use scirs2_core::ndarray::Array1;
use scirs2_core::parallel_ops::{IndexedParallelIterator, IntoParallelIterator, ParallelIterator};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, VecDeque};
use crate::circuit_interfaces::{
CircuitInterface, InterfaceCircuit, InterfaceGate, InterfaceGateType,
};
use crate::error::Result;
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub struct ConcatenationLevel {
pub level: usize,
pub distance: usize,
pub code_rate: usize,
}
#[derive(Debug)]
pub struct ConcatenatedCodeConfig {
pub levels: Vec<ConcatenationLevel>,
pub codes_per_level: Vec<Box<dyn ErrorCorrectionCode>>,
pub decoding_method: HierarchicalDecodingMethod,
pub error_threshold: f64,
pub parallel_decoding: bool,
pub max_decoding_iterations: usize,
}
pub trait ErrorCorrectionCode: Send + Sync + std::fmt::Debug {
fn get_parameters(&self) -> CodeParameters;
fn encode(&self, logical_state: &Array1<Complex64>) -> Result<Array1<Complex64>>;
fn decode(&self, encoded_state: &Array1<Complex64>) -> Result<DecodingResult>;
fn syndrome_circuit(&self, num_qubits: usize) -> Result<InterfaceCircuit>;
fn correct_errors(&self, state: &mut Array1<Complex64>, syndrome: &[bool]) -> Result<()>;
}
#[derive(Debug, Clone, Copy)]
pub struct CodeParameters {
pub n_logical: usize,
pub n_physical: usize,
pub distance: usize,
pub t: usize, }
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum HierarchicalDecodingMethod {
Sequential,
Parallel,
Adaptive,
BeliefPropagation,
}
#[derive(Debug, Clone)]
pub struct DecodingResult {
pub corrected_state: Array1<Complex64>,
pub syndrome: Vec<bool>,
pub error_pattern: Vec<ErrorType>,
pub confidence: f64,
pub errors_corrected: usize,
pub success: bool,
}
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ErrorType {
Identity,
BitFlip,
PhaseFlip,
BitPhaseFlip,
}
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ConcatenatedCorrectionResult {
pub final_state: Array1<Complex64>,
pub level_results: Vec<LevelDecodingResult>,
pub stats: ConcatenationStats,
pub execution_time_ms: f64,
pub success_probability: f64,
}
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct LevelDecodingResult {
pub level: usize,
pub syndromes: Vec<Vec<bool>>,
pub errors_corrected: usize,
pub error_patterns: Vec<String>,
pub confidence: f64,
pub processing_time_ms: f64,
}
#[derive(Debug, Clone, Default, Serialize, Deserialize)]
pub struct ConcatenationStats {
pub physical_qubits: usize,
pub logical_qubits: usize,
pub effective_distance: usize,
pub syndrome_measurements: usize,
pub total_errors_corrected: usize,
pub memory_overhead_factor: f64,
pub circuit_depth_overhead: usize,
pub decoding_iterations: usize,
}
pub struct ConcatenatedErrorCorrection {
config: ConcatenatedCodeConfig,
circuit_interface: CircuitInterface,
syndrome_history: VecDeque<Vec<Vec<bool>>>,
error_rates: HashMap<usize, f64>,
stats: ConcatenationStats,
}
impl ConcatenatedErrorCorrection {
pub fn new(config: ConcatenatedCodeConfig) -> Result<Self> {
let circuit_interface = CircuitInterface::new(Default::default())?;
let syndrome_history = VecDeque::with_capacity(100);
let error_rates = HashMap::new();
Ok(Self {
config,
circuit_interface,
syndrome_history,
error_rates,
stats: ConcatenationStats::default(),
})
}
pub fn encode_concatenated(
&mut self,
logical_state: &Array1<Complex64>,
) -> Result<Array1<Complex64>> {
let mut current_state = logical_state.clone();
for (level, code) in self.config.codes_per_level.iter().enumerate() {
current_state = code.encode(¤t_state)?;
let params = code.get_parameters();
self.stats.physical_qubits = params.n_physical;
self.stats.logical_qubits = params.n_logical;
if level == 0 {
self.stats.effective_distance = params.distance;
} else {
self.stats.effective_distance = self.stats.effective_distance.min(params.distance);
}
}
Ok(current_state)
}
pub fn decode_hierarchical(
&mut self,
encoded_state: &Array1<Complex64>,
) -> Result<ConcatenatedCorrectionResult> {
let start_time = std::time::Instant::now();
let result = match self.config.decoding_method {
HierarchicalDecodingMethod::Sequential => self.decode_sequential(encoded_state)?,
HierarchicalDecodingMethod::Parallel => self.decode_parallel(encoded_state)?,
HierarchicalDecodingMethod::Adaptive => self.decode_adaptive(encoded_state)?,
HierarchicalDecodingMethod::BeliefPropagation => {
self.decode_belief_propagation(encoded_state)?
