use crate::builder::Circuit;
use quantrs2_core::{
error::{QuantRS2Error, QuantRS2Result},
gate::GateOp,
qubit::QubitId,
};
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, HashSet, VecDeque};
use std::f64::consts::PI;
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub enum AnyonType {
Vacuum,
Ising,
Fibonacci,
Majorana,
SU2 { level: usize },
Parafermion { n: usize },
Custom {
name: String,
quantum_dimension: f64,
fusion_rules: Vec<FusionRule>,
},
}
impl AnyonType {
#[must_use]
pub fn quantum_dimension(&self) -> f64 {
match self {
Self::Vacuum => 1.0,
Self::Ising => (2.0_f64).sqrt(),
Self::Fibonacci => f64::midpoint(1.0, 5.0_f64.sqrt()), Self::Majorana => (2.0_f64).sqrt(),
Self::SU2 { level } => (*level as f64 + 1.0).sqrt(),
Self::Parafermion { n } => (2.0 * (*n as f64)).sqrt(),
Self::Custom {
quantum_dimension, ..
} => *quantum_dimension,
}
}
#[must_use]
pub const fn is_abelian(&self) -> bool {
matches!(self, Self::Vacuum)
}
#[must_use]
pub const fn is_universal(&self) -> bool {
match self {
Self::Fibonacci => true,
Self::SU2 { level } => *level >= 3,
Self::Parafermion { n } => *n >= 3,
_ => false,
}
}
}
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub struct FusionRule {
pub inputs: Vec<AnyonType>,
pub outputs: Vec<(AnyonType, usize)>,
}
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub struct Anyon {
pub id: usize,
pub anyon_type: AnyonType,
pub position: (f64, f64),
pub charge: Option<usize>,
}
impl Anyon {
#[must_use]
pub const fn new(id: usize, anyon_type: AnyonType, position: (f64, f64)) -> Self {
Self {
id,
anyon_type,
position,
charge: None,
}
}
#[must_use]
pub fn can_fuse_with(&self, other: &Self) -> bool {
self.anyon_type == other.anyon_type
|| self.anyon_type == AnyonType::Vacuum
|| other.anyon_type == AnyonType::Vacuum
}
}
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub struct BraidingOperation {
pub anyons: Vec<usize>,
pub braiding_type: BraidingType,
pub braiding_count: usize,
pub phase: Option<f64>,
}
#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
pub enum BraidingType {
Clockwise,
Counterclockwise,
Exchange,
YangBaxter,
}
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize)]
pub enum TopologicalGate {
Braiding {
anyon1: usize,
anyon2: usize,
braiding_type: BraidingType,
},
Fusion {
input_anyons: Vec<usize>,
output_anyon: usize,
fusion_channel: usize,
},
Splitting {
input_anyon: usize,
output_anyons: Vec<usize>,
splitting_channel: usize,
},
FusionMeasurement {
anyons: Vec<usize>,
measurement_basis: FusionBasis,
},
Creation {
anyon_type: AnyonType,
position: (f64, f64),
},
Annihilation { anyon: usize },
}
#[derive(Debug, Clone, PartialEq, Eq, Serialize, Deserialize)]
pub enum FusionBasis {
Vacuum,
NonTrivial { channel: usize },
}
#[derive(Debug, Clone)]
pub struct TopologicalCircuit {
pub anyons: HashMap<usize, Anyon>,
pub gates: Vec<TopologicalGate>,
pub braiding_sequence: Vec<BraidingOperation>,
pub fusion_rules: Vec<(AnyonType, Vec<FusionRule>)>,
pub layout: TopologicalLayout,
}
#[derive(Debug, Clone)]
pub struct TopologicalLayout {
pub width: f64,
pub height: f64,
pub forbidden_regions: Vec<Region>,
pub braiding_paths: Vec<Path>,
}
#[derive(Debug, Clone)]
pub struct Region {
pub center: (f64, f64),
pub radius: f64,
pub shape: RegionShape,
}
#[derive(Debug, Clone, PartialEq)]
pub enum RegionShape {
Circle,
