Quantum k-nearest neighbors algorithm
Abstract
One of the simplest and most effective classical machine learning algorithms is the k-nearest neighbors algorithm (kNN) which classifies an unknown test state by finding the k nearest neighbors from a set of M train states. Here we present a quantum analog of classical kNN - quantum kNN (QkNN) - based on fidelity as the similarity measure. We show that QkNN algorithm can be reduced to an instance of the quantum k-maxima algorithm, hence the query complexity of QkNN is O(kM). The non-trivial task in this reduction is to encode the fidelity information between the test state and all the train states as amplitudes of a quantum state. Converting this amplitude encoded information to a digital format enables us to compare them efficiently, thus completing the reduction. Unlike classical kNN and existing quantum kNN algorithms, the proposed algorithm can be directly used on quantum data thereby bypassing expensive processes such as quantum state tomography. As an example, we show the applicability of this algorithm in entanglement classification and quantum state discrimination.