Quantum computing, based on quantum theory, holds great promise as an advanced computational paradigm for achieving fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degrees of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms are theoretically faster than the classical algorithm, while experiments suggest that it is possible to obtain comparable clustering results.

Quantum algorithms evolve an initial quantum state into another during computation to obtain meaningful results.However, this evolution introduces the cost of re-preparing the same initial quantum state for different tasks.Unfortunately, since quantum memory is not yet available, this cost cannot be ignored in Quantum Artificial Intelligence (QAI), where the initial quantum state typically coincides with a quantum dataset.Redundant state preparations for different tasks on the same dataset can reduce the advantages of quantum computation.To address this issue, this work proposes a new technique: the Logarithmic Quantum Forking (LQF).LQF performs state preparation for an initial quantum state once and employs additional qubits to compute an exponential number of tasks over the initial quantum state.LQF enables more efficient use of quantum computation in QAI by amortizing the cost of preparing the initial quantum state.

The promise of quantum computation to achieve a speedup over classical computation led to a surge of interest in exploring new quantum algorithms for data analysis problems.Feature Selection, a technique that selects the most relevant features from a dataset, is a critical step in data analysis.With several Quantum Feature Selection techniques proposed in the literature, this study exhibits the potential of quantum algorithms to enhance Feature Selection and other tasks that leverage the variance.This study proposes a novel quantum algorithm for estimating the variance over a set of real data.Importantly, after state preparation, the algorithm's complexity exhibits logarithmic characteristics in both its width and depth.The quantum algorithm applies to the Feature Selection problem by designing a Hybrid Quantum Feature Selection (HQFS) algorithm.This work showcases an implementation of HQFS and assesses it on two synthetic datasets and a real dataset.* This study was carried out within the National Centre on HPC, Big Data and Quantum Computing -SPOKE 10 (Quantum Computing) and received funding from the European Union Next-GenerationEU -National Recovery and Resilience Plan (NRRP) -MISSION 4, COMPONENT 2 -CUP N. I53C22000690001.This manuscript reflects only the authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them.

We propose a new three-level XOR-AND-XOR form for autosymmetric functions, called XORAX expression. In general, a Boolean function f over n variables is k-autosymmetric if it can be projected onto a smaller function fk, which depends on n-k variables only. We show that XORAX expressions can ease the reversible synthesis of autosymmetric functions, producing compact reversible networks, without inserting additional new input lines. Autosymmetry occurs especially for functions that exhibit a regular structure, as for instance arithmetic functions. For this reason, compact reversible networks for autosymmetric functions might be interesting for quantum computing. Experimental results validate the proposed approach.