Further Applications of the Generalised Phase Kick-Back

• URL: http://arxiv.org/abs/2405.03850v2
• Date: Mon, 21 Oct 2024 10:23:59 GMT
• Title: Further Applications of the Generalised Phase Kick-Back
• Abstract summary: In our previous work, we defined a quantum algorithmic technique known as the Generalised Phase Kick-Back, or $GPK$. This paper defines the concept of $mathbfy$-balanced functions and solves a new problem, which further generalises the generalised Deutsch-Jozsa problem.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In our previous work, we defined a quantum algorithmic technique known as the Generalised Phase Kick-Back, or $GPK$, and analysed its applications in generalising some classical quantum problems, such as the Deutsch-Jozsa problem or the Bernstein-Vazirani problem. We also proved that using this technique we can solve Simon's problem in a more efficient manner. In this paper we continue analysing the potential of this technique, defining the concept of $\mathbf{y}$-balanced functions and solving a new problem, which further generalises the generalised Deutsch-Jozsa problem (the fully balanced image problem). This problem also underlines the relation between quantum computation and Boolean function theory, and, in particular, the Walsh and Fourier-Hadamard transforms. We finish our discussion by solving the generalised version of Simon's problem using the $GPK$ algorithm, while analysing the efficiency of this new solution.

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