A generalisation of the Phase Kick-Back

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. We will begin by recalling the Phase Kick-Back technique to then introduce the new generalised version for $$f:\{0,1\}^{n}\rightarrow \{0,1\}^{m}$$ f : { 0 , 1 } n → { 0 , 1 } m functions using the eigenvalues of the oracle function $$\textbf{U}_f$$ U f . After that, we will present a new generalised version of the Deutsch–Jozsa problem and how it can be solved using the previously defined technique. We will also deal with a generalised version of the Bernstein–Vazirani problem and solve it using the generalised Phase Kick-Back. Finally, we show how we can use this technique to obtain an algorithm for Simon’s problem that improves the classical one.