def _represent_ZGate(self, basis, **options):
        """Represent the SWAP gate in the computational basis.

        The following representation is used to compute this:

        SWAP = |1><1|x|1><1| + |0><0|x|0><0| + |1><0|x|0><1| + |0><1|x|1><0|
        """
        format = options.get('format', 'sympy')
        targets = [int(t) for t in self.targets]
        min_target = min(targets)
        max_target = max(targets)
        nqubits = options.get('nqubits',self.min_qubits)

        op01 = matrix_cache.get_matrix('op01', format)
        op10 = matrix_cache.get_matrix('op10', format)
        op11 = matrix_cache.get_matrix('op11', format)
        op00 = matrix_cache.get_matrix('op00', format)
        eye2 = matrix_cache.get_matrix('eye2', format)

        result = None
        for i, j in ((op01,op10),(op10,op01),(op00,op00),(op11,op11)):
            product = nqubits*[eye2]
            product[nqubits-min_target-1] = i
            product[nqubits-max_target-1] = j
            new_result = matrix_tensor_product(*product)
            if result is None:
                result = new_result
            else:
                result = result + new_result

        return result

def represent_zbasis(controls, targets, target_matrix, nqubits, format='sympy'):
    """Represent a gate with controls, targets and target_matrix.

    This function does the low-level work of representing gates as matrices
    in the standard computational basis (ZGate). Currently, we support two
    main cases:

    1. One target qubit and no control qubits.
    2. One target qubits and multiple control qubits.

    For the base of multiple controls, we use the following expression [1]:

    1_{2**n} + (|1><1|)^{(n-1)} x (target-matrix - 1_{2})

    Parameters
    ----------
    controls : list, tuple
        A sequence of control qubits.
    targets : list, tuple
        A sequence of target qubits.
    target_matrix : sympy.Matrix, numpy.matrix, scipy.sparse
        The matrix form of the transformation to be performed on the target
        qubits.  The format of this matrix must match that passed into
        the `format` argument.
    nqubits : int
        The total number of qubits used for the representation.
    format : str
        The format of the final matrix ('sympy', 'numpy', 'scipy.sparse').

    Examples
    --------

    References
    ----------
    [1] http://www.johnlapeyre.com/qinf/qinf_html/node6.html.
    """
    controls = [int(x) for x in controls]
    targets = [int(x) for x in targets]
    nqubits = int(nqubits)

    # This checks for the format as well.
    op11 = matrix_cache.get_matrix('op11', format)
    eye2 = matrix_cache.get_matrix('eye2', format)

    # Plain single qubit case
    if len(controls) == 0 and len(targets) == 1:
        product = []
        bit = targets[0]
        # Fill product with [I1,Gate,I2] such that the unitaries,
        # I, cause the gate to be applied to the correct Qubit
        if bit != nqubits-1:
            product.append(matrix_eye(2**(nqubits-bit-1), format=format))
        product.append(target_matrix)
        if bit != 0:
            product.append(matrix_eye(2**bit, format=format))
        return matrix_tensor_product(*product)

    # Single target, multiple controls.
    elif len(targets) == 1 and len(controls) >= 1:
        target =  targets[0]

        # Build the non-trivial part.
        product2 = []
        for i in range(nqubits):
            product2.append(matrix_eye(2, format=format))
        for control in controls:
            product2[nqubits-1-control] = op11
        product2[nqubits-1-target] = target_matrix - eye2

        return matrix_eye(2**nqubits, format=format) +\
               matrix_tensor_product(*product2)

    # Multi-target, multi-control is not yet implemented.
    else:
        raise NotImplementedError(
            'The representation of multi-target, multi-control gates '
            'is not implemented.'
        )

 def get_target_matrix(self, format='sympy'):
     return matrix_cache.get_matrix('SWAP', format)

def zy_basis_transform(self, format='sympy'):
    """Transformation matrix from Z to Y basis."""
    return matrix_cache.get_matrix('ZY', format)