# TODO: here can implement approximate decomposition, e.g. instead of satisfying has_element,
# the target gate just needs to be sufficiently close to the polytope.
# find the point in the polytope that minimizes the distance -> maximizes fidelity.
def coverage_lookup_operation(coverage_set:List[CircuitPolytope], target: Instruction) -> Tuple[float, List]:
    """Calculates the cost of an operation
    
    Finds the cost of an operation by iterating through the coverage set, sorted by cost.
    Args:
        coverage_set (List[CircuitPolytope]): The coverage set to search
        target (Instruction): The operation to find the cost of
    Returns:
        (float, List): The cost of the operation and the list of operations that make up the circuit
    """
    # convert gate to monodromy coordinate
    try:
        target_coords = unitary_to_monodromy_coordinate(target.to_matrix())
    except AttributeError:
        target_coords = unitary_to_monodromy_coordinate(Operator(target).data)
    
    # iterate through coverage set, sorted by cost
    for circuit_polytope in coverage_set:
        if circuit_polytope.has_element(target_coords):
            return circuit_polytope.cost, circuit_polytope.instructions
        
    raise TranspilerError("Operation not found in coverage set.")