Rectangle { width: f64, height: f64 },
Polygon { vertices: Vec<(f64, f64)> },
}
#[derive(Debug, Clone)]
pub struct Path {
pub waypoints: Vec<(f64, f64)>,
pub path_type: PathType,
}
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum PathType {
Straight,
Curved,
Optimized,
}
pub struct TopologicalCompiler {
default_anyon_model: AnyonModel,
braiding_optimizer: BraidingOptimizer,
layout_optimizer: LayoutOptimizer,
}
#[derive(Debug, Clone)]
pub struct AnyonModel {
pub primary_anyon: AnyonType,
pub supported_anyons: Vec<AnyonType>,
pub fusion_rules: Vec<(AnyonType, Vec<FusionRule>)>,
pub braiding_phases: Vec<((AnyonType, AnyonType), f64)>,
}
impl AnyonModel {
#[must_use]
pub fn fibonacci() -> Self {
let fusion_rules = vec![(
AnyonType::Fibonacci,
vec![FusionRule {
inputs: vec![AnyonType::Fibonacci, AnyonType::Fibonacci],
outputs: vec![(AnyonType::Vacuum, 1), (AnyonType::Fibonacci, 1)],
}],
)];
let braiding_phases = vec![(
(AnyonType::Fibonacci, AnyonType::Fibonacci),
2.0 * PI / 5.0, )];
Self {
primary_anyon: AnyonType::Fibonacci,
supported_anyons: vec![AnyonType::Vacuum, AnyonType::Fibonacci],
fusion_rules,
braiding_phases,
}
}
#[must_use]
pub fn ising() -> Self {
let fusion_rules = vec![(
AnyonType::Ising,
vec![FusionRule {
inputs: vec![AnyonType::Ising, AnyonType::Ising],
outputs: vec![
(AnyonType::Vacuum, 1),
(AnyonType::Majorana, 1), ],
}],
)];
let braiding_phases = vec![(
(AnyonType::Ising, AnyonType::Ising),
PI / 4.0, )];
Self {
primary_anyon: AnyonType::Ising,
supported_anyons: vec![AnyonType::Vacuum, AnyonType::Ising, AnyonType::Majorana],
fusion_rules,
braiding_phases,
}
}
}
#[derive(Debug, Clone)]
pub struct BraidingOptimizer {
pub strategy: OptimizationStrategy,
pub max_braiding_distance: f64,
pub optimize_paths: bool,
}
#[derive(Debug, Clone, PartialEq, Eq)]
pub enum OptimizationStrategy {
MinimizeLength,
MinimizeCrossings,
MinimizeTime,
Balanced,
}
#[derive(Debug, Clone)]
pub struct LayoutOptimizer {
pub target_density: f64,
pub auto_spacing: bool,
pub min_distance: f64,
}
impl TopologicalCompiler {
#[must_use]
pub const fn new(anyon_model: AnyonModel) -> Self {
Self {
default_anyon_model: anyon_model,
braiding_optimizer: BraidingOptimizer {
strategy: OptimizationStrategy::Balanced,
max_braiding_distance: 10.0,
optimize_paths: true,
},
layout_optimizer: LayoutOptimizer {
target_density: 0.5,
auto_spacing: true,
min_distance: 1.0,
},
}
}
pub fn compile_quantum_circuit<const N: usize>(
&self,
circuit: &Circuit<N>,
) -> QuantRS2Result<TopologicalCircuit> {
let mut anyons = HashMap::new();
let mut next_anyon_id = 0;
for qubit_id in 0..N {
let pos_x = qubit_id as f64 * 2.0;
let anyon1 = Anyon::new(
next_anyon_id,
self.default_anyon_model.primary_anyon.clone(),
(pos_x, 0.0),
);
let anyon2 = Anyon::new(
next_anyon_id + 1,
self.default_anyon_model.primary_anyon.clone(),
(pos_x + 1.0, 0.0),
);
anyons.insert(next_anyon_id, anyon1);
anyons.insert(next_anyon_id + 1, anyon2);
next_anyon_id += 2;
}
let mut topological_gates = Vec::new();
let mut braiding_sequence = Vec::new();
for gate in circuit.gates() {
let (topo_gates, braidings) = self.compile_gate(gate.as_ref(), &anyons)?;
topological_gates.extend(topo_gates);
braiding_sequence.extend(braidings);
}
let layout = self.create_layout(N)?;
Ok(TopologicalCircuit {
anyons,
gates: topological_gates,
braiding_sequence,
