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This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.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

Package: Microsoft.Quantum.Standard

Performs a modular increment of a qubit register by an integer constant.

operation IncrementPhaseByModularInteger (increment : Int, modulus : Int, target : Microsoft.Quantum.Arithmetic.PhaseLittleEndian) : Unit is Adj + Ctl

Description

Let us denote increment by $a$, modulus by $N$ and integer encoded in target by $y$. Then the operation performs the following transformation: \begin{align} \ket{y} \mapsto \ket{(y + a) \operatorname{mod} N} \end{align} Integers are encoded in little-endian format in QFT basis.

Input

increment : Int

Integer increment $a$ to be added to $y$.

modulus : Int

Integer $N$ that mods $y + a$.

target : PhaseLittleEndian

Integer $y$ in phase-encoded little-endian format that increment $a$ is added to.

Output : Unit

Remarks

Assumes that target has the highest bit set to 0. Also assumes that the value of target is less than $N$.

For the circuit diagram and explanation see Figure 5 on Page 5 of arXiv:quant-ph/0205095v3.

See Also