With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question. In this paper, we manage to combine the Hamming Weight Preserving ansatz with a topological-aware parity check on physical qubits to enforce error mitigation and further hard constraints. We demonstrate the combination significantly outperforms peer VQA methods on both quantum chemistry problems and constrained combinatorial optimization problems e.g.

Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question.

To address this issue, some researchers [3,35,18]havetried toembed BCs into the ansatz.

We introduce a generalized \textit{Probabilistic Approximate Optimization Algorithm (PAOA)}, a classical variational Monte Carlo framework that extends and formalizes prior work by Weitz \textit{et al.}~\cite{Combes_2023}, enabling parameterized and fast sampling on present-day Ising machines and probabilistic computers. PAOA operates by iteratively modifying the couplings of a network of binary stochastic units, guided by cost evaluations from independent samples. We establish a direct correspondence between derivative-free updates and the gradient of the full Markov flow over the exponentially large state space, showing that PAOA admits a principled variational formulation. Simulated annealing emerges as a limiting case under constrained parameterizations, and we implement this regime on an FPGA-based probabilistic computer with on-chip annealing to solve large 3D spin-glass problems. Benchmarking PAOA against QAOA on the canonical 26-spin Sherrington-Kirkpatrick model with matched parameters reveals superior performance for PAOA. We show that PAOA naturally extends simulated annealing by optimizing multiple temperature profiles, leading to improved performance over SA on heavy-tailed problems such as SK-Lévy.

This study explores the performance of Quantum Support Vector Classifiers (QSVCs) and Quantum Neural Networks (QNNs) in comparison to classical models for machine learning tasks. By evaluating these models on the Iris and MNIST-PCA datasets, we find that quantum models tend to outperform classical approaches as the problem complexity increases. While QSVCs generally provide more consistent results, QNNs exhibit superior performance in higher-complexity tasks due to their increased quantum load. Additionally, we analyze the impact of hyperparameter tuning, showing that feature maps and ansatz configurations significantly influence model accuracy. We also compare the PennyLane and Qiskit frameworks, concluding that Qiskit provides better optimization and efficiency for our implementation. These findings highlight the potential of Quantum Machine Learning (QML) for complex classification problems and provide insights into model selection and optimization strategies

In this work, we introduce the first type of non-Euclidean neural quantum state (NQS) ansatz, in the form of the hyperbolic GRU (a variant of recurrent neural networks (RNNs)), to be used in the Variational Monte Carlo method of approximating the ground state energy for quantum many-body systems. In particular, we examine the performances of NQS ansatzes constructed from both conventional or Euclidean RNN/GRU and from hyperbolic GRU in the prototypical settings of the one- and two-dimensional transverse field Ising models (TFIM) and the one-dimensional Heisenberg $J_1J_2$ and $J_1J_2J_3$ systems. By virtue of the fact that, for all of the experiments performed in this work, hyperbolic GRU can yield performances comparable to or better than Euclidean RNNs, which have been extensively studied in these settings in the literature, our work is a proof-of-concept for the viability of hyperbolic GRU as the first type of non-Euclidean NQS ansatz for quantum many-body systems. Furthermore, in settings where the Hamiltonian displays a clear hierarchical interaction structure, such as the 1D Heisenberg $J_1J_2$ & $J_1J_2J_3$ systems with the 1st, 2nd and even 3rd nearest neighbor interactions, our results show that hyperbolic GRU definitively outperforms its Euclidean version in almost all instances. The fact that these results are reminiscent of the established ones from natural language processing where hyperbolic GRU almost always outperforms Euclidean RNNs when the training data exhibit a tree-like or hierarchical structure leads us to hypothesize that hyperbolic GRU NQS ansatz would likely outperform Euclidean RNN/GRU NQS ansatz in quantum spin systems that involve different degrees of nearest neighbor interactions. Finally, with this work, we hope to initiate future studies of other types of non-Euclidean NQS beyond hyperbolic GRU.

Classical autoencoders are widely used to learn features of input data. To improve the feature learning, classical masked autoencoders extend classical autoencoders to learn the features of the original input sample in the presence of masked-out data. While quantum autoencoders exist, there is no design and implementation of quantum masked autoencoders that can leverage the benefits of quantum computing and quantum autoencoders. In this paper, we propose quantum masked autoencoders (QMAEs) that can effectively learn missing features of a data sample within quantum states instead of classical embeddings. We showcase that our QMAE architecture can learn the masked features of an image and can reconstruct the masked input image with improved visual fidelity in MNIST images. Experimental evaluation highlights that QMAE can significantly outperform (12.86% on average) in classification accuracy compared to state-of-the-art quantum autoencoders in the presence of masks.