Long short-term memory (LSTM) models are a particular type of recurrent neural networks (RNNs) that are central to sequential modeling tasks in domains such as urban telecommunication forecasting, where temporal correlations and nonlinear dependencies dominate. However, conventional LSTMs suffer from high parameter redundancy and limited nonlinear expressivity. In this work, we propose the Quantum-inspired Kolmogorov-Arnold Long Short-Term Memory (QKAN-LSTM), which integrates Data Re-Uploading Activation (DARUAN) modules into the gating structure of LSTMs. Each DARUAN acts as a quantum variational activation function (QVAF), enhancing frequency adaptability and enabling an exponentially enriched spectral representation without multi-qubit entanglement. The resulting architecture preserves quantum-level expressivity while remaining fully executable on classical hardware. Empirical evaluations on three datasets, Damped Simple Harmonic Motion, Bessel Function, and Urban Telecommunication, demonstrate that QKAN-LSTM achieves superior predictive accuracy and generalization with a 79
Super-resolution (SR) seeks to reconstruct high-resolution (HR) data from low-resolution (LR) observations. Classical deep learning methods have advanced SR substantially, but require increasingly deeper networks, large datasets, and heavy computation to capture fine-grained correlations. In this work, we present the first study to investigate quantum circuits for SR. We propose a framework based on Variational Quantum Circuits (VQCs) with Adaptive Non-Local Observable (ANO) measurements. Unlike conventional VQCs with fixed Pauli readouts, ANO introduces trainable multi-qubit Hermitian observables, allowing the measurement process to adapt during training. This design leverages the high-dimensional Hilbert space of quantum systems and the representational structure provided by entanglement and superposition. Experiments demonstrate that ANO-VQCs achieve up to five-fold higher resolution with a relatively small model size, suggesting a promising new direction at the intersection of quantum machine learning and super-resolution.
Quantum Fast Weight Programming replaces explicit recurrence with a slow-to-fast programming mechanism that updates a shallow variational circuit at each time step. We study Quantum Fast Weight Programming applied to real-world physical time series in different forecasting regimes, emphasizing parameter-parity and transparent resource accounting. The model uses hardware-efficient, data re-uploading ansatzes and local observables, shifting temporal information into a tractable trajectory of circuit parameters. Under matched budgets, Quantum Fast Weight Programming attains competitive accuracy against quantum recurrent baselines and strong classical deep learning comparators, while substantially reducing the quantum gradient-evaluation burden associated with backpropagation through time. We managed to identify stable, NISQ-friendly configurations and clarify expressivity-trainability trade-offs. Obtained results position the proposed approach as a practical template for resource-aware sequential modeling in time series prediction and related signal processing domains.
The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for solving combinatorial optimization problems on near-term quantum processors. However, finding good variational parameters remains a significant challenge due to the non-convex energy landscape, often resulting in slow convergence and poor solution quality. In this work, we propose a quantum meta-learning framework that trains advanced quantum sequence models to generate effective parameter initialization policies. We investigate four classical or quantum sequence models, including the Quantum Kernel-based Long Short-Term Memory (QK-LSTM), as learned optimizers in a "learning to learn" paradigm. Our numerical experiments on the Max-Cut problem demonstrate that the QK-LSTM optimizer achieves superior performance, obtaining the highest approximation ratios and exhibiting the fastest convergence rate across all tested problem sizes (n=10 to 13). Crucially, the QK-LSTM model achieves perfect parameter transferability by synthesizing a single, fixed set of near-optimal parameters, leading to a remarkable sustained acceleration of convergence even when generalizing to larger problems. This capability, enabled by the compact and expressive power of the quantum kernel architecture, underscores its effectiveness. The QK-LSTM, with only 43 trainable parameters, substantially outperforms the classical LSTM (56 parameters) and other quantum sequence models, establishing a robust pathway toward highly efficient parameter initialization for variational quantum algorithms in the NISQ era.
Adaptive Non-local Observables (ANOs) have shown that making quantum observables dynamic can substantially enlarge the function space of Variational Quantum Algorithms, partly shifting hardware demands from circuit synthesis to measurement design. However, this advantage is accompanied by a steep increase in the number of parameters, as well as the classical optimization cost for varying general Hermitian observables. We propose a special form of ANO that significantly reduces this burden by considering only diagonal observables paired with quantum circuits. Mathematically, this is equivalent to the full ANO of a large parameter space since diagonal matrices are canonical representatives of the ANO space modulo unitary similarity. As a result, Diagonal ANO retains the same capability of full ANO while reducing k-local observable complexity from O(4^k) to O(2^k) and lowering the corresponding measurement-side classical computation. In this sense, diagonal ANO preserves much of the benefit of full ANO while encompassing conventional VQCs as a special case.
