// This code is part of Qiskit.
//
// (C) Copyright IBM 2024
//
// This code is licensed under the Apache License, Version 2.0. You may
// obtain a copy of this license in the LICENSE.txt file in the root directory
// of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
//
// Any modifications or derivative works of this code must retain this
// copyright notice, and modified files need to carry a notice indicating
// that they have been altered from the originals.
#![allow(clippy::too_many_arguments)]

use std::f64::consts::PI;
#[cfg(feature = "cache_pygates")]
use std::sync::OnceLock;

use approx::relative_eq;
use hashbrown::{HashMap, HashSet};
use indexmap::{IndexMap, IndexSet};
use itertools::Itertools;
use ndarray::prelude::*;
use num_complex::{Complex, Complex64};
use numpy::IntoPyArray;
use qiskit_circuit::circuit_instruction::OperationFromPython;
use smallvec::{smallvec, SmallVec};

use pyo3::intern;
use pyo3::prelude::*;
use pyo3::types::{IntoPyDict, PyDict, PyString, PyType};
use pyo3::wrap_pyfunction;
use pyo3::Python;

use qiskit_circuit::converters::{circuit_to_dag, QuantumCircuitData};
use qiskit_circuit::dag_circuit::{DAGCircuit, NodeType};
use qiskit_circuit::imports;
use qiskit_circuit::operations::{Operation, OperationRef, Param, PyGate, StandardGate};
use qiskit_circuit::packed_instruction::{PackedInstruction, PackedOperation};
use qiskit_circuit::Qubit;

use crate::euler_one_qubit_decomposer::{
    unitary_to_gate_sequence_inner, EulerBasis, EulerBasisSet, EULER_BASES, EULER_BASIS_NAMES,
};
use crate::nlayout::PhysicalQubit;
use crate::target_transpiler::{NormalOperation, Target};
use crate::two_qubit_decompose::{
    RXXEquivalent, TwoQubitBasisDecomposer, TwoQubitControlledUDecomposer, TwoQubitGateSequence,
    TwoQubitWeylDecomposition,
};
use crate::QiskitError;

const PI2: f64 = PI / 2.;
const PI4: f64 = PI / 4.;

#[derive(Clone, Debug)]
enum DecomposerType {
    TwoQubitBasis(Box<TwoQubitBasisDecomposer>),
    TwoQubitControlledU(Box<TwoQubitControlledUDecomposer>),
    XX(PyObject),
}

#[derive(Clone, Debug)]
struct DecomposerElement {
    decomposer: DecomposerType,
    packed_op: PackedOperation,
    params: SmallVec<[Param; 3]>,
}

#[derive(Clone, Debug)]
struct TwoQubitUnitarySequence {
    gate_sequence: TwoQubitGateSequence,
    decomp_op: PackedOperation,
    decomp_params: SmallVec<[Param; 3]>,
}

// These two variables are used to exit the decomposer search early in
// `get_2q_decomposers_from_target`.
// If the available 2q basis is a subset of GOODBYE_SET, TwoQubitBasisDecomposer provides
// an ideal decomposition and we can exit the decomposer search. Similarly, if it is a
// subset of PARAM_SET, TwoQubitControlledUDecomposer provides an ideal decompostion.
static GOODBYE_SET: [&str; 3] = ["cx", "cz", "ecr"];
static PARAM_SET: [&str; 8] = ["rzz", "rxx", "ryy", "rzx", "crx", "cry", "crz", "cphase"];

/// Given a list of basis gates, find a corresponding euler basis to use.
/// This will determine the available 1q synthesis basis for different decomposers.
fn get_euler_basis_set(basis_list: IndexSet<&str>) -> EulerBasisSet {
    let mut euler_basis_set: EulerBasisSet = EulerBasisSet::new();
    EULER_BASES
        .iter()
        .enumerate()
        .filter_map(|(idx, gates)| {
            if !gates.iter().all(|gate| basis_list.contains(gate)) {
                return None;
            }
            let basis = EULER_BASIS_NAMES[idx];
            Some(basis)
        })
        .for_each(|basis| euler_basis_set.add_basis(basis));

    if euler_basis_set.basis_supported(EulerBasis::U3)
        && euler_basis_set.basis_supported(EulerBasis::U321)
    {
        euler_basis_set.remove(EulerBasis::U3);
    }
    if euler_basis_set.basis_supported(EulerBasis::ZSX)
        && euler_basis_set.basis_supported(EulerBasis::ZSXX)
    {
        euler_basis_set.remove(EulerBasis::ZSX);
    }
    euler_basis_set
}

/// Given a `Target`, find an euler basis that is supported for a specific `PhysicalQubit`.
/// This will determine the available 1q synthesis basis for different decomposers.
fn get_target_basis_set(target: &Target, qubit: PhysicalQubit) -> EulerBasisSet {
    let mut target_basis_set: EulerBasisSet = EulerBasisSet::new();
    let target_basis_list = target.operation_names_for_qargs(Some(&smallvec![qubit]));
    match target_basis_list {
        Ok(basis_list) => {
            target_basis_set = get_euler_basis_set(basis_list.into_iter().collect());
        }
        Err(_) => {
            target_basis_set.support_all();
            target_basis_set.remove(EulerBasis::U3);
            target_basis_set.remove(EulerBasis::ZSX);
        }
    }
    target_basis_set
}

/// Apply synthesis output (`synth_dag`) to final `DAGCircuit` (`out_dag`).
/// `synth_dag` is a subgraph, and the `qubit_ids` are relative to the subgraph
///  size/orientation, so `out_qargs` is used to track the final qubit ids where
/// it should be applied.
fn apply_synth_dag(
    py: Python<'_>,
    out_dag: &mut DAGCircuit,
    out_qargs: &[Qubit],
    synth_dag: &DAGCircuit,
) -> PyResult<()> {
    for out_node in synth_dag.topological_op_nodes()? {
        let mut out_packed_instr = synth_dag[out_node].unwrap_operation().clone();
        let synth_qargs = synth_dag.get_qargs(out_packed_instr.qubits);
        let mapped_qargs: Vec<Qubit> = synth_qargs
            .iter()
            .map(|qarg| out_qargs[qarg.0 as usize])
            .collect();
        out_packed_instr.qubits = out_dag.qargs_interner.insert(&mapped_qargs);
        out_dag.push_back(py, out_packed_instr)?;
    }
    out_dag.add_global_phase(py, &synth_dag.get_global_phase())?;
    Ok(())
}

