Wei-Bin Ewe

This paper introduces a quantum-enhanced finite element method (FEM) designed for noisy intermediate-scale quantum (NISQ) devices, leveraging variational quantum algorithms (VQAs) to solve engineering partial differential equations. We demonstrate the framework by solving the Euler–Bernoulli beam and the NAFEMS T4 heat transfer problems, which involve Dirichlet, Neumann, and Robin boundary conditions. A key innovation is a ‘set-to-zero’ strategy that incorporates boundary conditions through a correction matrix, K bc , allowing for flexible imposition at any node without domain decomposition. The global stiffness matrix is decomposed into a constant number of Pauli terms, O (1), using the method by Sato et al while boundary terms are handled with a sublinearly scaling partial Pauli measurement technique. The algorithm achieves logarithmic qubit scaling ( n = ⌈ log 2 ⁡ N ⌉ qubits for N degrees of freedom(DOF)) and employs shallow, hardware-efficient circuits with empirically trainable depth for small-scale systems. Validation on the Qiskit statevector simulator shows high accuracy. For the Euler–Bernoulli beam problem with 4 to 64 DOF, the algorithm achieves relative errors of 0.5%–1.5% and fidelities of 0.998–0.999. For the NAFEMS T4 heat transfer benchmark, a 5.4% relative error is observed. The VQA converges robustly within 77–350 iterations, though barren plateaus are a known challenge for scaling to larger systems. This work establishes a scalable framework for quantum FEM, offering a significant memory advantage over classical methods and advancing the potential for quantum-enhanced engineering simulations.

Advancements in ultrasonic imaging sensors (UISs), such as improvements in cost-effectiveness, low power consumption, and suitability for challenging environments, have been useful for drone navigation. However, existing microelectromechanical systems (MEMS) transducer arrays suffer from limitations due to the non-uniform stress distribution of the thin-film layers, which changes the resonant frequency of devices. To address this, a novel sector slitted transducer design was proposed, which enhances the acoustic pressure output while maintaining mechanical stability and reduces the sensitivity of the resonant frequency to residual stresses. In this study, finite element analysis was used to model the slitted transducer design, which demonstrated minimal variation in resonant frequencies under different stress conditions. The MEMS transducer array simulations have displayed effective beam-steering capabilities using different phase profiles and validation of performance metrics through the Fresnel and Fraunhofer diffraction propagations. Both the imaging resolution and signal-to-noise ratio (SNR) of the array were evaluated over various distances. The figures-of-merit (FoM) of the sector-slitted design indicate that the transducer array is 1.6 to 30 times smaller than existing designs while being able to generate 26 to 965 times greater acoustic pressure than the other designs reported in the literature. Thus, the array promises enhanced performance in 3D range-finding and imaging applications for drones and mobile devices, offering compactness and efficiency. Future applications could leverage these advancements to improve autonomous navigation and environmental sensing in complex scenarios.

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering applications, such as the subdiffusion equation, the nonlinear Burgers' equation, and a coupled diffusive epidemic model. We assess quantum hardware performance under realistic noise conditions, further validating the practical utility of our algorithm.

This paper presents a new conductive carbon fiber reinforced polymer (CFRP) aircraft composite and its electromagnetic characterization for tackling the lightning direct effect and enhancing the electromagnetic shielding effectiveness (SE). The CFRP composite design is deliberated for ameliorating the electrical conductivity of composite. With the aid of equivalent medium modeling, the inherent electromagnetic properties of the composite have been investigated. The simulated results illustrate that the lightning strike protection (LSP) capability and the electromagnetic shielding behavior of the newly developed aircraft composite have been improved as compared to the original neat CFRP composite, and comparable to that with copper mesh as a protective layer on top. Moreover, an artificial lightning experiment has been carried out in accordance with SAE ARP5416 by mimicking the natural lightning strike attachment. The shielding effectiveness of the proposed composite prototype has also been measured by using electromagnetic waveguide transmission line method. The physical experiments have effectively validated the simulation results and demonstrated the feasibility of the proposed conductive CFRP composite on LSP and SE.

We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions compared to those with partial or linear entangling layers. To efficiently encode impulse functions, we propose a graphical mapping technique for quantum states that often requires only a single bit-flip of a parametric gate. As a proof of concept, we simulate colloidal deposition on a planar wall by solving the Smoluchowski equation including the Derjaguin-Landau-Verwey-Overbeek (DLVO) potential energy. We find that over-parameterization is necessary to satisfy certain boundary conditions and that higher-order time-stepping can effectively reduce norm errors. Together, our work highlights the potential of variational quantum simulation for solving partial differential equations using near-term quantum devices.

Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through implicit time-stepping of the Laplacian operator. The use of encoded source states informed by preceding solution vectors results in faster convergence compared to random re-initialization. Through statevector simulations of the heat equation, we demonstrate how the time complexity of our algorithm scales with the Ansatz volume for gradient estimation and how the time-to-solution scales with the diffusion parameter. Our proposed algorithm extends economically to higher-order time-stepping schemes, such as the Crank–Nicolson method. We present a semi-implicit scheme for solving systems of evolution equations with non-linear terms, such as the reaction–diffusion and the incompressible Navier–Stokes equations, and demonstrate its validity by proof-of-concept results.

Variational quantum algorithms (VQAs) are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a VQA in conjunction with the finite difference method for the calculation of propagation modes of an electromagnetic wave in a hollow metallic waveguide. The two-dimensional (2-D) waveguide problem, described by the Helmholtz equation, is approximated by a system of linear equations, whose solutions are expressed in terms of simple quantum expectation values that can be evaluated efficiently on quantum hardware. Numerical examples are presented to validate the proposed method for solving 2-D waveguide problems.

Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a variational quantum algorithm in conjunction with the finite difference method for the calculation of propagation modes of an electromagnetic wave in a hollow metallic waveguide. The two-dimensional (2D) waveguide problem, described by the Helmholtz equation, is approximated by a system of linear equations, whose solutions are expressed in terms of simple quantum expectation values that can be evaluated efficiently on quantum hardware. Numerical examples are presented to validate the proposed method for solving 2D waveguide problems.