Reinforcement learning (RL) with limited samples is common in real-world applications. However, offline RL performance under this constraint is often suboptimal. We consider an alternative approach to dealing with limited samples by introducing the Quantum Metric Encoder (QME). In this methodology, instead of applying the RL framework directly on the original states and rewards, we embed the states into a more compact and meaningful representation, where the structure of the encoding is inspired by quantum circuits. For classical data, QME is a classically simulable, trainable unitary embedding and thus serves as a quantum-inspired module, on a classical device. For quantum data in the form of quantum states, QME can be implemented directly on quantum hardware, allowing for training without measurement or re-encoding. We evaluated QME on three datasets, each limited to 100 samples. We use Soft-Actor-Critic (SAC) and Implicit-Q-Learning (IQL), two well-known RL algorithms, to demonstrate the effectiveness of our approach. From the experimental results, we find that training offline RL agents on QME-embedded states with decoded rewards yields significantly better performance than training on the original states and rewards. On average across the three datasets, for maximum reward performance, we achieve a 116.2% improvement for SAC and 117.6% for IQL. We further investigate the $Δ$-hyperbolicity of our framework, a geometric property of the state space known to be important for the RL training efficacy. The QME-embedded states exhibit low $Δ$-hyperbolicity, suggesting that the improvement after embedding arises from the modified geometry of the state space induced by QME. Thus, the low $Δ$-hyperbolicity and the corresponding effectiveness of QME could provide valuable information for developing efficient offline RL methods under limited-sample conditions.

It should be needed to sample one million samples, achieving the required XEB. Figure 1 shows a corresponding circuit example. The sampling process using the quantum circuit is computed as follows, 1. Quantum circuits: There have been many quantum circuits proposed as follows, Sycamore quantum [3]: It consists of 53 qubits and 20 cycles. For the Boson sampling problem, it only needs 200 seconds to finish this task, while it needs 10, 000 years for classical simulation. For the Gaussian Boson Sampling problem, it can use 200 s to finish up to a million times compared with classical simulations.

Distributed quantum machine learning faces significant challenges due to heterogeneous client data and variations in local model structures, which hinder global model aggregation. To address these challenges, we propose a knowledge distillation framework for variational quantum convolutional neural networks on heterogeneous data. The framework features a quantum gate number estimation mechanism based on client data, which guides the construction of resource-adaptive VQCNN circuits. Particle swarm optimization is employed to efficiently generate personalized quantum models tailored to local data characteristics. During aggregation, a knowledge distillation strategy integrating both soft-label and hard-label supervision consolidates knowledge from heterogeneous clients using a public dataset, forming a global model while avoiding parameter exposure and privacy leakage. Theoretical analysis shows that proposed framework benefits from quantum high-dimensional representation, offering advantages over classical approaches, and minimizes communication by exchanging only model indices and test outputs. Extensive simulations on the PennyLane platform validate the effectiveness of the gate number estimation and distillation-based aggregation. Experimental results demonstrate that the aggregated global model achieves accuracy close to fully supervised centralized training. These results shown that proposed methods can effectively handle heterogeneity, reduce resource consumption, and maintain performance, highlighting its potential for scalable and privacy-preserving distributed quantum learning.

Decision-making in automated driving must consider interactions with surrounding agents to be effective. However, traditional methods often neglect or oversimplify these interactions because they are difficult to model and solve, which can lead to overly conservative behavior of the ego vehicle. To address this gap, we propose two quantum game models, QG-U1 (Quantum Game - Unitary 1) and QG-G4 (Quantum Game - Gates 4), for interaction-aware decision-making. These models extend classical game theory by incorporating principles of quantum mechanics, such as superposition, interference, and entanglement. Specifically, QG-U1 and QG-G4 are designed for two-player games with two strategies per player and can be executed in real time on a standard computer without requiring quantum hardware. We evaluate both models in merging and roundabout scenarios and compare them with classical game-theoretic methods and baseline approaches (IDM, MOBIL, and a utility-based technique). Results show that QG-G4 achieves lower collision rates and higher success rates compared to baseline methods, while both quantum models yield higher expected payoffs than classical game approaches under certain parameter settings.