fusion_rules: self.default_anyon_model.fusion_rules.clone(),
layout,
})
}
fn compile_gate(
&self,
gate: &dyn GateOp,
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
let gate_name = gate.name();
let qubits = gate.qubits();
match gate_name {
"H" => self.compile_hadamard_gate(&qubits, anyons),
"X" => self.compile_pauli_x_gate(&qubits, anyons),
"Z" => self.compile_pauli_z_gate(&qubits, anyons),
"CNOT" => self.compile_cnot_gate(&qubits, anyons),
"T" => self.compile_t_gate(&qubits, anyons),
_ => Err(QuantRS2Error::InvalidInput(format!(
"Gate {gate_name} not supported in topological compilation"
))),
}
}
fn compile_hadamard_gate(
&self,
qubits: &[QubitId],
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
if qubits.len() != 1 {
return Err(QuantRS2Error::InvalidInput(
"Hadamard requires one qubit".to_string(),
));
}
let qubit_id = qubits[0].id() as usize;
let anyon1_id = qubit_id * 2;
let anyon2_id = qubit_id * 2 + 1;
let braiding = BraidingOperation {
anyons: vec![anyon1_id, anyon2_id],
braiding_type: BraidingType::Clockwise,
braiding_count: 1,
phase: Some(PI / 2.0),
};
let topo_gate = TopologicalGate::Braiding {
anyon1: anyon1_id,
anyon2: anyon2_id,
braiding_type: BraidingType::Clockwise,
};
Ok((vec![topo_gate], vec![braiding]))
}
fn compile_pauli_x_gate(
&self,
qubits: &[QubitId],
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
if qubits.len() != 1 {
return Err(QuantRS2Error::InvalidInput(
"Pauli-X requires one qubit".to_string(),
));
}
let qubit_id = qubits[0].id() as usize;
let anyon1_id = qubit_id * 2;
let anyon2_id = qubit_id * 2 + 1;
let braiding = BraidingOperation {
anyons: vec![anyon1_id, anyon2_id],
braiding_type: BraidingType::Exchange,
braiding_count: 2,
phase: Some(PI),
};
let topo_gate = TopologicalGate::Braiding {
anyon1: anyon1_id,
anyon2: anyon2_id,
braiding_type: BraidingType::Exchange,
};
Ok((vec![topo_gate], vec![braiding]))
}
fn compile_pauli_z_gate(
&self,
qubits: &[QubitId],
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
let qubit_id = qubits[0].id() as usize;
let anyon1_id = qubit_id * 2;
let anyon2_id = qubit_id * 2 + 1;
let topo_gate = TopologicalGate::FusionMeasurement {
anyons: vec![anyon1_id, anyon2_id],
measurement_basis: FusionBasis::Vacuum,
};
Ok((vec![topo_gate], vec![]))
}
fn compile_cnot_gate(
&self,
qubits: &[QubitId],
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
if qubits.len() != 2 {
return Err(QuantRS2Error::InvalidInput(
"CNOT requires two qubits".to_string(),
));
}
let control_id = qubits[0].id() as usize;
let target_id = qubits[1].id() as usize;
let control_anyon1 = control_id * 2;
let control_anyon2 = control_id * 2 + 1;
let target_anyon1 = target_id * 2;
let target_anyon2 = target_id * 2 + 1;
let mut braidings = Vec::new();
let mut topo_gates = Vec::new();
braidings.push(BraidingOperation {
anyons: vec![control_anyon1, target_anyon1],
braiding_type: BraidingType::Clockwise,
braiding_count: 1,
phase: Some(PI / 4.0),
});
braidings.push(BraidingOperation {
anyons: vec![control_anyon2, target_anyon2],
braiding_type: BraidingType::Counterclockwise,
braiding_count: 1,
phase: Some(-PI / 4.0),
});
topo_gates.push(TopologicalGate::Braiding {
anyon1: control_anyon1,
anyon2: target_anyon1,
braiding_type: BraidingType::Clockwise,
});
topo_gates.push(TopologicalGate::Braiding {
anyon1: control_anyon2,
anyon2: target_anyon2,
