Abstract Adversarial noise attacks present a significant threat to quantum machine learning (QML) models, similar to their classical counterparts. This is especially true in the current Noisy Intermediate-Scale Quantum era, where noise is unavoidable. Therefore, it is essential to ensure the robustness of QML models before their deployment. To address this challenge, we introduce VeriQR, the first tool designed specifically for formally verifying and improving the robustness of QML models, to the best of our knowledge. This tool mimics real-world quantum hardware’s noisy impacts by incorporating random noise to formally validate a QML model’s robustness. VeriQR supports exact (sound and complete) algorithms for both local and global robustness verification. For enhanced efficiency, it implements an under-approximate (complete) algorithm and a tensor network-based algorithm to verify local and global robustness, respectively. As a formal verification tool, VeriQR can detect adversarial examples and utilize them for further analysis and to enhance the local robustness through adversarial training, as demonstrated by experiments on real-world quantum machine learning models. Moreover, it permits users to incorporate customized noise. Based on this feature, we assess VeriQR using various real-world examples, and experimental outcomes confirm that the addition of specific quantum noise can enhance the global robustness of QML models. These processes are made accessible through a user-friendly graphical interface provided by VeriQR, catering to general users without requiring a deep understanding of the counter-intuitive probabilistic nature of quantum computing.

Alignment-based RNA-seq quantification methods typically involve a time-consuming alignment process prior to estimating transcript abundances. In contrast, alignment-free RNA-seq quantification methods bypass this step, resulting in significant speed improvements. Existing alignment-free methods rely on the Expectation-Maximization (EM) algorithm for estimating transcript abundances. However, EM algorithms only guarantee locally optimal solutions, leaving room for further accuracy improvement by finding a globally optimal solution. In this study, we present TQSLE, the first alignment-free RNA-seq quantification method that provides a globally optimal solution for transcript abundances estimation. TQSLE adopts a two-step approach: first, it constructs a k-mer frequency matrix A for the reference transcriptome and a k-mer frequency vector b for the RNA-seq reads; then, it directly estimates transcript abundances by solving the linear equation ATAx = ATb. We evaluated the performance of TQSLE using simulated and real RNA-seq data sets and observed that, despite comparable speed to other alignment-free methods, TQSLE outperforms them in terms of accuracy. TQSLE is freely available at https://github.com/yhg926/TQSLE.

The electricity infrastructure is a critical lifeline system and of utmost importance to our daily lives. Power system resilience characterizes the ability to resist, adapt to, and timely recover from disruptions. The resilient power system is intended to cope with low probability, high risk extreme events including extreme natural disasters and man-made attacks. With an increasing awareness of such threats, the resilience of power systems has become a top priority for many countries. Facing the pressing urgency for resilience studies, the objective of this paper is to investigate the resilience of power systems. It summarizes practices taken by governments, utilities, and researchers to increase power system resilience. Based on a thorough review on the existing metrics system and evaluation methodologies, we present the concept, metrics, and a quantitative framework for power system resilience evaluation. Then, system hardening strategies and smart grid technologies as means to increase system resilience are discussed, with an emphasis on the new technologies such as topology reconfiguration, microgrids, and distribution automation; to illustrate how to increase system resilience against extreme events, we propose a load restoration framework based on smart distribution technology. The proposed method is applied on two test systems to validify its effectiveness. In the end, challenges to the power system resilience are discussed, including extreme event modeling, practical barriers, interdependence with other critical infrastructures, etc.