xyx_decomposition(U, wire, return_global_phase=False)[source]

Compute the decomposition of a single-qubit matrix \(U\) in terms of elementary operations, as a product of X and Y rotations in the form \(e^{i\gamma} RX(\phi) RY(\theta) RX(\lambda)\).

  • U (array[complex]) – A 2 x 2 unitary matrix.

  • wire (Union[Wires, Sequence[int] or int]) – The wire on which to apply the operation.

  • return_global_phase (bool) – Whether to return the global phase as a qml.s_prod between exp(1j)*gamma and qml.Identity as the last element of the returned list of operations.


Returns a list of of gates, an RX, an RY and another RX gate, which when applied in the order of appearance in the list is equivalent to the unitary \(U\) up to global phase. If return_global_phase=True, the global phase is returned as the last element of the list.

Return type



>>> U = np.array([[-0.28829348-0.78829734j,  0.30364367+0.45085995j],
...               [ 0.53396245-0.10177564j,  0.76279558-0.35024096j]])
>>> decomp = xyx_decomposition(U, 0, return_global_phase=True)
>>> decomp
[RX(array(0.45246584), wires=[0]),
RY(array(1.39749741), wires=[0]),
RX(array(-1.72101925), wires=[0]),