Quantum Algorithm for Finding Minimum Values in a Quantum Random Access Memory

doi:10.1007/s13538-025-01924-5

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Quantum Algorithm for Finding Minimum Values in a Quantum Random Access Memory

2025-10-15

PRE

Anton S. Albino

Lucas Q. Galvão

Mauro Q. Nooblath Neto

Ethan Hansen

Clebson Cruz *

DOI：10.1007/s13538-025-01924-5

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Abstract

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Finding the minimum value in a large unstructured database is a common and fundamental task in computer science with broad applications across science and industry. 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. We provide a detailed description of the quantum circuit implementation, analyze its complexity, and demonstrate a significant computational advantage, particularly for large-scale datasets. In addition, a complexity analysis was performed in order to demonstrate the advantage of this quantum algorithm over its classical counterparts. Thus, the presented quantum minimum search (QMS) algorithm represents a promising tool for practical computing scenarios, offering a robust foundation for further research into fault-tolerant quantum algorithms.

Keywords:

Quantum RAM

Minimum search

Grover's algorithm