FH Aachen

Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over 6 × fewer parameters, and for VQE on H_2 we achieve UCCSD-like accuracy at substantially reduced circuit complexity.

We consider an inverse shape problem for recovering an unknown simply supported obstacle in two dimensions from near–field point–source measurements for the biharmonic Helmholtz equation. The measured data consist of the scattered field and its Laplacian on a closed measurement curve surrounding the obstacle. By exploiting an operator splitting of the biharmonic operator, we decouple the scattered field into propagating and evanescent components. This decoupling allows us to reformulate the measured data in terms of an acoustic near–field operator for a sound–soft scatterer. Since the acoustic near–field operator does not directly admit the symmetric factorization required by the factorization method, we introduce a far–field transformation (defined independently of the obstacle) that augments the near–field operator into a far–field operator with a symmetric factorization. This yields a rigorous factorization method characterization of the obstacle and leads to a practical reconstruction algorithm based on spectral data of the transformed operator. Finally, we present numerical experiments with synthetic data that demonstrate stable reconstructions under noise and illustrate the role of regularization, including a variant that uses only the scattered field data.

In this study, we present an investigation of the recently identified aminoacylase MsAA for the synthesis of N-acyl-L-amino acids, focusing on N-lauroyl-L-methionine. We found optimal reaction conditions at pH 8.0 and a temperature of 40-45°C with substrate concentrations of 400 mM methionine and 150 mM lauric acid. The highest product concentration of 100 mM was achieved with 67% substrate conversion after 72 h reaction at 40°C and pH 8.0. The reaction could be upscaled with a nearly identical reaction course. Several other fatty acids were also found to be substrates of this enzyme. Besides methionine, only hydrophobic amino acids were accepted for acylation. For a detailed analysis of the catalytic reaction mechanism of MsAA, we performed in silico protein modeling studies. Molecular docking of lauric acid and methionine to the predicted MsAA structure resulted in a similar mode of substrate binding as described for the related N-succinyl-L,L-diaminopimelic acid desuccinylase from Haemophilus influenzae. Differences in amino acid sequence of structurally conserved substrate-binding residues explain the distinct substrate scope of the enzymes. The structure-function relationship of relevant amino acid residues was validated by a mutagenesis study.

Surface-imprinted polymer (SIP)-based biomimetic sensors are promising for direct whole-bacteria detection; however, the commonly used fabrication approach (micro-contact imprinting) often suffers from limited imprint density, heterogeneous template distribution, and poor reproducibility. Here, we introduce a photolithography-defined master stamp featuring E. coli mimics, enabling high-density, well-oriented cavity arrays (3 × 107 imprints/cm2). Crucially, the cavity arrangement is engineered such that the SIP layer functions simultaneously as the bioreceptor and as a diffraction grating, enabling label-free optical quantification by reflectance changes without additional transduction layers. Finite-difference time-domain (FDTD) simulations are used to model and visualize the optical response upon bacterial binding. Proof-of-concept experiments using a differential two-well configuration confirm concentration-dependent detection of E. coli in PBS, demonstrating a sensitive, low-cost, and scalable sensing concept that can be readily extended to other bacterial targets by redesigning the photolithographic master.