qml.ops.one_qubit_decomposition

one_qubit_decomposition(U, wire, rotations='ZYZ', return_global_phase=False)

Decompose a one-qubit unitary \(U\) in terms of elementary operations. (batched operation)

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

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([
...     [-0.28829348-0.78829734j, 0.30364367+0.45085995j],
...     [ 0.53396245-0.10177564j, 0.76279558-0.35024096j]
... ])
>>> decompositions = one_qubit_decomposition(U, 0, "ZXZ", return_global_phase=True)
>>> decompositions
[RZ(10.753478981934784, wires=[0]),
 RX(1.1493817777940707, wires=[0]),
 RZ(3.3038544749132295, wires=[0]),
 GlobalPhase(1.1759220332464762, wires=[])]

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