}
};
let execution_time_ms = start_time.elapsed().as_secs_f64() * 1000.0;
let all_syndromes: Vec<Vec<bool>> = result
.level_results
.iter()
.flat_map(|r| r.syndromes.iter().cloned())
.collect();
self.syndrome_history.push_back(all_syndromes);
if self.syndrome_history.len() > 100 {
self.syndrome_history.pop_front();
}
let success_probability = self.estimate_success_probability(&result);
Ok(ConcatenatedCorrectionResult {
final_state: result.final_state,
level_results: result.level_results,
stats: self.stats.clone(),
execution_time_ms,
success_probability,
})
}
fn decode_sequential(
&mut self,
encoded_state: &Array1<Complex64>,
) -> Result<ConcatenatedCorrectionResult> {
let mut current_state = encoded_state.clone();
let mut level_results = Vec::new();
for (level, code) in self.config.codes_per_level.iter().enumerate().rev() {
let level_start = std::time::Instant::now();
let decoding_result = code.decode(¤t_state)?;
current_state = decoding_result.corrected_state;
let error_patterns: Vec<String> = decoding_result
.error_pattern
.iter()
.map(|e| format!("{e:?}"))
.collect();
let level_result = LevelDecodingResult {
level,
syndromes: vec![decoding_result.syndrome],
errors_corrected: decoding_result.errors_corrected,
error_patterns,
confidence: decoding_result.confidence,
processing_time_ms: level_start.elapsed().as_secs_f64() * 1000.0,
};
level_results.push(level_result);
self.stats.total_errors_corrected += decoding_result.errors_corrected;
self.stats.decoding_iterations += 1;
}
level_results.reverse();
Ok(ConcatenatedCorrectionResult {
final_state: current_state,
level_results,
stats: self.stats.clone(),
execution_time_ms: 0.0, success_probability: 0.0, })
}
fn decode_parallel(
&mut self,
encoded_state: &Array1<Complex64>,
) -> Result<ConcatenatedCorrectionResult> {
if !self.config.parallel_decoding {
return self.decode_sequential(encoded_state);
}
let num_levels = self.config.codes_per_level.len();
let mut level_results = Vec::with_capacity(num_levels);
let results: Vec<_> = (0..num_levels)
.into_par_iter()
.map(|level| {
let level_start = std::time::Instant::now();
let mut state_copy = encoded_state.clone();
let decoding_result = self.config.codes_per_level[level]
.decode(&state_copy)
.unwrap_or_else(|_| DecodingResult {
corrected_state: state_copy,
syndrome: vec![false],
error_pattern: vec![ErrorType::Identity],
confidence: 0.0,
errors_corrected: 0,
success: false,
});
let error_patterns: Vec<String> = decoding_result
.error_pattern
.iter()
.map(|e| format!("{e:?}"))
.collect();
LevelDecodingResult {
level,
syndromes: vec![decoding_result.syndrome],
errors_corrected: decoding_result.errors_corrected,
error_patterns,
confidence: decoding_result.confidence,
processing_time_ms: level_start.elapsed().as_secs_f64() * 1000.0,
}
})
.collect();
level_results.extend(results);
let sequential_result = self.decode_sequential(encoded_state)?;
Ok(ConcatenatedCorrectionResult {
final_state: sequential_result.final_state,
level_results,
stats: self.stats.clone(),
execution_time_ms: 0.0,
success_probability: 0.0,
})
}
fn decode_adaptive(
&mut self,
encoded_state: &Array1<Complex64>,
) -> Result<ConcatenatedCorrectionResult> {
let mut result = self.decode_sequential(encoded_state)?;
let error_rate = self.calculate_current_error_rate(&result.level_results);
if error_rate > self.config.error_threshold {
for iteration in 1..self.config.max_decoding_iterations {
let alternative_result = if iteration % 2 == 1 {
self.decode_parallel(encoded_state)?
