R1Frac operation

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Warning

This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.

Please see https://aka.ms/qdk.api for the API documentation for the Modern QDK.

Namespace: Microsoft.Quantum.Intrinsic

Package: Microsoft.Quantum.Type2.Core

Applies a rotation about the $\ket{1}$ state by an angle specified as a dyadic fraction.

operation R1Frac (numerator : Int, power : Int, qubit : Qubit) : Unit is Adj + Ctl

Description

\begin{align} R_1(n, k) \mathrel{:=} \operatorname{diag}(1, e^{i \pi k / 2^n}). \end{align}

Warning

This operation uses the opposite sign convention from @"microsoft.quantum.intrinsic.r", and does not include the factor of $1/ 2$ included by @"microsoft.quantum.intrinsic.r1".

Input

numerator : Int

Numerator in the dyadic fraction representation of the angle by which the qubit is to be rotated. This angle is expressed in radians.

power : Int

Power of two specifying the denominator of the angle by which the qubit is to be rotated. This angle is expressed in radians.

qubit : Qubit

Qubit to which the gate should be applied.

Output : Unit

Remarks

Equivalent to:

RFrac(PauliZ, -numerator, denominator + 1, qubit);
RFrac(PauliI, numerator, denominator + 1, qubit);