Quantum search in a dictionary based on fingerprinting-hashing

• URL: http://arxiv.org/abs/2412.11422v1
• Date: Mon, 16 Dec 2024 03:43:59 GMT
• Title: Quantum search in a dictionary based on fingerprinting-hashing
• Authors: Farid Ablayev, Nailya Salikhova, Marat Ablayev,
• Abstract summary: We present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(sqrtn)$ queries (Grover operators), like previously known algorithms. What is new is that the algorithm is based on the quantum fingerprinting-hashing technique, which (a) provides a first level of amplitude amplification before applying the sequence of Grover amplitude amplification operators and (b) makes the algorithm more efficient in terms of memory use.
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• Abstract: In this work, we present a quantum query algorithm for searching a word of length $m$ in an unsorted dictionary of size $n$. The algorithm uses $O(\sqrt{n})$ queries (Grover operators), like previously known algorithms. What is new is that the algorithm is based on the quantum fingerprinting-hashing technique, which (a) provides a first level of amplitude amplification before applying the sequence of Grover amplitude amplification operators and (b) makes the algorithm more efficient in terms of memory use -- it requires $O(\log n + \log m)$ qubits. Note that previously developed algorithms by other researchers without hashing require $O(\log n + m)$ qubits.

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