Quantum Algorithm for the Longest Trail Problem

Khadiev, Kamil; Kapralov, Ruslan

doi:10.48550/arxiv.2112.13847

Cited by 1 publication

(1 citation statement)

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“…A well-known example is the so-called Dürr-Hoyer minimum finding algorithm [27], which employs Grover's Algorithm [17,[28][29][30][31] as a fundamental subroutine to find the greatest or smallest entry in a list [32]. Several suggested strategies for searching minimum values were proposed based on Dürr-Hoyer's algorithm [32][33][34][35][36][37][38], with applications in high energy physics [34], and wireless communications [35]. Recent implementations indicate that it can be improved, given the enormous number of qubits necessary to implement the approach and the impracticality of hard-coding a distinct oracle for each element [33,34].…”

Section: Introductionmentioning

confidence: 99%

Quantum algorithm for finding minimum values in a Quantum Random Access Memory

Albino,

Galvão,

Neto

et al. 2024

Preprint

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Finding the minimum value in an unordered database is a common and fundamental task in computer science. However, the optimal classical deterministic algorithm can find the minimum value with a time complexity that grows linearly with the number of elements in the database. In this paper, we present the proposal of a quantum algorithm for finding the minimum value of a database, which is quadratically faster than its best classical analogs. We assume a Quantum Random Access Memory (QRAM) that stores values from a database and performs an iterative search based on an oracle whose role is to limit the searched values by controlling the states of the most significant qubits. A complexity analysis was performed in order to demonstrate the advantage of this quantum algorithm over its classical counterparts.

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