/// Apply synthesis output (`sequence`) to final `DAGCircuit` (`out_dag`).
/// `sequence` contains a representation of gates to be applied to a subgraph,
/// and the `qubit_ids` are relative to the subgraph size/orientation,
/// so `out_qargs` is used to track the final qubit ids where they should be applied.
fn apply_synth_sequence(
    py: Python<'_>,
    out_dag: &mut DAGCircuit,
    out_qargs: &[Qubit],
    sequence: &TwoQubitUnitarySequence,
) -> PyResult<()> {
    let mut instructions = Vec::with_capacity(sequence.gate_sequence.gates().len());
    for (gate, params, qubit_ids) in sequence.gate_sequence.gates() {
        let packed_op = match gate {
            None => &sequence.decomp_op,
            Some(gate) => &PackedOperation::from_standard_gate(*gate),
        };
        let mapped_qargs: Vec<Qubit> = qubit_ids.iter().map(|id| out_qargs[*id as usize]).collect();
        let new_params: Option<Box<SmallVec<[Param; 3]>>> = match gate {
            Some(_) => Some(Box::new(params.iter().map(|p| Param::Float(*p)).collect())),
            None => {
                if !sequence.decomp_params.is_empty()
                    && matches!(sequence.decomp_params[0], Param::Float(_))
                {
                    Some(Box::new(sequence.decomp_params.clone()))
                } else {
                    Some(Box::new(params.iter().map(|p| Param::Float(*p)).collect()))
                }
            }
        };

        let new_op: PackedOperation = match packed_op.py_copy(py)?.view() {
            OperationRef::Gate(gate) => {
                gate.gate.setattr(
                    py,
                    "params",
                    new_params
                        .as_deref()
                        .map(SmallVec::as_slice)
                        .unwrap_or(&[])
                        .iter()
                        .map(|param| param.clone_ref(py))
                        .collect::<SmallVec<[Param; 3]>>(),
                )?;
                Box::new(PyGate {
                    gate: gate.gate.clone(),
                    qubits: gate.qubits,
                    clbits: gate.clbits,
                    params: gate.params,
                    op_name: gate.op_name.clone(),
                })
                .into()
            }
            OperationRef::StandardGate(_) => packed_op.clone(),
            _ => {
                return Err(QiskitError::new_err(
                    "Decomposed gate sequence contains unexpected operations.",
                ))
            }
        };

        let instruction = PackedInstruction {
            op: new_op,
            qubits: out_dag.qargs_interner.insert(&mapped_qargs),
            clbits: out_dag.cargs_interner.get_default(),
            params: new_params,
            label: None,
            #[cfg(feature = "cache_pygates")]
            py_op: OnceLock::new(),
        };
        instructions.push(instruction);
    }
    out_dag.extend(py, instructions.into_iter())?;
    out_dag.add_global_phase(py, &Param::Float(sequence.gate_sequence.global_phase()))?;
    Ok(())
}

/// Iterate over `DAGCircuit` to perform unitary synthesis.
/// For each elegible gate: find decomposers, select the synthesis
/// method with the highest fidelity score and apply decompositions. The available methods are:
///     * 1q synthesis: OneQubitEulerDecomposer
///     * 2q synthesis: TwoQubitBasisDecomposer, TwoQubitControlledUDecomposer, XXDecomposer (Python, only if target is provided)
///     * 3q+ synthesis: QuantumShannonDecomposer (Python)
/// This function is currently used in the Python `UnitarySynthesis`` transpiler pass as a replacement for the `_run_main_loop` method.
/// It returns a new `DAGCircuit` with the different synthesized gates.
#[pyfunction]
#[pyo3(name = "run_main_loop", signature=(dag, qubit_indices, min_qubits, target, basis_gates, coupling_edges, approximation_degree=None, natural_direction=None, pulse_optimize=None))]
fn py_run_main_loop(
    py: Python,
    dag: &mut DAGCircuit,
    qubit_indices: Vec<usize>,
    min_qubits: usize,
    target: Option<&Target>,
    basis_gates: HashSet<String>,
    coupling_edges: HashSet<[PhysicalQubit; 2]>,
    approximation_degree: Option<f64>,
    natural_direction: Option<bool>,
    pulse_optimize: Option<bool>,
) -> PyResult<DAGCircuit> {
    // We need to use the python converter because the currently available Rust conversion
    // is lossy. We need `QuantumCircuit` instances to be used in `replace_blocks`.
    let dag_to_circuit = imports::DAG_TO_CIRCUIT.get_bound(py);

    let mut out_dag = dag.copy_empty_like(py, "alike")?;

    // Iterate over dag nodes and determine unitary synthesis approach
    for node in dag.topological_op_nodes()? {
        let mut packed_instr = dag[node].unwrap_operation().clone();

