qml.ops.one_qubit_decomposition¶

one_qubit_decomposition(U, wire, rotations='ZYZ', return_global_phase=False)[source]¶

Decompose a one-qubit unitary $U$ in terms of elementary operations.

Any one qubit unitary operation can be implemented up to a global phase by composing RX, RY, and RZ gates. Currently supported values for rotations are “rot”, “ZYZ”, “XYX”, “XZX”, and “ZXZ”.

Parameters:

U (tensor) – A $2 \times 2$ unitary matrix.
wire (Union[Wires, Sequence[int] or int]) – The wire on which to apply the operation.
rotations (str) – A string defining the sequence of rotations to decompose $U$ into.
return_global_phase (bool) – Whether to return the global phase as a qml.GlobalPhase(-alpha) as the last element of the returned list of operations.

Returns:

A list of gates which when applied in the order of appearance in the list: is equivalent to the unitary $U$ up to a global phase. If return_global_phase=True, the global phase is returned as the last element of the list.

Return type:

list[Operation]

Example

>>> U = np.array([[1, 1], [1, -1]]) / np.sqrt(2)  # Hadamard
>>> qml.ops.one_qubit_decomposition(U, 0, rotations='ZYZ', return_global_phase=True)
[RZ(3.1415926535897927, wires=[0]),
 RY(1.5707963267948963, wires=[0]),
 RZ(0.0, wires=[0]),
 GlobalPhase(-1.5707963267948966, wires=[])]
>>> qml.ops.one_qubit_decomposition(U, 0, rotations='XZX', return_global_phase=True)
[RX(1.5707963267948966, wires=[0]),
 RZ(1.5707963267948968, wires=[0]),
 RX(1.5707963267948966, wires=[0]),
 GlobalPhase(-1.5707963267948966, wires=[])]

qml.ops.one_qubit_decomposition¶

Contents