We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by orders of magnitude.

One leading algorithmic paradigm on NISQ computers is theVariational Quantum Algorithm (VQA) with a few prominent examples like the Variational Quantum Eignensolver (VQE) [50], quantum approximate optimization algorithm (QAOA) [20], and more in [4]. Quantum machine learning isafast-developing emerging field (e.g., see the survey [5]) where variational quantum algorithms (VQAs) (e.g., see thesurvey[4]areoneofthemost promising candidates forNISQ applications.

Classical GNNs excel at graph learning but incur high computational costs in large-scale settings. We present a fully quantum Graph Neural Network (QGNN) that implements message passing via Parameterized Quantum Circuits (PQCs). Our Quantum Graph Convolutional Layers (QGCLs) encode features into quantum states, process graphs with NISQ-compatible unitaries, and retrieve embeddings through measurement. Applied to D2D power control for SINR maximization, our QGNN matches classical performance with fewer parameters and inherent parallelism. This end-to-end PQC-based GNN marks a step toward quantum-accelerated wireless optimization.

We introduce quantum agents trained by episodic, reward-based reinforcement learning to autonomously rediscover several seminal quantum algorithms and protocols. In particular, our agents learn: efficient logarithmic-depth quantum circuits for the Quantum Fourier Transform; Grover's search algorithm; optimal cheating strategies for strong coin flipping; and optimal winning strategies for the CHSH and other nonlocal games. The agents achieve these results directly through interaction, without prior access to known optimal solutions. This demonstrates the potential of quantum intelligence as a tool for algorithmic discovery, opening the way for the automated design of novel quantum algorithms and protocols.

The aim of this paper is to introduce a quantum fusion mechanism for multimodal learning and to establish its theoretical and empirical potential. The proposed method, called the Quantum Fusion Layer (QFL), replaces classical fusion schemes with a hybrid quantum-classical procedure that uses parameterized quantum circuits to learn entangled feature interactions without requiring exponential parameter growth. Supported by quantum signal processing principles, the quantum component efficiently represents high-order polynomial interactions across modalities with linear parameter scaling, and we provide a separation example between QFL and low-rank tensor-based methods that highlights potential quantum query advantages. In simulation, QFL consistently outperforms strong classical baselines on small but diverse multimodal tasks, with particularly marked improvements in high-modality regimes. These results suggest that QFL offers a fundamentally new and scalable approach to multimodal fusion that merits deeper exploration on larger systems.

The increasingly challenging task of maintaining power grid security requires innovative solutions. Novel approaches using reinforcement learning (RL) agents have been proposed to help grid operators navigate the massive decision space and nonlinear behavior of these complex networks. However, applying RL to power grid security assessment, specifically for combinatorially troublesome contingency analysis problems, has proven difficult to scale. The integration of quantum computing into these RL frameworks helps scale by improving computational efficiency and boosting agent proficiency by leveraging quantum advantages in action exploration and model-based interdependence. To demonstrate a proof-of-concept use of quantum computing for RL agent training and simulation, we propose a hybrid agent that runs on quantum hardware using IBM's Qiskit Runtime. We also provide detailed insight into the construction of parameterized quantum circuits (PQCs) for generating relevant quantum output. This agent's proficiency at maintaining grid stability is demonstrated relative to a benchmark model without quantum enhancement using N-k contingency analysis. Additionally, we offer a comparative assessment of the training procedures for RL models integrated with a quantum backend.

Transformer models have revolutionized sequential learning across various domains, yet their self-attention mechanism incurs quadratic computational cost, posing limitations for real-time and resource-constrained tasks. To address this, we propose Quantum Adaptive Self-Attention (QASA), a novel hybrid architecture that enhances classical Transformer models with a quantum attention mechanism. QASA replaces dot-product attention with a parameterized quantum circuit (PQC) that adaptively captures inter-token relationships in the quantum Hilbert space. Additionally, a residual quantum projection module is introduced before the feedforward network to further refine temporal features. Our design retains classical efficiency in earlier layers while injecting quantum expressiveness in the final encoder block, ensuring compatibility with current NISQ hardware. Experiments on synthetic time-series tasks demonstrate that QASA achieves faster convergence and superior generalization compared to both standard Transformers and reduced classical variants. Preliminary complexity analysis suggests potential quantum advantages in gradient computation, opening new avenues for efficient quantum deep learning models.

Understanding the power of parameterized quantum circuits (PQCs) in accomplishing machine learning tasks is one of the most important questions in quantum machine learning. In this paper, we focus on the PQC expressivity for general multivariate function classes. Previously established Universal Approximation Theorems for PQCs are either nonconstructive or assisted with parameterized classical data processing, making it hard to justify whether the expressive power comes from the classical or quantum parts. We explicitly construct data re-uploading PQCs for approximating multivariate polynomials and smooth functions and establish the first non-asymptotic approximation error bounds for such functions in terms of the number of qubits, the quantum circuit depth and the number of trainable parameters of the PQCs. Notably, we show that for multivariate polynomials and multivariate smooth functions, the quantum circuit size and the number of trainable parameters of our proposed PQCs can be smaller than the deep ReLU neural networks.

Variational quantum algorithms have been acknowledged as the leading strategy to realize near-term quantum advantages in meaningful tasks, including machine learning and optimization. When applied to tasks involving classical data, such algorithms generally begin with data encoding circuits and train quantum neural networks (QNNs) to minimize target functions. Although QNNs have been widely studied to improve these algorithms' performance on practical tasks, there is a gap in systematically understanding the influence of data encoding on the eventual performance. In this paper, we make progress in filling this gap by considering the common data encoding strategies based on parameterized quantum circuits. We prove that, under reasonable assumptions, the distance between the average encoded state and the maximally mixed state could be explicitly upper-bounded with respect to the width and depth of the encoding circuit.

Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function. Although there have been comprehensive studies to improve the performance of the PQCs on practical tasks, the errors caused by the quantum noise downgrade the performance when running on real quantum computers. In particular, when the quantum state is transformed through multiple quantum circuit layers, the effect of the quantum noise happens cumulatively and becomes closer to the maximally mixed state or complete noise. This paper studies the relationship between the quantum noise and the diffusion model. Then, we propose a novel diffusion-inspired learning approach to mitigate the quantum noise in the PQCs and reduce the error for specific tasks. Through our experiments, we illustrate the efficiency of the learning strategy and achieve state-of-the-art performance on classification tasks in the quantum noise scenarios.