Recent advancements highlight the pivotal role of quantum machine learning (QML) [4, 13] in processing quantum data derived from quantum systems [14]. A fundamental task in QML is generating quantum data by learning the underlying distribution, essential for understanding quantum systems, synthesizing new samples, and advancing applications in quantum chemistry and materials science. However, extending classical generative approaches to quantum data presents significant challenges, as quantum distributions exhibit superposition, entanglement, and non-locality that classical models struggle to replicate efficiently. Quantum generative models such as quantum generative adversarial networks [24, 42] and quantum variational autoencoders [20, 38] can be used to prepare a fixed single quantum state [21, 28, 37], but are inefficient for generating ensembles of quantum states [3] due to the need for training deep parameterized quantum circuits (PQCs). The quantum denoising diffusion probabilistic model [40] offers a promising approach that employs intermediate training steps to smoothly interpolate between the target distribution and noise, thereby enabling efficient training.

Fast parallel circuits for the quantum fourier transform.

Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable parameters on the edges instead of on the nodes, unlike traditional networks such as Multi-Layer Perceptrons (MLPs). However, KANs potential in quantum machine learning has not yet been well explored. In this work, we present an implementation of these KAN architectures in both hybrid and fully quantum forms using a Quantum Circuit Born Machine (QCBM). We adapt the KAN transfer using pre-trained residual functions, thereby exploiting the representational power of parametrized quantum circuits. In the hybrid model we combine classical KAN components with quantum subroutines, while the fully quantum version the entire architecture of the residual function is translated to a quantum model. We demonstrate the feasibility, interpretability and performance of the proposed Quantum KAN (QuKAN) architecture.

Since classical machine learning has become a powerful tool for developing data-driven algorithms, quantum machine learning is expected to similarly impact the development of quantum algorithms. The literature reflects a mutually beneficial relationship between machine learning and quantum computing, where progress in one field frequently drives improvements in the other. Motivated by the fertile connection between machine learning and quantum computing enabled by parameterized quantum circuits, we use a resource-efficient and scalable Single-Qubit Quantum Neural Network (SQQNN) for both regression and classification tasks. The SQQNN leverages parameterized single-qubit unitary operators and quantum measurements to achieve efficient learning. To train the model, we use gradient descent for regression tasks. For classification, we introduce a novel training method inspired by the Taylor series, which can efficiently find a global minimum in a single step. This approach significantly accelerates training compared to iterative methods. Evaluated across various applications, the SQQNN exhibits virtually error-free and strong performance in regression and classification tasks, including the MNIST dataset. These results demonstrate the versatility, scalability, and suitability of the SQQNN for deployment on near-term quantum devices.

The first artificial quantum neuron models followed a similar path to classic models, as they work only with discrete values. Here we introduce an algorithm that generalizes the binary model manipulating the phase of complex numbers. We propose, test, and implement a neuron model that works with continuous values in a quantum computer. Through simulations, we demonstrate that our model may work in a hybrid training scheme utilizing gradient descent as a learning algorithm. This work represents another step in the direction of evaluation of the use of artificial neural networks efficiently implemented on near-term quantum devices.

Based on the linearity of quantum unitary operations, we propose a method that runs the parameterized quantum circuits before encoding the input data. It enables a dataset owner to train machine learning models on quantum cloud computation platforms, without the risk of leaking the information of the data. It is also capable of encoding a huge number of data effectively at a later time using classical computations, thus saving the runtime on quantum computation devices. The trained quantum machine learning model can be run completely on classical computers, so that the dataset owner does not need to have any quantum hardware, nor even quantum simulators. Moreover, the method can mitigate the encoding bottom neck by reducing the required circuit depth from $O(2^{n})$ to $n/2$. These results manifest yet another advantage of quantum and quantum-inspired machine learning models over existing classical neural networks, and broaden the approaches for data security.

The conceptual idea of generating shadows of quantum models was already proposed by Schreiber et al. [18], albeit under the terminology of classical surrogates. In that Quantum machine learning is a rapidly growing field [1-3] work, as well as in that of Landman et al. [19], the authors driven by its potential to achieve quantum advantages make use of the general expression of quantum models as in practical applications. A particularly interesting approach trigonometric polynomials [20] to learn the Fourier representation to make quantum machine learning applicable of trained models and evaluate them classically in the near term is to develop learning models based on new data. However, these works also suggest that a on parametrized quantum circuits [4-6]. Indeed, such classical model could potentially be trained directly on quantum models have already been shown to achieve the training data and achieve the same performance as good learning performance in benchmarking tasks, both the shadow model, thus circumventing the need for a in numerical simulations [7-11] and on actual quantum quantum model in the first place. This raises the concern hardware [12-15]. Moreover, based on widely-believed that all quantum models that are compatible with a classical cryptography assumptions, these models also hold the deployment would also lose all quantum advantage, promise to solve certain learning tasks that are intractable hence severely limiting the prospects for a widespread use for classical algorithms [16, 17]. of quantum machine learning. Despite these advances, quantum machine learning is Therefore, two natural open questions are raised: facing a major obstacle for its use in practice. A typical workflow of a machine learning model involved, e.g., 1. Can shadow models achieve a quantum advantage in driving autonomous vehicles, is divided into: (i) a over entirely classical (classically trained and classically training phase, where the model is trained, typically using evaluated) models?

Quantum machine learning implemented by variational quantum circuits (VQCs) is considered a promising concept for the noisy intermediate-scale quantum computing era. Focusing on applications in quantum reinforcement learning, we propose a specific action decoding procedure for a quantum policy gradient approach. We introduce a novel quality measure that enables us to optimize the classical post-processing required for action selection, inspired by local and global quantum measurements. The resulting algorithm demonstrates a significant performance improvement in several benchmark environments. With this technique, we successfully execute a full training routine on a 5-qubit hardware device. Our method introduces only negligible classical overhead and has the potential to improve VQC-based algorithms beyond the field of quantum reinforcement learning.

The phonological structure of human languages is intricate, yet highly constrained. Through a combination of connectionist modeling and linguistic analysis, we are attempting to develop a computational basis for the nature of phonology. We present a connectionist architecture that performs multiple simultaneous insertion, deletion, and mutation operations on sequences of phonemes, and introduce a novel additional primitive, clustering. Clustering provides an interesting alternative to both iterative and relaxation accounts of assimilation processes such as vowel harmony. Our resulting model is efficient because it processes utterances entirely in parallel using only feed-forward circuitry.