Both of the techniques assume bitwise access to the oracle as a classical function.

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.

The Heisenberg uncertainty principle puts a limit on how precisely we can measure certain properties of quantum objects. But researchers may have found a way to bypass this limitation using a quantum version of a neural network. Given, for example, a chemically useful molecule, how can you predict what properties it might have in an hour or tomorrow? To make such predictions, researchers start by measuring its current properties. But for quantum objects, including some molecules, this can be unexpectedly difficult because each measurement can interfere with or change the outcome of the next measurement.

Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.

A strange kind of quantumness may be key to quantum computers' success What is it about quantum computers that makes them more powerful than conventional machines? A new experiment shows that the property of "quantum contextuality" may be a key ingredient. Quantum computers are fundamentally different from all other computers because they harness uniquely quantum phenomena absent from conventional electronics. For instance, their building blocks, which are called qubits, are routinely put into superposition states - they seemingly assume two properties at once that are normally mutually exclusive - or they get connected through the inextricable link of quantum entanglement . Quantum computers have finally arrived, but will they ever be useful? Now, researchers at Google Quantum AI have used their Willow quantum computer to carry out several demonstrations showing that the property of quantum contextuality also plays a significant role.

Abstract--Short-term voltage stability assessment (STVSA) is critical for secure power system operation. While classical machine learning-based methods have demonstrated strong performance, they still face challenges in robustness under adversarial conditions. This paper proposes QST Aformer--a tailored quantum-enhanced Transformer architecture that embeds parameterized quantum circuits (PQCs) into attention mechanisms--for robust and efficient STVSA. A dedicated adversarial training strategy is developed to defend against both white-box and gray-box attacks. Furthermore, diverse PQC architectures are benchmarked to explore trade-offs between expressiveness, convergence, and efficiency. T o the best of our knowledge, this is the first work to systematically investigate the adversarial vulnerability of quantum machine learning-based STVSA. Case studies on the IEEE 39-bus system demonstrate that QST Aformer achieves competitive accuracy, reduced complexity, and stronger robustness, underscoring its potential for secure and scalable STVSA under adversarial conditions. ITH the high penetration of converter-interfaced renewable energy sources and the growing deployment of fast-acting power electronic devices, maintaining short-term voltage stability (STVS) in modern power systems has become a pressing challenge [1]. STVS characterizes a power system's ability to preserve acceptable voltage profiles during the initial seconds following a disturbance [2], and this stability is primarily influenced by the dynamic behavior of fast acting loads, Li is with the School of Electrical Engineering, Northeast Electric Power University, Jilin 132012, China (e-mail: liyang@neepu.edu.cn). C. Ma is with State Grid Shandong Electric Power Company Jiaozhou Power Supply Company, Jiaozhou 266300, China (email:machong58112233@163.com). Z. Li is with the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China (email: Y uanzheng Li@hust.edu.cn). Sen Li is with the Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong.

In this paper we study the potential of using reinforcement learning (RL) in order to synthesize quantum circuits, while optimizing the T-count and CS-count, of unitaries that are exactly implementable by the Clifford+T and Clifford+CS gate sets, respectively. We have designed our RL framework to work with channel representation of unitaries, that enables us to perform matrix operations efficiently, using integers only. We have also incorporated pruning heuristics and a canonicalization of operators, in order to reduce the search complexity. As a result, compared to previous works, we are able to implement significantly larger unitaries, in less time, with much better success rate and improvement factor. Our results for Clifford+T synthesis on two qubit unitaries achieve close-to-optimal decompositions for up to 100 T gates, 5 times more than previous RL algorithms and to the best of our knowledge, the largest instances achieved with any method to date. Our RL algorithm is able to recover previously-known optimal linear complexity algorithm for T-count-optimal decomposition of 1 qubit unitaries. We illustrate significant reduction in the asymptotic T-count estimate of important primitives like controlled cyclic shift (43%), controlled adder (14.3%) and multiplier (14%), without adding any extra ancilla. For 2-qubit Clifford+CS unitaries, our algorithm achieves a linear complexity, something that could only be accomplished by a previous algorithm using SO(6) representation.

Quantum Machine Learning (QML) is a research area that focuses on the development of Machine Learning (ML) algorithms that can be executed by a quantum computer. Taking advantage of quantum phenomena such as quantum superposition and quantum entanglement, the incorporation of quantum computing in ML aims to leverage the power of the quantum computer to improve existing classical ML algorithms [1]. The process of manipulating the states of qubits by arbitrarily changing the gate parameters for the desired result is closely related to the training process of machine learning algorithms. For solving any specific problem, QML algorithms can be designed as a quantum circuit with a sequence of different quantum gate operations [2][3]. However, Noisy Intermediate Scale Quantum (NISQ) computers are limited in resources and subject to sources of error, such as noise induced by each quantum operation [4][5]. This makes it difficult to develop QML algorithms that perform as well as or better than conventional ones. Hence, developing QML algorithms with good performance, despite today's limited resources, has become a major challenge. To achieve this, it is important to look at several aspects of a QML task, such that the data encoding part. Quantum encoding involves the conversion of classical information into quantum states, enabling QML algorithms to operate efficiently.

In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and disentangling power of unitary transformations is investigated. In particular, we interpret entangling and disentangling power as information retention and forgetting mechanisms in LSTMs. Thus, entanglement emerges as a key component of the optimization (training) process. We believe that, by leveraging prior knowledge of the entangling power of unitaries, the proposed quantum-classical framework can guide the design of better-parameterized quantum circuits for various real-world applications.

Qubit control protocols have traditionally leveraged a characterisation of the qubit-bath coupling via its power spectral density. Previous work proposed the inference of noise operators that characterise the influence of a classical bath using a grey-box approach that combines deep neural networks with physics-encoded layers. This overall structure is complex and poses challenges in scaling and real-time operations. Here, we show that no expensive neural networks are needed and that this noise operator description admits an efficient parameterisation. We refer to the resulting parameter space as the \textit{quantum feature space} of the qubit dynamics resulting from the coupled bath. We show that the Euclidean distance defined over the quantum feature space provides an effective method for classifying noise processes in the presence of a given set of controls. Using the quantum feature space as the input space for a simple machine learning algorithm (random forest, in this case), we demonstrate that it can effectively classify the stationarity and the broad class of noise processes perturbing a qubit. Finally, we explore how control pulse parameters map to the quantum feature space.