        if packed_instr.op.control_flow() {
            let OperationRef::Instruction(py_instr) = packed_instr.op.view() else {
                unreachable!("Control flow op must be an instruction")
            };
            let raw_blocks: Vec<PyResult<Bound<PyAny>>> = py_instr
                .instruction
                .getattr(py, "blocks")?
                .bind(py)
                .try_iter()?
                .collect();
            let mut new_blocks = Vec::with_capacity(raw_blocks.len());
            for raw_block in raw_blocks {
                let new_ids = dag
                    .get_qargs(packed_instr.qubits)
                    .iter()
                    .map(|qarg| qubit_indices[qarg.0 as usize])
                    .collect_vec();
                let res = py_run_main_loop(
                    py,
                    &mut circuit_to_dag(
                        py,
                        QuantumCircuitData::extract_bound(&raw_block?)?,
                        false,
                        None,
                        None,
                    )?,
                    new_ids,
                    min_qubits,
                    target,
                    basis_gates.clone(),
                    coupling_edges.clone(),
                    approximation_degree,
                    natural_direction,
                    pulse_optimize,
                )?;
                new_blocks.push(dag_to_circuit.call1((res,))?);
            }
            let new_node = py_instr
                .instruction
                .bind(py)
                .call_method1("replace_blocks", (new_blocks,))?;
            let new_node_op: OperationFromPython = new_node.extract()?;
            packed_instr = PackedInstruction {
                op: new_node_op.operation,
                qubits: packed_instr.qubits,
                clbits: packed_instr.clbits,
                params: (!new_node_op.params.is_empty()).then(|| Box::new(new_node_op.params)),
                label: new_node_op.label,
                #[cfg(feature = "cache_pygates")]
                py_op: new_node.unbind().into(),
            };
        }
        if !(packed_instr.op.name() == "unitary"
            && packed_instr.op.num_qubits() >= min_qubits as u32)
        {
            out_dag.push_back(py, packed_instr)?;
            continue;
        }
        let unitary: Array<Complex<f64>, Dim<[usize; 2]>> = match packed_instr.op.matrix(&[]) {
            Some(unitary) => unitary,
            None => return Err(QiskitError::new_err("Unitary not found")),
        };
        match unitary.shape() {
            // Run 1q synthesis
            [2, 2] => {
                let qubit = dag.get_qargs(packed_instr.qubits)[0];
                let target_basis_set = match target {
                    Some(target) => get_target_basis_set(target, PhysicalQubit::new(qubit.0)),
                    None => {
                        let basis_gates: IndexSet<&str> =
                            basis_gates.iter().map(String::as_str).collect();
                        get_euler_basis_set(basis_gates)
                    }
                };
                let sequence = unitary_to_gate_sequence_inner(
                    unitary.view(),
                    &target_basis_set,
                    qubit.0 as usize,
                    None,
                    true,
                    None,
                );
                match sequence {
                    Some(sequence) => {
                        for (gate, params) in sequence.gates {
                            let new_params: SmallVec<[Param; 3]> =
                                params.iter().map(|p| Param::Float(*p)).collect();
                            out_dag.apply_operation_back(
                                py,
                                gate.into(),
                                &[qubit],
                                &[],
                                Some(new_params),
                                None,
                                #[cfg(feature = "cache_pygates")]
                                None,
                            )?;
                        }
                        out_dag.add_global_phase(py, &Param::Float(sequence.global_phase))?;
                    }
                    None => {
                        out_dag.push_back(py, packed_instr)?;
                    }
                }
            }
            // Run 2q synthesis
            [4, 4] => {
                // "out_qargs" is used to append the synthesized instructions to the output dag
                let out_qargs = dag.get_qargs(packed_instr.qubits);
                // "ref_qubits" is used to access properties in the target. It accounts for control flow mapping.
                let ref_qubits: &[PhysicalQubit; 2] = &[
                    PhysicalQubit::new(qubit_indices[out_qargs[0].0 as usize] as u32),
                    PhysicalQubit::new(qubit_indices[out_qargs[1].0 as usize] as u32),
                ];
                let apply_original_op = |out_dag: &mut DAGCircuit| -> PyResult<()> {
                    out_dag.push_back(py, packed_instr.clone())?;
                    Ok(())
                };
                run_2q_unitary_synthesis(
                    py,
                    unitary,
                    ref_qubits,
                    &coupling_edges,
                    target,
                    basis_gates.clone(),
                    approximation_degree,
                    natural_direction,
                    pulse_optimize,
                    &mut out_dag,
                    out_qargs,
                    apply_original_op,
                )?;
            }
            // Run 3q+ synthesis
            _ => {
                if basis_gates.is_empty() && target.is_none() {
                    out_dag.push_back(py, packed_instr.clone())?;
                } else {
                    let qs_decomposition: &Bound<'_, PyAny> =
                        imports::QS_DECOMPOSITION.get_bound(py);
                    let synth_circ = qs_decomposition.call1((unitary.into_pyarray(py),))?;
                    let synth_dag = circuit_to_dag(
                        py,
                        QuantumCircuitData::extract_bound(&synth_circ)?,
                        false,
                        None,
                        None,
                    )?;
                    let out_qargs = dag.get_qargs(packed_instr.qubits);
                    apply_synth_dag(py, &mut out_dag, out_qargs, &synth_dag)?;
                }
            }
        }
    }
    Ok(out_dag)
}

/// Return a single decomposer for the given `basis_gates`. If no decomposer is found,
/// return `None``. If a decomposer is found, the return type will be either
/// `DecomposerElement::TwoQubitBasis` or `DecomposerElement::TwoQubitControlledU`.
fn get_2q_decomposer_from_basis(
    basis_gates: IndexSet<&str>,
    approximation_degree: Option<f64>,
    pulse_optimize: Option<bool>,
) -> PyResult<Option<DecomposerElement>> {
    // Non-parametrized 2q basis candidates (TwoQubitBasisDecomposer)
    let basis_names: IndexMap<&str, StandardGate> = [
        ("cx", StandardGate::CXGate),
        ("cz", StandardGate::CZGate),
        ("iswap", StandardGate::ISwapGate),
        ("ecr", StandardGate::ECRGate),
    ]
    .into_iter()
    .collect();
    // Parametrized 2q basis candidates (TwoQubitControlledUDecomposer)
    let param_basis_names: IndexMap<&str, StandardGate> = [
        ("rxx", StandardGate::RXXGate),
        ("rzx", StandardGate::RZXGate),
        ("rzz", StandardGate::RZZGate),
        ("ryy", StandardGate::RYYGate),
        ("cphase", StandardGate::CPhaseGate),
        ("crx", StandardGate::CRXGate),
        ("cry", StandardGate::CRYGate),
        ("crz", StandardGate::CRZGate),
    ]
    .into_iter()
    .collect();
    // 1q basis (both decomposers)
    let euler_basis = match get_euler_basis_set(basis_gates.clone())
        .get_bases()
        .map(|basis| basis.as_str())
        .next()
    {
        Some(basis) => basis,
        None => return Ok(None),
    };

    // Try TwoQubitControlledUDecomposer first.
    let kak_gates: Vec<&str> = param_basis_names
        .keys()
        .copied()
        .collect::<IndexSet<&str>>()
        .intersection(&basis_gates)
        .copied()
        .collect();
    if !kak_gates.is_empty() {
        let std_gate = *param_basis_names.get(kak_gates[0]).unwrap();
        let rxx_equivalent_gate = RXXEquivalent::Standard(std_gate);
        if let Ok(decomposer) =
            TwoQubitControlledUDecomposer::new_inner(rxx_equivalent_gate, euler_basis)
        {
            return Ok(Some(DecomposerElement {
                decomposer: DecomposerType::TwoQubitControlledU(Box::new(decomposer)),
                packed_op: PackedOperation::from_standard_gate(std_gate),
                params: SmallVec::new(),
            }));
        };
    };

    // If there is no suitable TwoQubitControlledUDecomposer, try TwoQubitBasisDecomposer.
    let kak_gates: Vec<&str> = basis_names
        .keys()
        .copied()
        .collect::<IndexSet<&str>>()
        .intersection(&basis_gates)
        .copied()
        .collect();
    if !kak_gates.is_empty() {
        let std_gate = *basis_names.get(kak_gates[0]).unwrap();
        let decomposer = TwoQubitBasisDecomposer::new_inner(
            std_gate.name().to_string(),
            std_gate.matrix(&[]).unwrap().view(),
            approximation_degree.unwrap_or(1.0),
            euler_basis,
            pulse_optimize,
        )?;
        return Ok(Some(DecomposerElement {
            decomposer: DecomposerType::TwoQubitBasis(Box::new(decomposer)),
            packed_op: PackedOperation::from_standard_gate(std_gate),
            params: SmallVec::new(),
        }));
    }
    Ok(None)
}

