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This documentation refers to the Classic QDK, which has been replaced by the Modern QDK.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

Reflects a quantum register about a given classical integer.

operation ReflectAboutInteger (index : Int, reg : Microsoft.Quantum.Arithmetic.LittleEndian) : Unit is Adj + Ctl

Description

Given a quantum register initially in the state $\sum_i \alpha_i \ket{i}$, where each $\ket{i}$ is a basis state representing an integer $i$, reflects the state of the register about the basis state for a given integer $\ket{j}$, $$ \sum_i (-1)^{ \delta_{ij} } \alpha_i \ket{i} $$

Input

index : Int

The classical integer indexing the basis state about which to reflect.

reg : LittleEndian

Output : Unit

Remarks

This operation is implemented in-place, without explicit allocation of additional auxiliary qubits.