} else {
self.decode_sequential(encoded_state)?
};
let alt_error_rate =
self.calculate_current_error_rate(&alternative_result.level_results);
if alt_error_rate < error_rate {
result = alternative_result;
break;
}
self.stats.decoding_iterations += 1;
}
}
Ok(result)
}
fn decode_belief_propagation(
&mut self,
encoded_state: &Array1<Complex64>,
) -> Result<ConcatenatedCorrectionResult> {
let mut current_state = encoded_state.clone();
let mut level_results = Vec::new();
let num_levels = self.config.codes_per_level.len();
let mut beliefs: Vec<f64> = vec![1.0; num_levels];
for iteration in 0..self.config.max_decoding_iterations.min(5) {
for (level, code) in self.config.codes_per_level.iter().enumerate() {
let level_start = std::time::Instant::now();
let decoding_result = code.decode(¤t_state)?;
beliefs[level] = beliefs[level].mul_add(0.9, decoding_result.confidence * 0.1);
current_state = decoding_result.corrected_state;
let error_patterns: Vec<String> = decoding_result
.error_pattern
.iter()
.map(|e| format!("{e:?}"))
.collect();
let level_result = LevelDecodingResult {
level,
syndromes: vec![decoding_result.syndrome],
errors_corrected: decoding_result.errors_corrected,
error_patterns,
confidence: beliefs[level],
processing_time_ms: level_start.elapsed().as_secs_f64() * 1000.0,
};
if iteration == 0 || level_results.len() <= level {
level_results.push(level_result);
} else {
level_results[level] = level_result;
}
self.stats.total_errors_corrected += decoding_result.errors_corrected;
}
let avg_confidence: f64 = beliefs.iter().sum::<f64>() / beliefs.len() as f64;
if avg_confidence > 0.95 {
break;
}
self.stats.decoding_iterations += 1;
}
Ok(ConcatenatedCorrectionResult {
final_state: current_state,
level_results,
stats: self.stats.clone(),
execution_time_ms: 0.0,
success_probability: 0.0,
})
}
fn calculate_current_error_rate(&self, level_results: &[LevelDecodingResult]) -> f64 {
if level_results.is_empty() {
return 0.0;
}
let total_errors: usize = level_results.iter().map(|r| r.errors_corrected).sum();
let total_qubits = self.stats.physical_qubits.max(1);
total_errors as f64 / total_qubits as f64
}
fn estimate_success_probability(&self, result: &ConcatenatedCorrectionResult) -> f64 {
if result.level_results.is_empty() {
return 1.0;
}
let confidence_product: f64 = result.level_results.iter().map(|r| r.confidence).product();
let error_rate = self.calculate_current_error_rate(&result.level_results);
let error_penalty = (-error_rate * 10.0).exp();
(confidence_product * error_penalty).min(1.0).max(0.0)
}
#[must_use]
pub const fn get_stats(&self) -> &ConcatenationStats {
&self.stats
}
pub fn reset_stats(&mut self) {
self.stats = ConcatenationStats::default();
self.syndrome_history.clear();
self.error_rates.clear();
}
}
#[derive(Debug, Clone)]
pub struct BitFlipCode;
impl Default for BitFlipCode {
fn default() -> Self {
Self::new()
}
}
impl BitFlipCode {
#[must_use]
pub const fn new() -> Self {
Self
}
}
#[derive(Debug)]
pub struct ConcatenatedBitFlipCode {
inner_code: BitFlipCode,
}
impl Default for ConcatenatedBitFlipCode {
fn default() -> Self {
Self::new()
}
}
impl ConcatenatedBitFlipCode {
#[must_use]
pub const fn new() -> Self {
Self {
inner_code: BitFlipCode::new(),
}
}
}
impl ErrorCorrectionCode for ConcatenatedBitFlipCode {
fn get_parameters(&self) -> CodeParameters {
CodeParameters {
n_logical: 1,
n_physical: 3,
distance: 3,
t: 1,
}
}
fn encode(&self, logical_state: &Array1<Complex64>) -> Result<Array1<Complex64>> {
let n_logical = logical_state.len();
let n_physical = n_logical * 3;
let mut encoded = Array1::zeros(n_physical);
for i in 0..n_logical {
let amp = logical_state[i];