/// Return a list of decomposers for the given `target`. If no decomposer is found,
/// return `None``. The list can contain any `DecomposerElement`. This function
/// will exit early if an ideal decomposition is found.
fn get_2q_decomposers_from_target(
    py: Python,
    target: &Target,
    qubits: &[PhysicalQubit; 2],
    approximation_degree: Option<f64>,
    pulse_optimize: Option<bool>,
) -> PyResult<Option<Vec<DecomposerElement>>> {
    // Store elegible basis gates (1q and 2q) with corresponding qargs (PhysicalQubit)
    let qubits: SmallVec<[PhysicalQubit; 2]> = SmallVec::from_buf(*qubits);
    let reverse_qubits: SmallVec<[PhysicalQubit; 2]> = qubits.iter().rev().copied().collect();
    let mut qubit_gate_map = IndexMap::new();
    match target.operation_names_for_qargs(Some(&qubits)) {
        Ok(direct_keys) => {
            qubit_gate_map.insert(&qubits, direct_keys);
            if let Ok(reverse_keys) = target.operation_names_for_qargs(Some(&reverse_qubits)) {
                qubit_gate_map.insert(&reverse_qubits, reverse_keys);
            }
        }
        Err(_) => {
            if let Ok(reverse_keys) = target.operation_names_for_qargs(Some(&reverse_qubits)) {
                qubit_gate_map.insert(&reverse_qubits, reverse_keys);
            } else {
                return Err(QiskitError::new_err(
                    "Target has no gates available on qubits to synthesize over.",
                ));
            }
        }
    }

    // Define available 1q basis
    let available_1q_basis: IndexSet<&str> = IndexSet::from_iter(
        get_target_basis_set(target, qubits[0])
            .get_bases()
            .map(|basis| basis.as_str()),
    );

    // Define available 2q basis (setting apart parametrized 2q gates)
    let mut available_2q_basis: IndexMap<&str, (NormalOperation, Option<f64>)> = IndexMap::new();
    let mut available_2q_param_basis: IndexMap<&str, (NormalOperation, Option<f64>)> =
        IndexMap::new();
    for (q_pair, gates) in qubit_gate_map {
        for key in gates {
            match target.operation_from_name(key) {
                Ok(op) => {
                    match op.operation.view() {
                        OperationRef::Gate(_) => (),
                        OperationRef::StandardGate(_) => (),
                        _ => continue,
                    }
                    // Filter out non-2q-gate candidates
                    if op.operation.num_qubits() != 2 {
                        continue;
                    }
                    // Add to param_basis if the gate parameters aren't bound (not Float)
                    if !op.params.iter().all(|p| matches!(p, Param::Float(_))) {
                        available_2q_param_basis.insert(
                            key,
                            (
                                op.clone(),
                                match &target[key].get(Some(q_pair)) {
                                    Some(Some(props)) => props.error,
                                    _ => None,
                                },
                            ),
                        );
                    }
                    available_2q_basis.insert(
                        key,
                        (
                            op.clone(),
                            match &target[key].get(Some(q_pair)) {
                                Some(Some(props)) => props.error,
                                _ => None,
                            },
                        ),
                    );
                }
                _ => continue,
            }
        }
    }
    if available_2q_basis.is_empty() && available_2q_param_basis.is_empty() {
        return Err(QiskitError::new_err(
            "Target has no gates available on qubits to synthesize over.",
        ));
    }

    // If there are available 2q gates, start search for decomposers:
    let mut decomposers: Vec<DecomposerElement> = Vec::new();

    // Step 1: Try TwoQubitBasisDecomposers
    #[inline]
    fn is_supercontrolled(op: &NormalOperation) -> bool {
        match op.operation.matrix(&op.params) {
            None => false,
            Some(unitary_matrix) => {
                let kak = TwoQubitWeylDecomposition::new_inner(unitary_matrix.view(), None, None)
                    .unwrap();
                relative_eq!(kak.a(), PI4) && relative_eq!(kak.c(), 0.0)
            }
        }
    }
    let supercontrolled_basis: IndexMap<&str, (NormalOperation, Option<f64>)> = available_2q_basis
        .iter()
        .filter(|(_, (gate, _))| is_supercontrolled(gate))
        .map(|(k, (gate, props))| (*k, (gate.clone(), *props)))
        .collect();
    for basis_1q in &available_1q_basis {
        for (_, (gate, props)) in supercontrolled_basis.iter() {
            let mut basis_2q_fidelity: f64 = match props {
                Some(error) => 1.0 - error,
                _ => 1.0,
            };
            if let Some(approx_degree) = approximation_degree {
                basis_2q_fidelity *= approx_degree;
            }
            let decomposer = TwoQubitBasisDecomposer::new_inner(
                gate.operation.name().to_string(),
                gate.operation.matrix(&gate.params).unwrap().view(),
                basis_2q_fidelity,
                basis_1q,
                pulse_optimize,
            )?;

            decomposers.push(DecomposerElement {
                decomposer: DecomposerType::TwoQubitBasis(Box::new(decomposer)),
                packed_op: gate.operation.clone(),
                params: gate.params.clone(),
            });
        }
    }
    // If the 2q basis gates are a subset of GOODBYE_SET, exit here.
    if available_2q_basis
        .keys()
        .all(|gate| GOODBYE_SET.contains(gate))
        && !available_2q_basis.is_empty()
    {
        return Ok(Some(decomposers));
    }

    // Step 2: Try TwoQubitControlledUDecomposers
    for basis_1q in &available_1q_basis {
        for (_, (gate, _)) in available_2q_param_basis.iter() {
            let rxx_equivalent_gate = if let Some(std_gate) = gate.operation.try_standard_gate() {
                RXXEquivalent::Standard(std_gate)
            } else {
                let module = PyModule::import(py, "builtins")?;
                let py_type = module.getattr("type")?;
                let gate_type = py_type
                    .call1((gate.clone().into_pyobject(py)?,))?
                    .downcast_into::<PyType>()?
                    .unbind();

