A Generalisation of the Phase Kick-Back

TL;DR

This paper introduces a generalized version of the Phase Kick-Back technique, expanding its application to new variants of the Deutsch-Jozsa and Bernstein-Vazirani problems in quantum computing.

Contribution

The paper develops a new generalized Phase Kick-Back method and demonstrates its effectiveness on extended Deutsch-Jozsa and Bernstein-Vazirani problems.

Findings

Generalized Phase Kick-Back enhances algorithmic flexibility

Successfully applied to new versions of Deutsch-Jozsa and Bernstein-Vazirani problems

Provides deeper understanding of quantum algorithm mechanisms

Abstract

In this paper, we present a generalisation of the Phase Kick-Back technique, which is central to some of the classical algorithms in quantum computing, such as the Deutsch--Jozsa algorithm, Simon's algorithm or Grover's algorithm. We will begin by recalling the Phase Kick-Back technique to then introduce the new generalised version and analyse it. After that, we will present a new generalised version of the Deutsch--Jozsa problem and it will be solved using the previously defined technique. Finally, we will present a generalised version of the Bernstein-Vazirani problem and solve it using this technique to better understand its inner workings.