Fidelity Between Unitary Operators and the Generation of Gates Robust Against Off-Resonance Perturbations

We perform a functional expansion of the fidelity between two unitary matrices in order to find the necessary conditions for the robust implementation of a target gate. Comparison of these conditions with those obtained from the Magnus expansion and Dyson series shows that they are equivalent in first order. By exploiting techniques from robust design optimization, we account for issues of experimental feasibility by introducing an additional criterion to the search for control pulses. This search is accomplished by exploring the competition between the multiple objectives in the implementation of the NOT gate by means of evolutionary multi-objective optimization

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Evidence Transfer for Improving Clustering Tasks Using External Categorical Evidence

In this paper we introduce evidence transfer for clustering, a deep learning method that can incrementally manipulate the latent representations of an autoencoder, according to external categorical evidence, in order to improve a clustering outcome. By evidence transfer we define the process by which the categorical outcome of an external, auxiliary task is exploited to improve a primary task, in this case representation learning for clustering. Our proposed method makes no assumptions regarding the categorical evidence presented, nor the structure of the latent space. We compare our method, against the baseline solution by performing k-means clustering before and after its deployment. Experiments with three different kinds of evidence show that our method effectively manipulates the latent representations when introduced with real corresponding evidence, while remaining robust when presented with low quality evidence

Solution Repair/Recovery in Uncertain Optimization Environment

Operation management problems (such as Production Planning and Scheduling) are represented and formulated as optimization models. The resolution of such optimization models leads to solutions which have to be operated in an organization. However, the conditions under which the optimal solution is obtained rarely correspond exactly to the conditions under which the solution will be operated in the organization.Therefore, in most practical contexts, the computed optimal solution is not anymore optimal under the conditions in which it is operated. Indeed, it can be "far from optimal" or even not feasible. For different reasons, we hadn't the possibility to completely re-optimize the existing solution or plan. As a consequence, it is necessary to look for "repair solutions", i.e., solutions that have a good behavior with respect to possible scenarios, or with respect to uncertainty of the parameters of the model. To tackle the problem, the computed solution should be such that it is possible to "repair" it through a local re-optimization guided by the user or through a limited change aiming at minimizing the impact of taking into consideration the scenarios

A Practical Guide to Robust Optimization

Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. It is therefore remarkable that real-life applications of robust optimization are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to understand robust optimization and to successfully apply it in practice. We provide a brief introduction to robust optimization, and also describe important do's and don'ts for using it in practice. We use many small examples to illustrate our discussions