                RXXEquivalent::CustomPython(gate_type)
            };

            match TwoQubitControlledUDecomposer::new_inner(rxx_equivalent_gate, basis_1q) {
                Ok(decomposer) => {
                    decomposers.push(DecomposerElement {
                        decomposer: DecomposerType::TwoQubitControlledU(Box::new(decomposer)),
                        packed_op: gate.operation.clone(),
                        params: gate.params.clone(),
                    });
                }
                Err(_) => continue,
            };
        }
    }
    // If the 2q basis gates are a subset of PARAM_SET, exit here
    if available_2q_param_basis
        .keys()
        .all(|gate| PARAM_SET.contains(gate))
        && !available_2q_param_basis.is_empty()
    {
        return Ok(Some(decomposers));
    }

    // Step 3: Try XXDecomposers (Python)
    #[inline]
    fn is_controlled(op: &NormalOperation) -> bool {
        match op.operation.matrix(&op.params) {
            None => false,
            Some(unitary_matrix) => {
                let kak = TwoQubitWeylDecomposition::new_inner(unitary_matrix.view(), None, None)
                    .unwrap();
                relative_eq!(kak.b(), 0.0) && relative_eq!(kak.c(), 0.0)
            }
        }
    }
    let controlled_basis: IndexMap<&str, (NormalOperation, Option<f64>)> = available_2q_basis
        .iter()
        .filter(|(_, (gate, _))| is_controlled(gate))
        .map(|(k, (gate, props))| (*k, (gate.clone(), *props)))
        .collect();
    let mut pi2_basis: Option<&str> = None;
    let xx_embodiments: &Bound<'_, PyAny> = imports::XX_EMBODIMENTS.get_bound(py);
    // The Python XXDecomposer args are the interaction strength (f64), basis_2q_fidelity (f64),
    // and embodiments (Bound<'_, PyAny>).
    let xx_decomposer_args = controlled_basis.iter().map(
        |(name, (op, props))| -> PyResult<(f64, f64, pyo3::Bound<'_, pyo3::PyAny>)> {
            let strength = 2.0
                * TwoQubitWeylDecomposition::new_inner(
                    op.operation.matrix(&op.params).unwrap().view(),
                    None,
                    None,
                )
                .unwrap()
                .a();
            let mut fidelity_value = match props {
                Some(error) => 1.0 - error,
                None => 1.0,
            };
            if let Some(approx_degree) = approximation_degree {
                fidelity_value *= approx_degree;
            }
            let mut embodiment =
                xx_embodiments.get_item(op.into_pyobject(py)?.getattr("base_class")?)?;

            if embodiment.getattr("parameters")?.len()? == 1 {
                embodiment = embodiment.call_method1("assign_parameters", (vec![strength],))?;
            }
            // basis equivalent to CX are well optimized so use for the pi/2 angle if available
            if relative_eq!(strength, PI2) && supercontrolled_basis.contains_key(name) {
                pi2_basis = Some(op.operation.name());
            }
            Ok((strength, fidelity_value, embodiment))
        },
    );
    let basis_2q_fidelity_dict = PyDict::new(py);
    let embodiments_dict = PyDict::new(py);
    for (strength, fidelity, embodiment) in xx_decomposer_args.flatten() {
        basis_2q_fidelity_dict.set_item(strength, fidelity)?;
        embodiments_dict.set_item(strength, embodiment)?;
    }
    if basis_2q_fidelity_dict.len() > 0 {
        let xx_decomposer: &Bound<'_, PyAny> = imports::XX_DECOMPOSER.get_bound(py);
        for basis_1q in available_1q_basis {
            let pi2_decomposer = if let Some(pi_2_basis) = pi2_basis {
                if pi_2_basis == "cx" && basis_1q == "ZSX" {
                    let fidelity = match approximation_degree {
                        Some(approx_degree) => approx_degree,
                        None => match &target["cx"][Some(&qubits)] {
                            Some(props) => 1.0 - props.error.unwrap_or_default(),
                            None => 1.0,
                        },
                    };
                    Some(TwoQubitBasisDecomposer::new_inner(
                        pi_2_basis.to_string(),
                        StandardGate::CXGate.matrix(&[]).unwrap().view(),
                        fidelity,
                        basis_1q,
                        Some(true),
                    )?)
                } else {
                    None
                }
            } else {
                None
            };

            let decomposer = xx_decomposer.call1((
                &basis_2q_fidelity_dict,
                PyString::new(py, basis_1q),
                &embodiments_dict,
                pi2_decomposer,
            ))?;
            let decomposer_gate = decomposer
                .getattr(intern!(py, "gate"))?
                .extract::<NormalOperation>()?;

            decomposers.push(DecomposerElement {
                decomposer: DecomposerType::XX(decomposer.into()),
                packed_op: decomposer_gate.operation,
                params: decomposer_gate.params.clone(),
            });
        }
    }
    Ok(Some(decomposers))
}

/// Function to evaluate hardware-native direction, this allows to correct
/// the synthesis output to match the target constraints.
/// Returns:
///     * `true` if gate qubits are in the hardware-native direction
///     * `false` if gate qubits must be flipped to match hardware-native direction
fn preferred_direction(
    ref_qubits: &[PhysicalQubit; 2],
    natural_direction: Option<bool>,
    coupling_edges: &HashSet<[PhysicalQubit; 2]>,
    target: Option<&Target>,
    decomposer: &DecomposerElement,
) -> PyResult<Option<bool>> {
    let qubits: [PhysicalQubit; 2] = *ref_qubits;
    let mut reverse_qubits: [PhysicalQubit; 2] = qubits;
    reverse_qubits.reverse();

    let preferred_direction = match natural_direction {
        Some(false) => None,
        _ => {
            // None or Some(true)
            let zero_one = coupling_edges.contains(&qubits);
            let one_zero = coupling_edges.contains(&[qubits[1], qubits[0]]);

            match (zero_one, one_zero) {
                (true, false) => Some(true),
                (false, true) => Some(false),
                _ => {
                    match target {
                        Some(target) => {
                            let mut cost_0_1: f64 = f64::INFINITY;
                            let mut cost_1_0: f64 = f64::INFINITY;

                            let compute_cost = |lengths: bool,
                                                q_tuple: [PhysicalQubit; 2],
                                                in_cost: f64|
                             -> PyResult<f64> {
                                let cost = match target
                                    .qargs_for_operation_name(decomposer.packed_op.name())
                                {
                                    Ok(_) => match target[decomposer.packed_op.name()].get(Some(
                                        &q_tuple
                                            .into_iter()
                                            .collect::<SmallVec<[PhysicalQubit; 2]>>(),
                                    )) {
                                        Some(Some(_props)) => {
                                            if lengths {
                                                _props.duration.unwrap_or(in_cost)
                                            } else {
                                                _props.error.unwrap_or(in_cost)
                                            }
                                        }
                                        _ => in_cost,
                                    },
                                    Err(_) => in_cost,
                                };
                                Ok(cost)
                            };
                            // Try to find the cost in gate_lengths
                            cost_0_1 = compute_cost(true, qubits, cost_0_1)?;
                            cost_1_0 = compute_cost(true, reverse_qubits, cost_1_0)?;

