Quantum K-Nearest Neighbors: Utilizing QRAM and SWAP-Test Techniques for Enhanced Performance

Abstract

This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with O(log(n)) space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving Om search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM.