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

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 perform 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. Furthermore, we demonstrate how the proposed algorithm would be used in an unsupervised machine learning task through a quantum version of the K-means algorithm.