                            // If no valid cost was found in gate_lengths, check gate_errors
                            if !(cost_0_1 < f64::INFINITY || cost_1_0 < f64::INFINITY) {
                                cost_0_1 = compute_cost(false, qubits, cost_0_1)?;
                                cost_1_0 = compute_cost(false, reverse_qubits, cost_1_0)?;
                            }

                            if cost_0_1 < cost_1_0 {
                                Some(true)
                            } else if cost_1_0 < cost_0_1 {
                                Some(false)
                            } else {
                                None
                            }
                        }
                        None => None,
                    }
                }
            }
        }
    };
    if natural_direction == Some(true) && preferred_direction.is_none() {
        return Err(QiskitError::new_err(format!(
            concat!(
                "No preferred direction of gate on qubits {:?} ",
                "could be determined from coupling map or gate lengths / gate errors."
            ),
            qubits
        )));
    }
    Ok(preferred_direction)
}

/// Apply synthesis for decomposers that return a SEQUENCE (TwoQubitBasis and TwoQubitControlledU).
fn synth_su4_sequence(
    su4_mat: &Array2<Complex64>,
    decomposer_2q: &DecomposerElement,
    preferred_direction: Option<bool>,
    approximation_degree: Option<f64>,
) -> PyResult<TwoQubitUnitarySequence> {
    let is_approximate = approximation_degree.is_none() || approximation_degree.unwrap() != 1.0;
    let synth = if let DecomposerType::TwoQubitBasis(decomp) = &decomposer_2q.decomposer {
        decomp.call_inner(su4_mat.view(), None, is_approximate, None)?
    } else if let DecomposerType::TwoQubitControlledU(decomp) = &decomposer_2q.decomposer {
        decomp.call_inner(su4_mat.view(), None)?
    } else {
        unreachable!("synth_su4_sequence should only be called for TwoQubitBasisDecomposer.")
    };
    let sequence = TwoQubitUnitarySequence {
        gate_sequence: synth,
        decomp_op: decomposer_2q.packed_op.clone(),
        decomp_params: decomposer_2q.params.clone(),
    };
    match preferred_direction {
        None => Ok(sequence),
        Some(preferred_dir) => {
            let mut synth_direction: Option<SmallVec<[u8; 2]>> = None;
            // if the gates in synthesis are in the opposite direction of the preferred direction
            // resynthesize a new operator which is the original conjugated by swaps.
            // this new operator is doubly mirrored from the original and is locally equivalent.
            for (gate, _, qubits) in sequence.gate_sequence.gates() {
                if gate.is_none() || gate.unwrap().name() == "cx" {
                    synth_direction = Some(qubits.clone());
                }
            }
            match synth_direction {
                None => Ok(sequence),
                Some(synth_direction) => {
                    let synth_dir = match synth_direction.as_slice() {
                        [0, 1] => true,
                        [1, 0] => false,
                        _ => unreachable!(),
                    };
                    if synth_dir != preferred_dir {
                        reversed_synth_su4_sequence(
                            su4_mat.clone(),
                            decomposer_2q,
                            approximation_degree,
                        )
                    } else {
                        Ok(sequence)
                    }
                }
            }
        }
    }
}

/// Apply reverse synthesis for decomposers that return a SEQUENCE (TwoQubitBasis and TwoQubitControlledU).
/// This function is called by `synth_su4_sequence`` if the "direct" synthesis
/// doesn't match the hardware restrictions.
fn reversed_synth_su4_sequence(
    mut su4_mat: Array2<Complex64>,
    decomposer_2q: &DecomposerElement,
    approximation_degree: Option<f64>,
) -> PyResult<TwoQubitUnitarySequence> {
    let is_approximate = approximation_degree.is_none() || approximation_degree.unwrap() != 1.0;
    // Swap rows 1 and 2
    let (mut row_1, mut row_2) = su4_mat.multi_slice_mut((s![1, ..], s![2, ..]));
    azip!((x in &mut row_1, y in &mut row_2) (*x, *y) = (*y, *x));

    // Swap columns 1 and 2
    let (mut col_1, mut col_2) = su4_mat.multi_slice_mut((s![.., 1], s![.., 2]));
    azip!((x in &mut col_1, y in &mut col_2) (*x, *y) = (*y, *x));

    let synth = if let DecomposerType::TwoQubitBasis(decomp) = &decomposer_2q.decomposer {
        decomp.call_inner(su4_mat.view(), None, is_approximate, None)?
    } else if let DecomposerType::TwoQubitControlledU(decomp) = &decomposer_2q.decomposer {
        decomp.call_inner(su4_mat.view(), None)?
    } else {
        unreachable!(
            "reversed_synth_su4_sequence should only be called for TwoQubitBasisDecomposer."
        )
    };
    let flip_bits: [u8; 2] = [1, 0];
    let mut reversed_gates = Vec::with_capacity(synth.gates().len());
    for (gate, params, qubit_ids) in synth.gates() {
        let new_qubit_ids = qubit_ids
            .into_iter()
            .map(|x| flip_bits[*x as usize])
            .collect::<SmallVec<[u8; 2]>>();
        reversed_gates.push((*gate, params.clone(), new_qubit_ids.clone()));
    }
    let mut reversed_synth: TwoQubitGateSequence = TwoQubitGateSequence::new();
    reversed_synth.set_state((reversed_gates, synth.global_phase()));
    let sequence = TwoQubitUnitarySequence {
        gate_sequence: reversed_synth,
        decomp_op: decomposer_2q.packed_op.clone(),
        decomp_params: decomposer_2q.params.clone(),
    };
    Ok(sequence)
}

