World models for partially observed environments must imagine multiple compatible hidden futures and steer between them under counterfactual actions. Joint Embedding Predictive Architectures (JEPAs) do this in latent space, but a vector-valued latent has no internal structure for carrying the belief over hidden continuations through blind rollout. We introduce the Unitary World Model JEPA (UWM-JEPA), a JEPA world model with a density-matrix latent on a joint system-environment space and a learned unitary predictor. The construction preserves the joint-state spectrum exactly during rollout, so the predictor itself cannot dissipate the represented uncertainty. On a hidden-velocity indicator task requiring five-step forward simulation under a given action sequence with the target observation masked, UWM-JEPA reaches 0.77 accuracy and degrades monotonically as actions are perturbed; a parameter-matched LSTM-JEPA trained under the same counterfactual-target objective and action head collapses to majority-class accuracy (0.53) under every action condition. Under blind rollout, UWM-JEPA loses fewer than ten points of probe R^2 at short horizons while vector-latent baselines lose forty-one and sixty-eight; both nevertheless tie on a held-out context probe, locating the separation in the predictor rather than the encoder. Action sensitivity itself requires training against counterfactual rather than teacher-forced targets, a finding that applies beyond the unitary parameterisation. For JEPA world models to imagine under partial observability, latent geometry and predictor dynamics matter, not frozen context-encoding capacity alone.

Measurement-induced entanglement (MIE) captures how local measurements generate long-range quantum correlations and drive dynamical phase transitions in many-body systems. Yet estimating MIE experimentally remains challenging: direct evaluation requires extensive post-selection over measurement outcomes, raising the question of whether MIE is accessible with only polynomial resources. We address this challenge by reframing MIE detection as a data-driven learning problem that assumes no prior knowledge of state preparation. Using measurement records alone, we train a neural network in a self-supervised manner to predict the uncertainty metric for MIE--the gap between upper and lower bounds of the average post-measurement bipartite entanglement. Applied to random circuits with one-dimensional all-to-all connectivity and two-dimensional nearest-neighbor coupling, our method reveals a learnability transition with increasing circuit depth: below a threshold, the uncertainty is small and decreases with polynomial measurement data and model parameters, while above it the uncertainty remains large despite increasing resources. We further verify this transition experimentally on current noisy quantum devices, demonstrating its robustness to realistic noise. These results highlight the power of data-driven approaches for learning MIE and delineate the practical limits of its classical learnability.

In this paper, we present a framework for modeling quantum recurrent neural networks (RNNs) and their enhanced version, long short-term memory (LSTM) networks using the core ideas presented by Linden et al. (2009), where the entangling and disentangling power of unitary transformations is investigated. In particular, we interpret entangling and disentangling power as information retention and forgetting mechanisms in LSTMs. Thus, entanglement emerges as a key component of the optimization (training) process. We believe that, by leveraging prior knowledge of the entangling power of unitaries, the proposed quantum-classical framework can guide the design of better-parameterized quantum circuits for various real-world applications.

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces.

Machine learning models are used for pattern recognition analysis of big data, without direct human intervention. The task of unsupervised learning is to find the probability distribution that would best describe the available data, and then use it to make predictions for observables of interest. Classical models generally fit the data to Boltzmann distribution of Hamiltonians with a large number of tunable parameters. Quantum extensions of these models replace classical probability distributions with quantum density matrices. An advantage can be obtained only when features of density matrices that are absent in classical probability distributions are exploited. Such situations depend on the input data as well as the targeted observables. Explicit examples are discussed that bring out the constraints limiting possible quantum advantage. The problem-dependent extent of quantum advantage has implications for both data analysis and sensing applications.

Functional connectivity has been widely investigated to understand brain disease in clinical studies and imaging-based neuroscience, and analyzing changes in functional connectivity has proven to be valuable for understanding and computationally evaluating the effects on brain function caused by diseases or experimental stimuli. By using Mahalanobis data whitening prior to the use of dimensionality reduction algorithms, we are able to distill meaningful information from fMRI signals about subjects and the experimental stimuli used to prompt them. Furthermore, we offer an interpretation of Mahalanobis whitening as a two-stage de-individualization of data which is motivated by similarity as captured by the Bures distance, which is connected to quantum mechanics. These methods have potential to aid discoveries about the mechanisms that link brain function with cognition and behavior and may improve the accuracy and consistency of Alzheimer's diagnosis, especially in the preclinical stage of disease progression.

Recently, sophisticated deep learning-based approaches have been developed for generating efficient initial guesses to accelerate the convergence of density functional theory (DFT) calculations. While the actual initial guesses are often density matrices (DM), quantities that can convert into density matrices also qualify as alternative forms of initial guesses. Hence, existing works mostly rely on the prediction of the Hamiltonian matrix for obtaining high-quality initial guesses. However, the Hamiltonian matrix is both numerically difficult to predict and intrinsically non-transferable, hindering the application of such models in real scenarios. In light of this, we propose a method that constructs DFT initial guesses by predicting the electron density in a compact auxiliary basis representation using E(3)-equivariant neural networks. Trained on small molecules with up to 20 atoms, our model is able to achieve an average 33.3% self-consistent field (SCF) step reduction on systems up to 60 atoms, substantially outperforming Hamiltonian-centric and DM-centric models. Critically, this acceleration remains nearly constant with increasing system sizes and exhibits strong transferring behaviors across orbital basis sets and exchange-correlation (XC) functionals. To the best of our knowledge, this work represents the first and robust candidate for a universally transferable DFT acceleration method. We are also releasing the SCFbench dataset and its accompanying code to facilitate future research in this promising direction.

Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and complex syndrome decoding, we propose a machine learning approach that directly reconstructs clean quantum states from noisy density matrices without additional qubits. We formulate quantum noise reduction as a supervised learning problem using a convolutional neural network (CNN) autoencoder architecture with a novel fidelity-aware composite loss function. Our method is trained and evaluated on a comprehensive synthetic dataset of 10,000 density matrices derived from random 5-qubit quantum circuits, encompassing five noise types (depolarizing, amplitude damping, phase damping, bit-flip, and mixed noise) across four intensity levels (0.05-0.20). The CNN successfully reconstructs quantum states across all noise conditions, achieving an average fidelity improvement from 0.298 to 0.774 (Δ = 0.476). Notably, the model demonstrates superior performance on complex mixed noise scenarios and higher noise intensities, with mixed noise showing the highest corrected fidelity (0.807) and improvement (0.567). The approach effectively preserves both diagonal elements (populations) and off-diagonal elements (quantum coherences), making it suitable for entanglement-dependent quantum algorithms. While phase damping presents fundamental information-theoretic limitations, our results suggest that CNN-based density matrix reconstruction offers a promising, resource-efficient alternative to traditional quantum error correction for NISQ-era devices. This data-driven approach could enable practical quantum advantage with fewer physical qubits than conventional error correction schemes require.

An efficient and data-driven encoding scheme is proposed to enhance the performance of variational quantum classifiers. This encoding is specially designed for complex datasets like images and seeks to help the classification task by producing input states that form well-separated clusters in the Hilbert space according to their classification labels. The encoding circuit is trained using a triplet loss function inspired by classical facial recognition algorithms, and class separability is measured via average trace distances between the encoded density matrices. Benchmark tests performed on various binary classification tasks on MNIST and MedMNIST datasets demonstrate considerable improvement over amplitude encoding with the same VQC structure while requiring a much lower circuit depth.