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We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate sub-problems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting sub-problems small enough to be solved on quantum computers currently accessible with small numbers of quits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the state-of-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.

In this paper, we report the use of rational Triangular Bezier Splines (rTBS) to numerically solve the von Karman equations, a system of fourth order PDEs. $C^{1}$ smoothness of the mesh, generated by triangular Bezier elements, enables us to directly solve the von Karman systems of equations without using mixed formulation. Numerical results of benchmark problems show high accuracy and optimal convergence rate in L1, H1 and H2 norm for quadratic and cubic triangular Bezier elements. Results of this study show that triangular isogeometric analysis can efficiently and accurately solve systems of high order PDEs. Keywords: Rational triangular Bezier splines; Isogeometric analysis; Von Karman; Optimal convergence rate; High order PDEs; Smooth mesh; Triangular elements., Comment: This manuscript is accepted for publication in the Springer INdAM volume entitled "Geometric Challenges in Isogeometric Analysis"

Adjoint optimization is an effective method in the inverse design of nanophotonic devices. In order to ensure the manufacturability, one would like to have control over the minimal feature sizes. Here we propose utilizing a level-set method based on b-spline surfaces in order to control the feature sizes. This approach is first used to design a wavelength demultiplexer. It is also used to implement a nanophotonic structure for artificial neural computing. In both cases, we show that the minimal feature sizes can be easily parameterized and controlled., Comment: 6 pages, 4 figures