Quantum Information-Assisted Complete Active Space Optimization (QICAS)

Automated active space selection is arguably one of the most challenging and essential aspects of multiconfigurational methods. In this work we propose an effective quantum information-assisted complete active space optimization (QICAS) scheme. What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner, and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features QICAS yields for smaller correlated molecules sets of optimized orbitals with respect to which the CASCI energy reaches the corresponding CASSCF energy within chemical accuracy. For more challenging systems such as the Chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal non-active spaces are predominantly those that contain the least entanglement

symQV: Automated Symbolic Verification of Quantum Programs

We present symQV, a symbolic execution framework for writing and verifying quantum computations in the quantum circuit model. symQV can automatically verify that a quantum program complies with a first-order specification. We formally introduce a symbolic quantum program model. This allows to encode the verification problem in an SMT formula, which can then be checked with a delta-complete decision procedure. We also propose an abstraction technique to speed up the verification process. Experimental results show that the abstraction improves symQV's scalability by an order of magnitude to quantum programs with 24 qubits (a 2^24-dimensional state space).Comment: This is the extended version of a paper with the same title that appeared at FM 2023. Tool available at doi.org/10.5281/zenodo.740032

Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.Comment: 32 pages, 3 figure

On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters

Recently, a stability theory has been developed to study the linear stability of modified Patankar--Runge--Kutta (MPRK) schemes. This stability theory provides sufficient conditions for a fixed point of an MPRK scheme to be stable as well as for the convergence of an MPRK scheme towards the steady state of the corresponding initial value problem, whereas the main assumption is that the initial value is sufficiently close to the steady state. Initially, numerical experiments in several publications indicated that these linear stability properties are not only local, but even global, as is the case for general linear methods. Recently, however, it was discovered that the linear stability of the MPDeC(8) scheme is indeed only local in nature. Our conjecture is that this is a result of negative Runge--Kutta (RK) parameters of MPDeC(8) and that linear stability is indeed global, if the RK parameters are nonnegative. To support this conjecture, we examine the family of MPRK22($\alpha$) methods with negative RK parameters and show that even among these methods there are methods for which the stability properties are only local. However, this local linear stability is not observed for MPRK22($\alpha$) schemes with nonnegative Runge-Kutta parameters.Comment: 19 pages, 3 figure

SpecAttack: Specification-Based Adversarial Training for Deep Neural Networks

Safety specification-based adversarial training aims to generate examples violating a formal safety specification and therefore provides approaches for repair. The need for maintaining high prediction accuracy while ensuring the save behavior remains challenging. Thus we present SpecAttack, a query-efficient counter-example generation and repair method for deep neural networks. Using SpecAttack allows specifying safety constraints on the model to find inputs that violate these constraints. These violations are then used to repair the neural network via re-training such that it becomes provably safe. We evaluate SpecAttack's performance on the task of counter-example generation and repair. Our experimental evaluation demonstrates that SpecAttack is in most cases more query-efficient than comparable attacks, yields counter-examples of higher quality, with its repair technique being more efficient, maintaining higher functional correctness, and provably guaranteeing safety specification compliance

Self-Supervised Learning for Annotation Efficient Biomedical Image Segmentation

The scarcity of high-quality annotated data is omnipresent in machine learning. Especially in biomedical segmentation applications, experts need to spend a lot of their time into annotating due to the complexity. Hence, methods to reduce such efforts are desired. Self-Supervised Learning (SSL) is an emerging field that increases performance when unannotated data is present. However, profound studies regarding segmentation tasks and small datasets are still absent. A comprehensive qualitative and quantitative evaluation is conducted, examining SSL's applicability with a focus on biomedical imaging. We consider various metrics and introduce multiple novel application-specific measures. All metrics and state-of-the-art methods are provided in a directly applicable software package. We show that SSL can lead to performance improvements of up to 10%, which is especially notable for methods designed for segmentation tasks. SSL is a sensible approach to data-efficient learning, especially for biomedical applications, where generating annotations requires much effort. Additionally, our extensive evaluation pipeline is vital since there are significant differences between the various approaches. We provide biomedical practitioners with an overview of innovative data-efficient solutions and a novel toolbox for their own application of new approaches. Our pipeline for analyzing SSL methods is provided as a ready-to-use software package

Lingunite-a high-pressure plagioclase polymorph at mineral interfaces in doleritic rock of the Lockne impact structure (Sweden)

Lingunite nanocrystals and amorphous plagioclase (maskelynite) are identified at the contacts between augite and labradorite wedge-shaped interfaces in the doleritic rocks of the Lockne impact structure in Sweden. The occurrence of lingunite suggests that the local pressure was above 19 GPa and the local temperature overwhelmed 1000 °C. These values are up to 10 times higher than previous values estimated numerically for bulk pressure and temperature. High shock-induced temperatures are manifested by maskelynite injections into microfractures in augite located next to the wedges. We discuss a possible model of shock heterogeneity at mineral interfaces, which may lead to longer duration of the same shock pressure and a concentration of high temperature thus triggering the kinetics of labradorite transformation into lingunite and maskelynite