The study of V ariational Quantum Eigensolvers (VQEs) has been in the spotlight in recent times as they may lead to real-world applications of near-term quantum devices. However, their performance depends on the structure of the used variational ansatz, which requires balancing the depth and expressivity of the corresponding circuit. At the same time, near-term restrictions limit the depth of the circuit we can expect to run. Thus, the optimization of the VQE ansatz requires maximizing the expressivity of the circuit while maintaining low depth. In recent years, various methods for VQE structure optimization have been introduced but the capacities of machine learning to aid with this problem have not yet been extensively investigated. In this work, we propose a reinforcement learning algorithm that autonomously explores the space of possible ansatzes, identifying economic circuits which still yield accurate ground energy estimates. The algorithm uses a feedback-driven curriculum learning method that autonomously adapts the complexity of the learning problem to the current performance of the learning algorithm and it incrementally improves the accuracy of the result while minimizing the circuit depth.

Quantum Machine Learning (QML) offers a new paradigm for addressing complex financial problems intractable for classical methods. This work specifically tackles the challenge of few-shot credit risk assessment, a critical issue in inclusive finance where data scarcity and imbalance limit the effectiveness of conventional models. To address this, we design and implement a novel hybrid quantum-classical workflow. The methodology first employs an ensemble of classical machine learning models (Logistic Regression, Random Forest, XGBoost) for intelligent feature engineering and dimensionality reduction. Subsequently, a Quantum Neural Network (QNN), trained via the parameter-shift rule, serves as the core classifier. This framework was evaluated through numerical simulations and deployed on the Quafu Quantum Cloud Platform's ScQ-P21 superconducting processor. On a real-world credit dataset of 279 samples, our QNN achieved a robust average AUC of 0.852 +/- 0.027 in simulations and yielded an impressive AUC of 0.88 in the hardware experiment. This performance surpasses a suite of classical benchmarks, with a particularly strong result on the recall metric. This study provides a pragmatic blueprint for applying quantum computing to data-constrained financial scenarios in the NISQ era and offers valuable empirical evidence supporting its potential in high-stakes applications like inclusive finance.

--Conventional V ariational Quantum Circuits (VQCs) for Quantum Machine Learning typically rely on a fixed Her-mitian observable, often built from Pauli operators. Inspired by the Heisenberg picture, we propose an adaptive non-local measurement framework that substantially increases the model complexity of the quantum circuits. Our introduction of dynamical Hermitian observables with evolving parameters shows that optimizing VQC rotations corresponds to tracing a trajectory in the observable space. This viewpoint reveals that standard VQCs are merely a special case of the Heisenberg representation. Furthermore, we show that properly incorporating variational rotations with non-local observables enhances qubit interaction and information mixture, admitting flexible circuit designs. Two non-local measurement schemes are introduced, and numerical simulations on classification tasks confirm that our approach outperforms conventional VQCs, yielding a more powerful and resource-efficient approach as a Quantum Neural Network. Quantum Machine Learning (QML) is a developing field that leverages the principles of quantum mechanics to advance machine learning (ML) models. With the rapid advancement of quantum computing hardware, QML aims to exploit quantum phenomena--such as superposition, entanglement, and quantum interference--to provide computational advantages over classical approaches. Despite the current limitations of quantum hardware, hybrid quantum-classical algorithms have been developed to harness the strengths of both computing paradigms, allowing near-term quantum devices to contribute meaningfully to real-world ML tasks.

Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer separated components. In this article, we present QuForge, a Python-based library designed to simulate quantum circuits with qudits. This library provides the necessary quantum gates for implementing quantum algorithms, tailored to any chosen qudit dimension. Built on top of differentiable frameworks, QuForge supports execution on accelerating devices such as GPUs and TPUs, significantly speeding up simulations. It also supports sparse operations, leading to a reduction in memory consumption compared to other libraries. Additionally, by constructing quantum circuits as differentiable graphs, QuForge facilitates the implementation of quantum machine learning algorithms, enhancing the capabilities and flexibility of quantum computing research.

Quantum machine learning (QML) is a rapidly emerging area of research, driven by the capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices. With the progress in the research of QML models, there is a rise in third-party quantum cloud services to cater to the increasing demand for resources. New security concerns surface, specifically regarding the protection of intellectual property (IP) from untrustworthy service providers. One of the most pressing risks is the potential for reverse engineering (RE) by malicious actors who may steal proprietary quantum IPs such as trained parameters and QML architecture, modify them to remove additional watermarks or signatures and re-transpile them for other quantum hardware. Prior work presents a brute force approach to RE the QML parameters which takes exponential time overhead. In this paper, we introduce an autoencoder-based approach to extract the parameters from transpiled QML models deployed on untrusted third-party vendors. We experiment on multi-qubit classifiers and note that they can be reverse-engineered under restricted conditions with a mean error of order 10^-1. The amount of time taken to prepare the dataset and train the model to reverse engineer the QML circuit being of the order 10^3 seconds (which is 10^2x better than the previously reported value for 4-layered 4-qubit classifiers) makes the threat of RE highly potent, underscoring the need for continued development of effective defenses.