braiding_type: BraidingType::Counterclockwise,
});
Ok((topo_gates, braidings))
}
fn compile_t_gate(
&self,
qubits: &[QubitId],
anyons: &HashMap<usize, Anyon>,
) -> QuantRS2Result<(Vec<TopologicalGate>, Vec<BraidingOperation>)> {
if !self.default_anyon_model.primary_anyon.is_universal() {
return Err(QuantRS2Error::InvalidInput(
"T gate requires universal anyon model".to_string(),
));
}
let qubit_id = qubits[0].id() as usize;
let anyon1_id = qubit_id * 2;
let anyon2_id = qubit_id * 2 + 1;
let braiding = BraidingOperation {
anyons: vec![anyon1_id, anyon2_id],
braiding_type: BraidingType::YangBaxter,
braiding_count: 1,
phase: Some(PI / 4.0),
};
let topo_gate = TopologicalGate::Braiding {
anyon1: anyon1_id,
anyon2: anyon2_id,
braiding_type: BraidingType::YangBaxter,
};
Ok((vec![topo_gate], vec![braiding]))
}
fn create_layout(&self, num_qubits: usize) -> QuantRS2Result<TopologicalLayout> {
let width = (num_qubits as f64).mul_add(2.0, 2.0).max(10.0);
let height = 10.0;
Ok(TopologicalLayout {
width,
height,
forbidden_regions: Vec::new(),
braiding_paths: Vec::new(),
})
}
pub fn optimize_braiding_sequence(
&self,
circuit: &mut TopologicalCircuit,
) -> QuantRS2Result<OptimizationStats> {
let initial_length = self.calculate_total_braiding_length(&circuit.braiding_sequence);
let initial_crossings = self.count_braiding_crossings(&circuit.braiding_sequence);
match self.braiding_optimizer.strategy {
OptimizationStrategy::MinimizeLength => {
self.optimize_for_length(&circuit.braiding_sequence)?;
}
OptimizationStrategy::MinimizeCrossings => {
self.optimize_for_crossings(&circuit.braiding_sequence)?;
}
OptimizationStrategy::MinimizeTime => {
self.optimize_for_time(&circuit.braiding_sequence)?;
}
OptimizationStrategy::Balanced => {
self.optimize_balanced(&circuit.braiding_sequence)?;
}
}
let final_length = self.calculate_total_braiding_length(&circuit.braiding_sequence);
let final_crossings = self.count_braiding_crossings(&circuit.braiding_sequence);
Ok(OptimizationStats {
initial_length,
final_length,
initial_crossings,
final_crossings,
length_improvement: (initial_length - final_length) / initial_length,
crossings_improvement: (initial_crossings as f64 - final_crossings as f64)
/ initial_crossings as f64,
})
}
fn calculate_total_braiding_length(&self, braidings: &[BraidingOperation]) -> f64 {
braidings.iter().map(|b| b.braiding_count as f64).sum()
}
const fn count_braiding_crossings(&self, braidings: &[BraidingOperation]) -> usize {
braidings.len()
}
const fn optimize_for_length(&self, braidings: &[BraidingOperation]) -> QuantRS2Result<()> {
Ok(())
}
const fn optimize_for_crossings(&self, braidings: &[BraidingOperation]) -> QuantRS2Result<()> {
Ok(())
}
const fn optimize_for_time(&self, braidings: &[BraidingOperation]) -> QuantRS2Result<()> {
Ok(())
}
const fn optimize_balanced(&self, braidings: &[BraidingOperation]) -> QuantRS2Result<()> {
Ok(())
}
}
#[derive(Debug, Clone)]
pub struct OptimizationStats {
pub initial_length: f64,
pub final_length: f64,
pub initial_crossings: usize,
pub final_crossings: usize,
pub length_improvement: f64,
pub crossings_improvement: f64,
}
impl TopologicalCircuit {
#[must_use]
pub fn total_braiding_operations(&self) -> usize {
self.braiding_sequence
.iter()
.map(|b| b.braiding_count)
.sum()
}
#[must_use]
pub fn anyon_count(&self) -> usize {
self.anyons.len()
}
#[must_use]
