Over the course of the last decade, an interest has emerged in nearest neighbor constraints for quantum circuit design. The challenge herein is to bothminimize the running time of a circuit and tomodify it such that quantum gates only act on adjacent qubits while leaving the desired computational operation intact. These modifications involve the insertion of SWAP gates, which introduces computational overhead. Several exact and heuristic methods have been developed to determine the minimal number of required SWAP gates. Until now, the model sizes of exact methods scale superexponentionally in the number of qubits of the quantum circuit. The main research goal of this project was to develop an integer linear program that instead scales polynomially both in the number of qubits and the number of quantum gates in the quantumcircuit. 7 First, qubits located on a linear array were considered. The resulting integer linear program proposed requires O(n^2 m) variables and constraints, where n denotes the number of qubits and m denotes the number of quantum gates of the quantum circuit under consideration. Second, qubits located on a two- or threedimensional grid were considered. The programs both require O(n4m) variables and O(n^3 m) constraints. Subsequently we prove that, for a fixed quantum circuit, the optimal objective value of the one-dimensional problem is an upper bound for the optimal objective value of the corresponding two- and three-dimensional problems. Using CPLEX’s Branch & Bound method, 131 benchmark instances of various circuit sizes were evaluated. The largest of which contained either eighteen qubits and sixteen quantum gates, or five qubits and 112 quantumgates. Furthermore, we identify problems on the interface of nearest neighbor compliant quantum circuit design and distributed quantum computing. Integer linear program formulations are provided for these additional problems.

Logistics service providers (LSPs) offering container transport to the hinterland of the Netherlands face the challenge of efficiently using the capacity of the barge in order to minimize cost, while part of the relevant information is still lacking at the moment decisions have to be made. The existing infrastructure and the transportation activities are studied and modeled as an online optimization problem with simultaneously vehicle routing and container-to-mode assignment. A characteristic of great importance in the problem is the uncertainty element that reflects in the requested appointment times that have to be confirmed by another agent in the network. An online optimization approach is proposed, where the input data come in sequentially and decisions have to be made in between, because new information becomes available only after the decision has been made. At each decision moment, the uncertainty element is converted to an offline optimization problem by disregarding the uncertainty or by simulating various potential future scenarios. Subsequently, the problem is modeled as a multi-commodity network design problem on a time-space graph. Four different solution methods are developed in order to solve the online optimization problem. Three confirmation based methods concern a model in which the uncertainty element is partially disregarded, by assuming that each requested appointment time will be scheduled at a specific time relative to the requested one. Alternatively, a much more complex method is developed in which various future scenarios are simulated for the requested appointment times given their probability vector. The simulation based model seeks robust solutions that are resistant to change, i.e., feasible and (sub)optimal for every potential future scenario that has been simulated. Using randomly generated (but realistic) instances, the computational results show that the proposed simulation model surpasses the simpler models both in terms of outcomes, robustness and reliability. However, the practical relevance is somewhat restricted in the sense that the model is built on several assumptions.