/// Apply synthesis for decomposers that return a DAG (XX).
fn synth_su4_dag(
    py: Python,
    su4_mat: &Array2<Complex64>,
    decomposer_2q: &DecomposerElement,
    preferred_direction: Option<bool>,
    approximation_degree: Option<f64>,
) -> PyResult<DAGCircuit> {
    let is_approximate = approximation_degree.is_none() || approximation_degree.unwrap() != 1.0;
    let synth_dag = if let DecomposerType::XX(decomposer) = &decomposer_2q.decomposer {
        let kwargs: HashMap<&str, bool> = [("approximate", is_approximate), ("use_dag", true)]
            .into_iter()
            .collect();
        decomposer
            .call(
                py,
                (su4_mat.clone().into_pyarray(py),),
                Some(&kwargs.into_py_dict(py)?),
            )?
            .extract::<DAGCircuit>(py)?
    } else {
        unreachable!("synth_su4_dag should only be called for XXDecomposer.")
    };
    match preferred_direction {
        None => Ok(synth_dag),
        Some(preferred_dir) => {
            let mut synth_direction: Option<Vec<u32>> = None;
            for node in synth_dag.topological_op_nodes()? {
                let inst = &synth_dag[node].unwrap_operation();
                if inst.op.num_qubits() == 2 {
                    let qargs = synth_dag.get_qargs(inst.qubits);
                    synth_direction = Some(vec![qargs[0].0, qargs[1].0]);
                }
            }
            match synth_direction {
                None => Ok(synth_dag),
                Some(synth_direction) => {
                    let synth_dir = match synth_direction.as_slice() {
                        [0, 1] => true,
                        [1, 0] => false,
                        _ => unreachable!("There are no more than 2 possible synth directions."),
                    };
                    if synth_dir != preferred_dir {
                        reversed_synth_su4_dag(
                            py,
                            su4_mat.clone(),
                            decomposer_2q,
                            approximation_degree,
                        )
                    } else {
                        Ok(synth_dag)
                    }
                }
            }
        }
    }
}

/// Apply reverse synthesis for decomposers that return a DAG (XX).
/// This function is called by `synth_su4_dag`` if the "direct" synthesis
/// doesn't match the hardware restrictions.
fn reversed_synth_su4_dag(
    py: Python<'_>,
    mut su4_mat: Array2<Complex64>,
    decomposer_2q: &DecomposerElement,
    approximation_degree: Option<f64>,
) -> PyResult<DAGCircuit> {
    let is_approximate = approximation_degree.is_none() || approximation_degree.unwrap() != 1.0;

    // Swap rows 1 and 2
    let (mut row_1, mut row_2) = su4_mat.multi_slice_mut((s![1, ..], s![2, ..]));
    azip!((x in &mut row_1, y in &mut row_2) (*x, *y) = (*y, *x));

    // Swap columns 1 and 2
    let (mut col_1, mut col_2) = su4_mat.multi_slice_mut((s![.., 1], s![.., 2]));
    azip!((x in &mut col_1, y in &mut col_2) (*x, *y) = (*y, *x));

    let synth_dag = if let DecomposerType::XX(decomposer) = &decomposer_2q.decomposer {
        let kwargs: HashMap<&str, bool> = [("approximate", is_approximate), ("use_dag", true)]
            .into_iter()
            .collect();
        decomposer
            .call(
                py,
                (su4_mat.clone().into_pyarray(py),),
                Some(&kwargs.into_py_dict(py)?),
            )?
            .extract::<DAGCircuit>(py)?
    } else {
        unreachable!("reversed_synth_su4_dag should only be called for XXDecomposer")
    };

    let mut target_dag = synth_dag.copy_empty_like(py, "alike")?;
    let flip_bits: [Qubit; 2] = [Qubit(1), Qubit(0)];
    for node in synth_dag.topological_op_nodes()? {
        let mut inst = synth_dag[node].unwrap_operation().clone();
        let qubits: Vec<Qubit> = synth_dag
            .qargs_interner()
            .get(inst.qubits)
            .iter()
            .map(|x| flip_bits[x.0 as usize])
            .collect();
        inst.qubits = target_dag.qargs_interner.insert_owned(qubits);
        target_dag.push_back(py, inst)?;
    }
    Ok(target_dag)
}

/// Score the synthesis output (DAG or sequence) based on the expected gate fidelity/error score.
fn synth_error(
    py: Python<'_>,
    synth_circuit: impl Iterator<
        Item = (
            String,
            Option<SmallVec<[Param; 3]>>,
            SmallVec<[PhysicalQubit; 2]>,
        ),
    >,
    target: &Target,
) -> f64 {
    let (lower_bound, upper_bound) = synth_circuit.size_hint();
    let mut gate_fidelities = match upper_bound {
        Some(bound) => Vec::with_capacity(bound),
        None => Vec::with_capacity(lower_bound),
    };
    let mut score_instruction =
        |inst_name: &str,
         inst_params: &Option<SmallVec<[Param; 3]>>,
         inst_qubits: &SmallVec<[PhysicalQubit; 2]>| {
            if let Ok(names) = target.operation_names_for_qargs(Some(inst_qubits)) {
                for name in names {
                    if let Ok(target_op) = target.operation_from_name(name) {
                        let are_params_close = if let Some(params) = inst_params {
                            params.iter().zip(target_op.params.iter()).all(|(p1, p2)| {
                                p1.is_close(py, p2, 1e-10)
                                    .expect("Unexpected parameter expression error.")
                            })
                        } else {
                            false
                        };
                        let is_parametrized = target_op
                            .params
                            .iter()
                            .any(|param| matches!(param, Param::ParameterExpression(_)));
                        if target_op.operation.name() == inst_name
                            && (is_parametrized || are_params_close)
                        {
                            match target[name].get(Some(inst_qubits)) {
                                Some(Some(props)) => {
                                    gate_fidelities.push(1.0 - props.error.unwrap_or(0.0))
                                }
                                _ => gate_fidelities.push(1.0),
                            }
                            break;
                        }
                    }
                }
            }
        };

    for (inst_name, inst_params, inst_qubits) in synth_circuit {
        score_instruction(&inst_name, &inst_params, &inst_qubits);
    }
    1.0 - gate_fidelities.into_iter().product::<f64>()
}