encoded[i * 3] = amp;
encoded[i * 3 + 1] = amp;
encoded[i * 3 + 2] = amp;
}
Ok(encoded)
}
fn decode(&self, encoded_state: &Array1<Complex64>) -> Result<DecodingResult> {
let n_physical = encoded_state.len();
let n_logical = n_physical / 3;
let mut corrected_state = Array1::zeros(n_logical);
let mut syndrome = Vec::new();
let mut error_pattern = Vec::new();
let mut errors_corrected = 0;
for i in 0..n_logical {
let block_start = i * 3;
let a0 = encoded_state[block_start];
let a1 = encoded_state[block_start + 1];
let a2 = encoded_state[block_start + 2];
let distances = [(a0 - a1).norm(), (a1 - a2).norm(), (a0 - a2).norm()];
let min_dist_idx = distances
.iter()
.enumerate()
.min_by(|a, b| a.1.partial_cmp(b.1).unwrap_or(std::cmp::Ordering::Equal))
.map(|(idx, _)| idx)
.unwrap_or(0);
match min_dist_idx {
0 => {
corrected_state[i] = (a0 + a1) / 2.0;
if (a2 - a0).norm() > 1e-10 {
syndrome.push(true);
error_pattern.push(ErrorType::BitFlip);
errors_corrected += 1;
} else {
syndrome.push(false);
error_pattern.push(ErrorType::Identity);
}
}
1 => {
corrected_state[i] = (a1 + a2) / 2.0;
if (a0 - a1).norm() > 1e-10 {
syndrome.push(true);
error_pattern.push(ErrorType::BitFlip);
errors_corrected += 1;
} else {
syndrome.push(false);
error_pattern.push(ErrorType::Identity);
}
}
2 => {
corrected_state[i] = (a0 + a2) / 2.0;
if (a1 - a0).norm() > 1e-10 {
syndrome.push(true);
error_pattern.push(ErrorType::BitFlip);
errors_corrected += 1;
} else {
syndrome.push(false);
error_pattern.push(ErrorType::Identity);
}
}
_ => unreachable!(),
}
}
let confidence = 1.0 - (errors_corrected as f64 / n_logical as f64);
Ok(DecodingResult {
corrected_state,
syndrome,
error_pattern,
confidence,
errors_corrected,
success: errors_corrected <= n_logical,
})
}
fn syndrome_circuit(&self, num_qubits: usize) -> Result<InterfaceCircuit> {
let mut circuit = InterfaceCircuit::new(num_qubits + 2, 2);
for i in (0..num_qubits).step_by(3) {
if i + 2 < num_qubits {
circuit.add_gate(InterfaceGate::new(
InterfaceGateType::CNOT,
vec![i, num_qubits],
));
circuit.add_gate(InterfaceGate::new(
InterfaceGateType::CNOT,
vec![i + 1, num_qubits],
));
circuit.add_gate(InterfaceGate::new(
InterfaceGateType::CNOT,
vec![i + 1, num_qubits + 1],
));
circuit.add_gate(InterfaceGate::new(
InterfaceGateType::CNOT,
vec![i + 2, num_qubits + 1],
));
}
}
Ok(circuit)
}
fn correct_errors(&self, state: &mut Array1<Complex64>, syndrome: &[bool]) -> Result<()> {
for (i, &has_error) in syndrome.iter().enumerate() {
if has_error && i * 3 + 2 < state.len() {
let block_start = i * 3;
let majority =
(state[block_start] + state[block_start + 1] + state[block_start + 2]) / 3.0;
state[block_start] = majority;
state[block_start + 1] = majority;
state[block_start + 2] = majority;
}
}
Ok(())
}
}
pub fn create_standard_concatenated_code(levels: usize) -> Result<ConcatenatedErrorCorrection> {
let mut concatenation_levels = Vec::new();
let mut codes_per_level: Vec<Box<dyn ErrorCorrectionCode>> = Vec::new();
for level in 0..levels {
concatenation_levels.push(ConcatenationLevel {
level,
distance: 3,
code_rate: 3,
});
codes_per_level.push(Box::new(ConcatenatedBitFlipCode::new()));
}
let config = ConcatenatedCodeConfig {
levels: concatenation_levels,
codes_per_level,
decoding_method: HierarchicalDecodingMethod::Sequential,
error_threshold: 0.1,
parallel_decoding: true,
max_decoding_iterations: 10,
};
ConcatenatedErrorCorrection::new(config)
}
pub fn benchmark_concatenated_error_correction() -> Result<HashMap<String, f64>> {
let mut results = HashMap::new();
let levels = vec![1, 2, 3];
for &level in &levels {
let start = std::time::Instant::now();
let mut concatenated = create_standard_concatenated_code(level)?;
