A Generalisation of the Phase Kick-Back

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.