Linear Pauli Rotation

linear_pauli_rotation

Functions:

Name	Description
linear_pauli_rotations	[Qmod Classiq-library function]

linear_pauli_rotations

linear_pauli_rotations(
    bases: CArray[Pauli],
    slopes: CArray[CReal],
    offsets: CArray[CReal],
    x: QArray[QBit],
    q: QArray[QBit],
) -> None

[Qmod Classiq-library function]

Performs a rotation on a series of \(m\) target qubits, where the rotation angle is a linear function of an \(n\)-qubit control register.

Corresponds to the braket notation:

\[ \left|x\right\rangle _{n}\left|q\right\rangle _{m}\rightarrow\left|x\right\rangle _{n}\prod_{k=1}^{m}\left(\cos\left(\frac{a_{k}}{2}x+\frac{b_{k}}{2}\right)- i\sin\left(\frac{a_{k}}{2}x+\frac{b_{k}}{2}\right)P_{k}\right)\left|q_{k}\right\rangle \]

where \(\left|x\right\rangle\) is the control register, \(\left|q\right\rangle\) is the target register, each \(P_{k}\) is one of the three Pauli matrices \(X\), \(Y\), or \(Z\), and \(a_{k}\), \(b_{k}\) are the user given slopes and offsets, respectively.

Parameters:

Name	Type	Description	Default
bases	CArray[Pauli]	List of Pauli Enums.	required
slopes	CArray[CReal]	Rotation slopes for each of the given Pauli bases.	required
offsets	CArray[CReal]	Rotation offsets for each of the given Pauli bases.	required
x	QArray[QBit]	Quantum state to apply the rotation based on its value.	required
q	QArray[QBit]	List of indicator qubits for each of the given Pauli bases.	required

Notice that bases, slopes, offset and q should be of the same size.