let logical_state = Array1::from_vec(vec![
Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
]);
let encoded = concatenated.encode_concatenated(&logical_state)?;
let mut noisy_encoded = encoded.clone();
for i in 0..noisy_encoded.len().min(5) {
noisy_encoded[i] += Complex64::new(0.01 * fastrand::f64(), 0.01 * fastrand::f64());
}
let _result = concatenated.decode_hierarchical(&noisy_encoded)?;
let time = start.elapsed().as_secs_f64() * 1000.0;
results.insert(format!("level_{level}"), time);
}
Ok(results)
}
#[cfg(test)]
mod tests {
use super::*;
use approx::assert_abs_diff_eq;
#[test]
fn test_concatenated_code_creation() {
let concatenated = create_standard_concatenated_code(2);
assert!(concatenated.is_ok());
}
#[test]
fn test_bit_flip_code_parameters() {
let code = ConcatenatedBitFlipCode::new();
let params = code.get_parameters();
assert_eq!(params.n_logical, 1);
assert_eq!(params.n_physical, 3);
assert_eq!(params.distance, 3);
assert_eq!(params.t, 1);
}
#[test]
fn test_bit_flip_encoding() {
let code = ConcatenatedBitFlipCode::new();
let logical_state =
Array1::from_vec(vec![Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)]);
let encoded = code
.encode(&logical_state)
.expect("Encoding should succeed in test");
assert_eq!(encoded.len(), 6);
assert!((encoded[0] - logical_state[0]).norm() < 1e-10);
assert!((encoded[1] - logical_state[0]).norm() < 1e-10);
assert!((encoded[2] - logical_state[0]).norm() < 1e-10);
}
#[test]
fn test_concatenated_encoding_decoding() {
let mut concatenated = create_standard_concatenated_code(1)
.expect("Concatenated code creation should succeed in test");
let logical_state = Array1::from_vec(vec![
Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
]);
let encoded = concatenated
.encode_concatenated(&logical_state)
.expect("Encoding should succeed in test");
assert!(encoded.len() >= logical_state.len());
let result = concatenated
.decode_hierarchical(&encoded)
.expect("Decoding should succeed in test");
assert!(!result.level_results.is_empty());
assert!(result.success_probability >= 0.0);
}
#[test]
fn test_syndrome_circuit_creation() {
let code = ConcatenatedBitFlipCode::new();
let circuit = code
.syndrome_circuit(6)
.expect("Syndrome circuit creation should succeed in test");
assert_eq!(circuit.num_qubits, 8); assert!(!circuit.gates.is_empty());
}
#[test]
fn test_decoding_methods() {
let mut concatenated = create_standard_concatenated_code(1)
.expect("Concatenated code creation should succeed in test");
let logical_state = Array1::from_vec(vec![Complex64::new(1.0, 0.0)]);
let encoded = concatenated
.encode_concatenated(&logical_state)
.expect("Encoding should succeed in test");
concatenated.config.decoding_method = HierarchicalDecodingMethod::Sequential;
let seq_result = concatenated
.decode_hierarchical(&encoded)
.expect("Sequential decoding should succeed in test");
assert!(!seq_result.level_results.is_empty());
concatenated.config.decoding_method = HierarchicalDecodingMethod::Adaptive;
let adapt_result = concatenated
.decode_hierarchical(&encoded)
.expect("Adaptive decoding should succeed in test");
assert!(!adapt_result.level_results.is_empty());
}
#[test]
fn test_error_rate_calculation() {
let concatenated = create_standard_concatenated_code(1)
.expect("Concatenated code creation should succeed in test");
let level_results = vec![LevelDecodingResult {
level: 0,
syndromes: vec![vec![true, false]],
errors_corrected: 1,
error_patterns: vec!["BitFlip".to_string()],
confidence: 0.9,
processing_time_ms: 1.0,
}];
let error_rate = concatenated.calculate_current_error_rate(&level_results);
assert!(error_rate > 0.0);
}
}