Long-range time series forecasting remains challenging, as it requires capturing non-stationary and multi-scale temporal dependencies while maintaining noise robustness, efficiency, and stability. Transformer-based architectures such as Autoformer and Informer improve generalization but suffer from quadratic complexity and degraded performance on very long time horizons. State space models, notably S-Mamba, provide linear-time updates but often face unstable training dynamics, sensitivity to initialization, and limited robustness for multivariate forecasting. To address such challenges, we propose the Quantum-Optimized Selective State Space Model (Q-SSM), a hybrid quantum-optimized approach that integrates state space dynamics with a variational quantum gate. Instead of relying on expensive attention mechanisms, Q-SSM employs a simple parametrized quantum circuit (RY-RX ansatz) whose expectation values regulate memory updates adaptively. This quantum gating mechanism improves convergence stability, enhances the modeling of long-term dependencies, and provides a lightweight alternative to attention. We empirically validate Q-SSM on three widely used benchmarks, i.e., ETT, Traffic, and Exchange Rate. Results show that Q-SSM consistently improves over strong baselines (LSTM, TCN, Reformer), Transformer-based models, and S-Mamba. These findings demonstrate that variational quantum gating can address current limitations in long-range forecasting, leading to accurate and robust multivariate predictions.

Quantum computing holds the potential to solve complex problems that classical computers struggle to address. Since its inception, quantum algorithms have showcased capabilities beyond classical limits, exemplified by Shor's factoring algorithm and Grover's search algorithm--both of which can solve important computational problems provably faster than classical methods.16,20 For many years, the lack of hardware posed a barrier to implementing these algorithms, but recent advancements--including Google's 2019 demonstration of a quantum computational advantage on a programmable superconducting processor--have marked significant milestones, though their results remain the subject of ongoing debate.3 As quantum computing moves toward practical applications, programming languages and systems for quantum computers are under active development to meet growing demands. Efficient algorithms have begun to emerge in fields such as optimization, machine learning (ML), and quantum chemistry, creating a pressing need for reliable verification methods to ensure circuit correctness in these applications.19

Implicit neural representations have shown potential in various applications. However, accurately reconstructing the image or providing clear details via image super-resolution remains challenging. This paper introduces Quantum Fourier Gaussian Network (QFGN), a quantum-based machine learning model for better signal representations. The frequency spectrum is well balanced by penalizing the low-frequency components, leading to the improved expressivity of quantum circuits. The results demonstrate that with minimal parameters, QFGN outperforms the current state-of-the-art (SOT A) models. Despite noise on hardware, the model achieves accuracy comparable to that of SIREN, highlighting the potential applications of quantum machine learning in this field.

Large language model (LLM)-based tools such as ChatGPT seem useful for classical programming assignments. The more specialized the field, the more likely they lack reliability because of the lack of data to train them. In the case of quantum computing, the quality of answers of generic chatbots is low. C4Q is a chatbot focused on quantum programs that addresses this challenge through a software architecture that integrates specialized LLMs to classify requests and specialized question answering modules with a deterministic logical engine to provide trustworthy quantum computing support. This article describes the latest version (2.0) of C4Q, which delivers several enhancements: ready-to-run Qiskit code for gate definitions and circuit operations, expanded features to solve software engineering tasks such as the travelling salesperson problem and the knapsack problem, and a feedback mechanism for iterative improvement. Extensive testing of the backend confirms the system's reliability, while empirical evaluations show that C4Q 2.0's classification LLM reaches near-perfect accuracy. The evaluation of the result consists in a comparative study with three existing chatbots highlighting C4Q 2.0's maintainability and correctness, reflecting on how software architecture decisions, such as separating deterministic logic from probabilistic text generation impact the quality of the results.

This study introduces a continuous-variable quantum neural network (CV-QNN) model designed as a transfer-learning approach for forecasting problems. The proposed quantum technique features a simple structure with only eight trainable parameters, a single quantum layer with two wires to create entanglement, and ten quantum gates, hence the name QNNet10, effectively mimicking the functionality of classical neural networks. A notable aspect is that the quantum network achieves high accuracy with random initialization after a single iteration. This pretrained model is innovative as it requires no training or parameter tuning when applied to new datasets, allowing for parameter freezing while enabling the addition of a final layer for fine-tuning. Additionally, an equivalent discrete-variable quantum neural network (DV-QNN) is presented, structured similarly to the CV model. However, analysis shows that the two-wire DV model does not significantly enhance performance. As a result, a four-wire DV model is proposed, achieving comparable results but requiring a larger and more complex structure with additional gates. The pretrained model is applied to five forecasting problems of varying sizes, demonstrating its effectiveness.