The k-nearest neighbors (k-NN) is a basic machine learning (ML) algorithm, and several quantum versions of it, employing different distance metrics, have been presented in the last few years. Although the Euclidean distance is one of the most widely used distance metrics in ML, it has not received much consideration in the development of these quantum variants. In this article, a novel quantum k-NN algorithm based on the Euclidean distance is introduced. Specifically, the algorithm is characterized by a quantum encoding requiring a low number of qubits and a simple quantum circuit not involving oracles, aspects that favor its realization. In addition to the mathematical formulation and some complexity observations, a detailed empirical evaluation with simulations is presented. In particular, the results have shown the correctness of the formulation, a drop in the performance of the algorithm when the number of measurements is limited, the competitiveness with respect to some classical baseline methods in the ideal case, and the possibility of improving the performance by increasing the number of measurements.

The abundance of transcriptomic data and the development of causal inference methods have paved the way for gene network analyses in grapevine. Vitis OneGenE is a transcriptomic data mining tool that finds direct correlations between genes, thus producing association networks. As a proof of concept, the stilbene synthase gene regulatory network obtained with OneGenE has been compared with published co-expression analysis and experimental data, including cistrome data for MYB stilbenoid regulators. As a case study, the two secondary metabolism pathways of stilbenoids and lignin synthesis were explored. Several isoforms of laccase, peroxidase, and dirigent protein genes, putatively involved in the final oxidative oligomerization steps, were identified as specifically belonging to either one of these pathways. Manual curation of the predicted sequences exploiting the last available genome assembly, and the integration of phylogenetic and OneGenE analyses, identified a group of laccases exclusively present in grapevine and related to stilbenoids. Here we show how network analysis by OneGenE can accelerate knowledge discovery by suggesting new candidates for functional characterization and application in breeding programs.

Support vector machines (SVMs) are widely used machine learning models, with formulations for both classification and regression tasks. In the last years, with the advent of working quantum annealers, hybrid SVM models characterised by quantum training and classical execution have been introduced. These models have demonstrated comparable performance to their classical counterparts. However, they are limited in the training set size due to the restricted connectivity of the current quantum annealers. Hence, to take advantage of large datasets, a strategy is required. In the classical domain, local SVMs, namely, SVMs trained on the data samples selected by a $k$ -nearest neighbors model, have already proven successful. Here, the local application of quantum-trained SVM models is proposed and empirically assessed. In particular, this approach allows overcoming the constraints on the training set size of the quantum-trained models while enhancing their performance. In practice, the Fast Local Kernel Support Vector Machine (FaLK-SVM) method, designed for efficient local SVMs, has been combined with quantum-trained SVM models for binary and multiclass classification. In addition, for comparison, FaLK-SVM has been interfaced for the first time with a classical single-step multiclass SVM model (CS SVM). Concerning the empirical evaluation, D-Wave's quantum annealers and real-world datasets taken from the remote sensing domain have been employed. The results have shown the effectiveness and scalability of the proposed approach, but also its practical applicability in a real-world large-scale scenario.

The automatic discovery of causal relationships among human genes can shed light on gene regulatory processes and guide drug repositioning. To this end, a computationally-heavy method for causal discovery is distributed on a volunteer computing grid and, taking advantage of variable subsetting and stratification, proves to be useful for expanding local gene regulatory networks. The input data are purely observational measures of transcripts expression in human tissues and cell lines collected within the FANTOM project. The system relies on the BOINC platform and on optimized client code. The functional relevance of results, measured by analyzing the annotations of the identified interactions, increases significantly over the simple Pearson correlation between the transcripts. Additionally, in 82 percent of cases networks significantly overlap with known protein-protein interactions annotated in biological databases. In the two case studies presented, this approach has been used to expand the networks of genes associated with two severe human pathologies: prostate cancer and coronary artery disease. The method identified respectively 22 and 36 genes to be evaluated as novel targets for already approved drugs, demonstrating the effective applicability of the approach in pipelines aimed to drug repositioning.