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. We will begin by recalling the Phase Kick-Back technique to then introduce the new generalised version for f : { 0 , 1 } n → { 0 , 1 } m functions u...

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Bibliographic Details
Published in:Quantum information processing 2023-03, Vol.22 (3), Article 143
Main Authors: Ossorio-Castillo, Joaquín, Pastor–Díaz, Ulises, Tornero, José M.
Format: Article
Language:English
Subjects:
Data Structures and Information Theory
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
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Summary: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 → { 0 , 1 } m functions using the eigenvalues of the oracle function 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.
ISSN:1573-1332
1573-1332
DOI:10.1007/s11128-023-03884-8