Quantum Machine Learning (QML) amalgamates quantum computing paradigms with machine learning models, providing significant prospects for solving complex problems. However, with the expansion of numerous third-party vendors in the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing, the security of QML models is of prime importance, particularly against reverse engineering, which could expose trained parameters and algorithms of the models. We assume the untrusted quantum cloud provider is an adversary having white-box access to the transpiled user-designed trained QML model during inference. Reverse engineering (RE) to extract the pre-transpiled QML circuit will enable re-transpilation and usage of the model for various hardware with completely different native gate sets and even different qubit technology. Such flexibility may not be obtained from the transpiled circuit which is tied to a particular hardware and qubit technology. The information about the number of parameters, and optimized values can allow further training of the QML model to alter the QML model, tamper with the watermark, and/or embed their own watermark or refine the model for other purposes. In this first effort to investigate the RE of QML circuits, we perform RE and compare the training accuracy of original and reverse-engineered Quantum Neural Networks (QNNs) of various sizes. We note that multi-qubit classifiers can be reverse-engineered under specific conditions with a mean error of order 1e-2 in a reasonable time. We also propose adding dummy fixed parametric gates in the QML models to increase the RE overhead for defense. For instance, adding 2 dummy qubits and 2 layers increases the overhead by ~1.76 times for a classifier with 2 qubits and 3 layers with a performance overhead of less than 9%. We note that RE is a very powerful attack model which warrants further efforts on defenses.

Variational quantum algorithms are gaining attention as an early application of Noisy Intermediate-Scale Quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of Barren Plateaus, present in the optimization of variational parameters. Adding geometric inductive bias to the quantum models has been proposed as a potential solution to mitigate this problem, leading to a new field called Geometric Quantum Machine Learning. In this work, an equivariant architecture for variational quantum classifiers is introduced to create a label-invariant model for image classification with $C_4$ rotational label symmetry. The equivariant circuit is benchmarked against two different architectures, and it is experimentally observed that the geometric approach boosts the model's performance. Finally, a classical equivariant convolution operation is proposed to extend the quantum model for the processing of larger images, employing the resources available in NISQ devices.

The present study aims to explore the feasibility of language translation using quantum natural language processing algorithms on noisy intermediate-scale quantum (NISQ) devices. Classical methods in natural language processing (NLP) struggle with handling large-scale computations required for complex language tasks, but quantum NLP on NISQ devices holds promise in harnessing quantum parallelism and entanglement to efficiently process and analyze vast amounts of linguistic data, potentially revolutionizing NLP applications. Our research endeavors to pave the way for quantum neural machine translation, which could potentially offer advantages over classical methods in the future. We employ Shannon entropy to demonstrate the significant role of some appropriate angles of rotation gates in the performance of parametrized quantum circuits. In particular, we utilize these angles (parameters) as a means of communication between quantum circuits of different languages. To achieve our objective, we adopt the encoder-decoder model of classical neural networks and implement the translation task using long short-term memory (LSTM). Our experiments involved 160 samples comprising English sentences and their Persian translations. We trained the models with different optimisers implementing stochastic gradient descent (SGD) as primary and subsequently incorporating two additional optimizers in conjunction with SGD. Notably, we achieved optimal results-with mean absolute error of 0.03, mean squared error of 0.002, and 0.016 loss-by training the best model, consisting of two LSTM layers and using the Adam optimiser. Our small dataset, though consisting of simple synonymous sentences with word-to-word mappings, points to the utility of Shannon entropy as a figure of merit in more complex machine translation models for intricate sentence structures.

Generalization is an important feature of neural network, and there have been many studies on it. Recently, with the development of quantum compu-ting, it brings new opportunities. In this paper, we studied a class of quantum neural network constructed by quantum gate. In this model, we mapped the feature data to a quantum state in Hilbert space firstly, and then implement unitary evolution on it, in the end, we can get the classification result by im-plement measurement on the quantum state. Since all the operations in quan-tum neural networks are unitary, the parameters constitute a hypersphere of Hilbert space. Compared with traditional neural network, the parameter space is flatter. Therefore, it is not easy to fall into local optimum, which means the quantum neural networks have better generalization. In order to validate our proposal, we evaluated our model on three public datasets, the results demonstrated that our model has better generalization than the classical neu-ral network with the same structure.