MultiplexPauli operation
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Namespace: Microsoft.Quantum.Canon
Package: Microsoft.Quantum.Standard
Applies a Pauli rotation conditioned on an array of qubits.
operation MultiplexPauli (coefficients : Double[], pauli : Pauli, control : Microsoft.Quantum.Arithmetic.LittleEndian, target : Qubit) : Unit is Adj + Ctl
Description
This applies a multiply controlled unitary operation that performs rotations by angle $\theta_j$ about single-qubit Pauli operator $P$ when controlled by the $n$-qubit number state $\ket{j}$. In particular, the action of this operation is represented by the unitary
$$ \begin{align} U = \sum^{2^n - 1}_{j=0} \ket{j}\bra{j} \otimes e^{i P \theta_j}. \end{align} $$
Input
coefficients : Double[]
Array of up to $2^n$ coefficients $\theta_j$. The $j$th coefficient indexes the number state $\ket{j}$ encoded in little-endian format.
pauli : Pauli
Pauli operator $P$ that determines axis of rotation.
control : LittleEndian
$n$-qubit control register that encodes number states $\ket{j}$ in little-endian format.
target : Qubit
Single qubit register that is rotated by $e^{i P \theta_j}$.
Output : Unit
Remarks
coefficients
will be padded with elements $\theta_j = 0.0$ if
fewer than $2^n$ are specified.
See Also
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