Transition role of entangled data in quantum machine learning.

Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

Detecting abnormal connectivity in schizophrenia via a joint directed acyclic graph estimation model.

Functional connectivity (FC) between brain region has been widely studied and linked with cognition and behavior of an individual. FC is usually defined as the correlation or partial correlation of fMRI blood oxygen level-dependent (BOLD) signals between two brain regions. Although FC has been effective to understand brain organization, it cannot reveal the direction of interactions. Many directed acyclic graph (DAG) based methods have been applied to study the directed interactions but their performance was limited by the small sample size while high dimensionality of the available data. By enforcing group regularization and utilizing samples from both case and control groups, we propose a joint DAG model to estimate the directed FC. We first demonstrate that the proposed model is efficient and accurate through a series of simulation studies. We then apply it to the case-control study of schizophrenia (SZ) with data collected from the MIND Clinical Imaging Consortium (MCIC). We have successfully identified decreased functional integration, disrupted hub structures and characteristic edges (CtEs) in SZ patients. Those findings have been confirmed by previous studies with some identified to be potential markers for SZ patients. A comparison of the results between the directed FC and undirected FC showed substantial differences in the selected features. In addition, we used the identified features based on directed FC for the classification of SZ patients and achieved better accuracy than using undirected FC or raw features, demonstrating the advantage of using directed FC for brain network analysis.

Efficient Measure for the Expressivity of Variational Quantum Algorithms.

The superiority of variational quantum algorithms (VQAs) such as quantum neural networks (QNNs) and variational quantum eigensolvers (VQEs) heavily depends on the expressivity of the employed Ansätze. Namely, a simple Ansatz is insufficient to capture the optimal solution, while an intricate Ansatz leads to the hardness of trainability. Despite its fundamental importance, an effective strategy of measuring the expressivity of VQAs remains largely unknown. Here, we exploit an advanced tool in statistical learning theory, i.e., covering number, to study the expressivity of VQAs. Particularly, we first exhibit how the expressivity of VQAs with an arbitrary Ansätze is upper bounded by the number of quantum gates and the measurement observable. We next explore the expressivity of VQAs on near-term quantum chips, where the system noise is considered. We observe an exponential decay of the expressivity with increasing circuit depth. We also utilize the achieved expressivity to analyze the generalization of QNNs and the accuracy of VQE. We numerically verify our theory employing VQAs with different levels of expressivity. Our Letter opens the avenue for quantitative understanding of the expressivity of VQAs.