Abstract
AbstractIn 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.
Funder
Ministerio de Ciencia e InnovaciÓn
Junta de Andalucía and ERDF
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Modeling and Simulation,Signal Processing,Theoretical Computer Science,Statistical and Nonlinear Physics,Electronic, Optical and Magnetic Materials
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