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Quantum control aims to manipulate quantum systems toward specific quantum states or desired operations. Designing highly accurate and effective control steps is vitally important to various quantum applications, including energy minimization and circuit compilation. In this paper we focus on discrete binary quantum control problems and apply different optimization algorithms and techniques to improve computational efficiency and solution quality. Specifically, we develop a generic model and extend it in several ways. We introduce a squared $L_2$-penalty function to handle additional side constraints, to model requirements such as allowing at most one control to be active. We introduce a total variation (TV) regularizer to reduce the number of switches in the control. We modify the popular gradient ascent pulse engineering (GRAPE) algorithm, develop a new alternating direction method of multipliers (ADMM) algorithm to solve the continuous relaxation of the penalized model, and then apply rounding techniques to obtain binary control solutions. We propose a modified trust-region method to further improve the solutions. Our algorithms can obtain high-quality control results, as demonstrated by numerical studies on diverse quantum control examples. 

The outbreak of coronavirus disease 2019 (COVID-19) has led to significant challenges for schools and communities during the pandemic, requiring policy makers to ensure both safety and operational feasibility. In this paper, we develop mixed-integer programming models and simulation tools to redesign routes and bus schedules for operating a real university campus bus system during the COVID-19 pandemic. We propose a hub-and-spoke design and utilize real data of student activities to identify hub locations and bus stops to be used in the new routes. To reduce disease transmission via expiratory aerosol, we design new bus routes that are shorter than 15 minutes to travel and operate using at most 50% seat capacity and the same number of buses before the pandemic. We sample a variety of scenarios that cover variations of peak demand, social distancing requirements, and bus breakdowns to demonstrate the system resiliency of the new routes and schedules via simulation. The new bus routes were implemented and used during the academic year 2020–2021 to ensure social distancing and short travel time. Our approach can be generalized to redesign public transit systems with a social distancing requirement to reduce passengers’ infection risk. History: This paper was refereed. This article has been selected for inclusion in the Special Issue on Analytics Remedies to COVID-19. Funding: This work was supported by the National Science Foundation [Grant CMMI-2041745] and the University of Michigan, College of Engineering.