    fn get_classical_complexity(algorithm_type: &str, _input_size: usize) -> String {
        match algorithm_type {
            "Shor" => "O(exp(n^(1/3) * log²n)) - Sub-exponential".to_string(),
            "Grover" => "O(N) - Linear search".to_string(),
            "VQE" => "O(exp(n)) - Exponential for general Hamiltonians".to_string(),
            "QAOA" => "O(exp(n)) - Exponential for general optimization".to_string(),
            "HHL" => "O(Ns κ log κ / ε) - Classical iterative methods".to_string(),
            _ => "Problem-dependent".to_string(),
        }
    }

    fn analyze_computational_advantage(algorithm_type: &str, _input_size: usize) -> String {
        match algorithm_type {
            "Shor" => "Exponential advantage over best known classical algorithms for integer factorization.".to_string(),
            "Grover" => "Quadratic advantage over classical unstructured search algorithms.".to_string(),
            "HHL" => "Exponential advantage for solving linear systems under specific conditions.".to_string(),
            "VQE" => "Potential advantage for quantum chemistry problems on NISQ devices.".to_string(),
            _ => "Advantage depends on problem structure and implementation details.".to_string(),
        }
    }

    fn analyze_sampling_advantage(algorithm_type: &str) -> String {
        match algorithm_type {
            "Random Circuit Sampling" => "Demonstrated quantum computational advantage for sampling tasks.".to_string(),
            "Boson Sampling" => "Conjectured exponential advantage for sampling from boson distributions.".to_string(),
            "IQP" => "Instantaneous Quantum Polynomial-time sampling advantage under complexity assumptions.".to_string(),
            _ => "Sampling advantage not typically applicable for this algorithm type.".to_string(),
        }
    }

    fn analyze_optimization_advantage(algorithm_type: &str) -> String {
        match algorithm_type {
            "QAOA" => "Potential advantage for combinatorial optimization problems with quantum annealing.".to_string(),
            "VQE" => "Advantage for finding ground states of quantum many-body systems.".to_string(),
            "Quantum Annealing" => "Advantage for certain optimization landscapes with quantum tunneling.".to_string(),
            _ => "Optimization advantage not typically applicable for this algorithm type.".to_string(),
        }
    }

    fn update_circuit_metrics(&mut self, gates: &[(String, Vec<u32>, Option<Vec<f64>>)]) {
        self.circuit_metrics.total_gates = gates.len();

        for (_gate_type, qubits, _) in gates {
            match qubits.len() {
                1 => self.circuit_metrics.single_qubit_gates += 1,
                2 => self.circuit_metrics.two_qubit_gates += 1,
                _ => self.circuit_metrics.multi_qubit_gates += 1,
            }
        }

        // Simplified metrics calculations
        self.circuit_metrics.parallel_depth = gates.len(); // Would need proper scheduling
        self.circuit_metrics.gate_density = gates.len() as f64
            / (self.circuit_metrics.single_qubit_gates + self.circuit_metrics.two_qubit_gates)
                .max(1) as f64;
    }
}

/// Module-level functions for complexity analysis
#[pyfunction]
pub fn analyze_algorithm_complexity(
    algorithm_type: String,
    input_size: usize,
    gates: Vec<(String, Vec<u32>, Option<Vec<f64>>)>,
) -> PyResult<String> {
    let mut analyzer = PyQuantumComplexityAnalyzer::new(algorithm_type.clone());
    analyzer.analyze_circuit(gates, algorithm_type, input_size)?;
    Ok(analyzer.get_analysis_report())
}

/// Compare quantum vs classical complexity
#[pyfunction]
pub fn compare_quantum_classical_complexity(
    algorithm_type: String,
    input_sizes: Vec<usize>,
) -> HashMap<String, Vec<(usize, String)>> {
    let mut comparison = HashMap::new();

    let mut quantum_complexities = Vec::new();
    let mut classical_complexities = Vec::new();

    for size in input_sizes {
        let (quantum_time, _) =
            PyQuantumComplexityAnalyzer::analyze_complexity_class(&algorithm_type, size);
        let classical_time =
            PyQuantumComplexityAnalyzer::get_classical_complexity(&algorithm_type, size);

        quantum_complexities.push((size, quantum_time));
        classical_complexities.push((size, classical_time));
    }

    comparison.insert("quantum".to_string(), quantum_complexities);
    comparison.insert("classical".to_string(), classical_complexities);

    comparison
}

/// Calculate theoretical quantum volume
#[pyfunction]
pub fn calculate_theoretical_quantum_volume(qubit_count: usize, circuit_depth: usize) -> f64 {
    PyQuantumComplexityAnalyzer::calculate_quantum_volume(qubit_count, circuit_depth)
}

/// Module initialization
pub const fn init_complexity_analysis() {
    // Initialization code for complexity analysis tools
}