pub fn is_universal(&self) -> bool {
self.anyons
.values()
.any(|anyon| anyon.anyon_type.is_universal())
}
#[must_use]
pub fn braiding_depth(&self) -> usize {
self.braiding_sequence.len()
}
}
#[cfg(test)]
mod tests {
use super::*;
use quantrs2_core::gate::multi::CNOT;
use quantrs2_core::gate::single::Hadamard;
#[test]
fn test_anyon_types() {
let fibonacci = AnyonType::Fibonacci;
assert!(fibonacci.is_universal());
assert!(!fibonacci.is_abelian());
assert!((fibonacci.quantum_dimension() - 1.618).abs() < 0.01);
let ising = AnyonType::Ising;
assert!(!ising.is_universal());
assert!(!ising.is_abelian());
assert!((ising.quantum_dimension() - 1.414).abs() < 0.01);
}
#[test]
fn test_anyon_creation() {
let anyon = Anyon::new(0, AnyonType::Fibonacci, (1.0, 2.0));
assert_eq!(anyon.id, 0);
assert_eq!(anyon.position, (1.0, 2.0));
assert_eq!(anyon.anyon_type, AnyonType::Fibonacci);
}
#[test]
fn test_anyon_model_creation() {
let fibonacci_model = AnyonModel::fibonacci();
assert_eq!(fibonacci_model.primary_anyon, AnyonType::Fibonacci);
assert!(fibonacci_model
.fusion_rules
.iter()
.any(|(anyon_type, _)| *anyon_type == AnyonType::Fibonacci));
let ising_model = AnyonModel::ising();
assert_eq!(ising_model.primary_anyon, AnyonType::Ising);
assert!(ising_model
.braiding_phases
.iter()
.any(|((a1, a2), _)| *a1 == AnyonType::Ising && *a2 == AnyonType::Ising));
}
#[test]
fn test_topological_compiler() {
let model = AnyonModel::fibonacci();
let compiler = TopologicalCompiler::new(model);
assert_eq!(
compiler.default_anyon_model.primary_anyon,
AnyonType::Fibonacci
);
assert_eq!(
compiler.braiding_optimizer.strategy,
OptimizationStrategy::Balanced
);
}
#[test]
fn test_braiding_operation() {
let braiding = BraidingOperation {
anyons: vec![0, 1],
braiding_type: BraidingType::Clockwise,
braiding_count: 2,
phase: Some(PI / 4.0),
};
assert_eq!(braiding.anyons.len(), 2);
assert_eq!(braiding.braiding_count, 2);
assert_eq!(braiding.braiding_type, BraidingType::Clockwise);
}
#[test]
fn test_topological_gates() {
let fusion_gate = TopologicalGate::Fusion {
input_anyons: vec![0, 1],
output_anyon: 2,
fusion_channel: 0,
};
let braiding_gate = TopologicalGate::Braiding {
anyon1: 0,
anyon2: 1,
braiding_type: BraidingType::Exchange,
};
assert!(matches!(fusion_gate, TopologicalGate::Fusion { .. }));
assert!(matches!(braiding_gate, TopologicalGate::Braiding { .. }));
}
#[test]
fn test_layout_creation() {
let layout = TopologicalLayout {
width: 10.0,
height: 8.0,
forbidden_regions: vec![],
braiding_paths: vec![],
};
assert_eq!(layout.width, 10.0);
assert_eq!(layout.height, 8.0);
assert!(layout.forbidden_regions.is_empty());
}
#[test]
fn test_circuit_properties() {
let mut anyons = HashMap::new();
anyons.insert(0, Anyon::new(0, AnyonType::Fibonacci, (0.0, 0.0)));
anyons.insert(1, Anyon::new(1, AnyonType::Fibonacci, (1.0, 0.0)));
let circuit = TopologicalCircuit {
anyons,
gates: vec![],
braiding_sequence: vec![BraidingOperation {
anyons: vec![0, 1],
braiding_type: BraidingType::Clockwise,
braiding_count: 3,
phase: Some(PI / 4.0),
}],
fusion_rules: Vec::new(),
layout: TopologicalLayout {
width: 5.0,
height: 5.0,
forbidden_regions: vec![],
braiding_paths: vec![],
},
};
assert_eq!(circuit.anyon_count(), 2);
assert_eq!(circuit.total_braiding_operations(), 3);
assert!(circuit.is_universal());
assert_eq!(circuit.braiding_depth(), 1);
}
}