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.

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

In conclusion, our message is a somewhat sobering one: we conjecture that quantum machine learning models can offer speed-ups only if we manage to encode knowledge about the problem at hand into quantum circuits, while encoding the same bias into a classical model would be hard.

In conclusion, our message is a somewhat sobering one: we conjecture that quantum machine learning models can offer speed-ups only if we manage to encode knowledge about the problem at hand into quantum circuits, while encoding the same bias into a classical model would be hard.

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.