The paper presents a deterministic quantum search algorithm for complete bipartite graphs. The key aspects are:
The algorithm adopts a simple form of alternating iterations between an oracle and a continuous-time quantum walk operator, generalizing Grover's search algorithm.
The algorithm addresses the general case of multiple marked states, requiring an estimation of the number of marked states. This is achieved through a quantum counting algorithm based on the spectrum structure of the search operator.
The continuous-time quantum walk operator is implemented efficiently using Hamiltonian simulation, with the complexity of the quantum circuit independent of the evolution time.
As an application, the algorithm is used to solve the problem of perfect state transfer on complete bipartite graphs.
The deterministic nature of the search algorithm and the efficient implementation through Hamiltonian simulation are the key contributions of this work.
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by Honghong Lin... om arxiv.org 04-03-2024
https://arxiv.org/pdf/2404.01640.pdfDiepere vragen