/// Perform 2q unitary synthesis for a given `unitary`. If some `target` is provided,
/// the decomposition will be hardware-aware and take into the account the reported
/// gate errors to select the best method among the options. If `target` is `None``,
/// the decompostion will use the given `basis_gates` and the first valid decomposition
/// will be returned (no selection).
fn run_2q_unitary_synthesis(
    py: Python,
    unitary: Array2<Complex64>,
    ref_qubits: &[PhysicalQubit; 2],
    coupling_edges: &HashSet<[PhysicalQubit; 2]>,
    target: Option<&Target>,
    basis_gates: HashSet<String>,
    approximation_degree: Option<f64>,
    natural_direction: Option<bool>,
    pulse_optimize: Option<bool>,
    out_dag: &mut DAGCircuit,
    out_qargs: &[Qubit],
    mut apply_original_op: impl FnMut(&mut DAGCircuit) -> PyResult<()>,
) -> PyResult<()> {
    // Find decomposer candidates
    let decomposers = match target {
        Some(target) => {
            let decomposers_2q = get_2q_decomposers_from_target(
                py,
                target,
                ref_qubits,
                approximation_degree,
                pulse_optimize,
            )?;
            decomposers_2q.unwrap_or_default()
        }
        None => {
            let basis_gates: IndexSet<&str> = basis_gates.iter().map(String::as_str).collect();
            let decomposer_item: Option<DecomposerElement> =
                get_2q_decomposer_from_basis(basis_gates, approximation_degree, pulse_optimize)?;
            if decomposer_item.is_none() {
                apply_original_op(out_dag)?;
                return Ok(());
            };
            vec![decomposer_item.unwrap()]
        }
    };

    // If there's a single decomposer candidate, avoid computing synthesis score.
    // This will ALWAYS be the path if the `target` is `None` (`basis_gates` used).
    if decomposers.len() == 1 {
        let decomposer_item = decomposers.first().unwrap();
        let preferred_dir = preferred_direction(
            ref_qubits,
            natural_direction,
            coupling_edges,
            target,
            decomposer_item,
        )?;

        match decomposer_item.decomposer {
            DecomposerType::TwoQubitBasis(_) => {
                let synth = synth_su4_sequence(
                    &unitary,
                    decomposer_item,
                    preferred_dir,
                    approximation_degree,
                )?;
                apply_synth_sequence(py, out_dag, out_qargs, &synth)?;
            }
            DecomposerType::TwoQubitControlledU(_) => {
                let synth = synth_su4_sequence(
                    &unitary,
                    decomposer_item,
                    preferred_dir,
                    approximation_degree,
                )?;
                apply_synth_sequence(py, out_dag, out_qargs, &synth)?;
            }
            DecomposerType::XX(_) => {
                let synth = synth_su4_dag(
                    py,
                    &unitary,
                    decomposer_item,
                    preferred_dir,
                    approximation_degree,
                )?;
                apply_synth_dag(py, out_dag, out_qargs, &synth)?;
            }
        }
        return Ok(());
    }

    // If there is more than one available decomposer, select the one with the best synthesis score.
    // This will only happen if `target` is not `None`, so we can assume that there is some target from
    // this point onwards. The scored SEQUENCEs and DAGs are stored in independent vectors to avoid defining
    // yet another custom type.
    let mut synth_errors_sequence = Vec::new();
    let mut synth_errors_dag = Vec::new();

    // The sequence synthesis logic can be shared between TwoQubitBasis and TwoQubitControlledU,
    // but the DAG logic needs to stay independent.
    let synth_sequence = |decomposer, preferred_dir| -> PyResult<(TwoQubitUnitarySequence, f64)> {
        let sequence =
            synth_su4_sequence(&unitary, decomposer, preferred_dir, approximation_degree)?;
        let scoring_info =
            sequence
                .gate_sequence
                .gates()
                .iter()
                .map(|(gate, params, qubit_ids)| {
                    let inst_qubits = qubit_ids.iter().map(|q| ref_qubits[*q as usize]).collect();
                    match gate {
                        Some(gate) => (
                            gate.name().to_string(),
                            Some(params.iter().map(|p| Param::Float(*p)).collect()),
                            inst_qubits,
                        ),
                        None => (
                            sequence.decomp_op.name().to_string(),
                            Some(params.iter().map(|p| Param::Float(*p)).collect()),
                            inst_qubits,
                        ),
                    }
                });
        let score = synth_error(py, scoring_info, target.unwrap());
        Ok((sequence, score))
    };

    for decomposer in &decomposers {
        let preferred_dir = preferred_direction(
            ref_qubits,
            natural_direction,
            coupling_edges,
            target,
            decomposer,
        )?;
        match &decomposer.decomposer {
            DecomposerType::TwoQubitBasis(_) => {
                synth_errors_sequence.push(synth_sequence(decomposer, preferred_dir)?);
            }
            DecomposerType::TwoQubitControlledU(_) => {
                synth_errors_sequence.push(synth_sequence(decomposer, preferred_dir)?);
            }
            DecomposerType::XX(_) => {
                let synth_dag = synth_su4_dag(
                    py,
                    &unitary,
                    decomposer,
                    preferred_dir,
                    approximation_degree,
                )?;
                let scoring_info = synth_dag
                    .topological_op_nodes()
                    .expect("Unexpected error in dag.topological_op_nodes()")
                    .map(|node| {
                        let NodeType::Operation(inst) = &synth_dag[node] else {
                            unreachable!("DAG node must be an instruction")
                        };
                        let inst_qubits = synth_dag
                            .get_qargs(inst.qubits)
                            .iter()
                            .map(|q| ref_qubits[q.0 as usize])
                            .collect();
                        (
                            inst.op.name().to_string(),
                            inst.params.clone().map(|boxed| *boxed),
                            inst_qubits,
                        )
                    });
                let score = synth_error(py, scoring_info, target.unwrap());
                synth_errors_dag.push((synth_dag, score));
            }
        }
    }

    // Resolve synthesis scores between sequence and DAG.
    let synth_sequence = synth_errors_sequence
        .iter()
        .enumerate()
        .min_by(|error1, error2| error1.1 .1.partial_cmp(&error2.1 .1).unwrap())
        .map(|(index, _)| &synth_errors_sequence[index]);

    let synth_dag = synth_errors_dag
        .iter()
        .enumerate()
        .min_by(|error1, error2| error1.1 .1.partial_cmp(&error2.1 .1).unwrap())
        .map(|(index, _)| &synth_errors_dag[index]);

    match (synth_sequence, synth_dag) {
        (None, None) => apply_original_op(out_dag)?,
        (Some((sequence, _)), None) => apply_synth_sequence(py, out_dag, out_qargs, sequence)?,
        (None, Some((dag, _))) => apply_synth_dag(py, out_dag, out_qargs, dag)?,
        (Some((sequence, sequence_error)), Some((dag, dag_error))) => {
            if sequence_error > dag_error {
                apply_synth_dag(py, out_dag, out_qargs, dag)?
            } else {
                apply_synth_sequence(py, out_dag, out_qargs, sequence)?
            }
        }
    };
    Ok(())
}

#[pymodule]
pub fn unitary_synthesis(m: &Bound<PyModule>) -> PyResult<()> {
    m.add_wrapped(wrap_pyfunction!(py_run_main_loop))?;
    Ok(())
}
