A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

We present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs multiple numerical optimal control cycles to update the gate duration based on the resulting energy norm of the optimized pulses. We provide multiple numerical examples that each demonstrate fast convergence towards a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound

Simultaneous single-step one-shot optimization with unsteady PDEs

The single-step one-shot method has proven to be very efficient for PDE-constrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is non-trivial. In this paper, we provide a framework that makes the single-step one-shot method applicable for unsteady PDEs that are solved by classical time-marching schemes. The one-shot method is applied to an optimal control problem with unsteady incompressible Navier-Stokes equations that are solved by an industry standard simulation code. With the Van-der-Pol oscillator as a generic model problem, the modified simulation scheme is further improved using adaptive time scales. Finally, numerical results for the advection-diffusion equation are presented. Keywords: Simultaneous optimization; One-shot method; PDE-constrained optimization; Unsteady PDE; Adaptive time scal

Artificial neural network surrogate modeling for uncertainty quantification and structural optimization of reinforced concrete structures

Optimization approaches are important to design sustainable structures. In structural mechanics, different design objectives can be defined, for example, to minimize the required construction material or to maximize the structural durability. In this paper, the durability of a reinforced concrete (RC) structure is assessed by advanced finite element (FE) models to simulate the cracking behavior and the chloride transport process. The corrosion initiation time is used as durability measure to be maximized within an optimization approach, where the concrete cover is defined as design variable. The variability of structural loads and material parameters and unavoidable construction imprecision leads to a probabilistic reliability and durability assessment, where aleatory as well as epistemic uncertainties are quantified by random variables, intervals and probability-boxes. The FE simulation models cannot directly be applied to structural analyses and optimizations with polymorphic uncertain parameters and design variables because of the high computational demand of the multi-loop algorithm (Monte Carlo simulation, interval analysis, global optimization). In this paper, a new surrogate modeling strategy is presented, where artificial neural networks are trained sequentially to speed-up the coupled mechanical and transport simulation FE models. The new approach is applied to the uncertainty quantification and the structural durability optimization of a RC structure