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arXiv:2210.12644 · Information and Computation

Deterministic quantum search with adjustable parameters: Implementations and applications

Guanzhong Li, Lvzhou Li

Published Apr 24, 2023• 19 citations
arXivHTMLPDF
DOI
10.1016/j.ic.2023.105042

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Searching via quantum walk is a topic that has been extensively studied. Most previous results provide approximate solutions, while in this paper we prove an algorithm that can find a marked vertex certainly. We adopt the coined discrete-time quantum walk (DTQW) model with adjusted operators and prove that, on complete bipartite graphs, when parameters are set properly, coined DTQW can deterministically find a marked vertex, i.e., the success probability is exactly 1. Before this paper there have been results of an alternating continuous-time quantum walk method that achieve deterministic spatial search, but this paper provides a deterministic quantum spatial search result via DTQW, while maintaining a quadratic speedup compared to classical algorithms. We also provide the quantum circuit implementation. Published by the American Physical Society 2024
Grover's search algorithm is a well-known quantum algorithm that has been extensively studied and improved to increase its success rate and enhance its flexibility. However, most improved search algorithms require an adjustment of the oracle, which may not be feasible in practical problem-solving scenarios. In this work, we report an experimental demonstration of a deterministic quantum search for multiple marked states without adjusting the oracle. A linear optical setup is designed to search for two marked states, one in a 16-state database with an initial equal-superposition state and the other in an 8-state database with different initial nonequal-superposition states. The evolution of the probability of finding each state in the database is also measured and displayed. Our experimental results agree well with the theoretical predictions, thereby proving the feasibility of the search protocol and the implementation scheme. This work is a pioneering experimental demonstration of deterministic quantum search for multiple marked states without adjusting the oracle.
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