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

>>> from pprint import pprint
>>> U = np.array([[1, 1], [1, -1]]) / np.sqrt(2)  # Hadamard
>>> decomp = qml.ops.one_qubit_decomposition(U, 0, rotations='ZYZ', return_global_phase=True)
>>> pprint(decomp)
[RZ(np.float64(3.14159...), wires=[0]),
 RY(np.float64(1.57079...), wires=[0]),
 RZ(np.float64(0.0), wires=[0]),
 GlobalPhase(np.float64(-1.57079...), wires=[])]
>>> decomp = qml.ops.one_qubit_decomposition(U, 0, rotations='XZX', return_global_phase=True)
>>> pprint(decomp)
[RX(np.float64(1.57079...), wires=[0]),
 RZ(np.float64(1.57079...), wires=[0]),
 RX(np.float64(1.57079...), wires=[0]),
 GlobalPhase(np.float64(-1.57079...), wires=[])]

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qml.ops.one_qubit_decomposition¶

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