#### Route planning of truck fleets in supply chain management (TSP / SPP)

In this demonstrator we show how a vehicle routing problem (VRP) can be solved on the quantum computer. A VRP is a generalized Traveling Salesperson Problem (TSP) in which a round trip has to be divided among several agents (trucks). The Jupyter Notebook first explains how a VRP can be understood as a so-called Quadratic Unbounded Binary Optimization (QUBO) problem and then how it can be coded for the quantum computer. Examples are used to illustrate how many qubits are required to solve each problem. Finally, it is possible to interactively execute the QAOA algorithm (as a simulation) for a single example and to change optimization parameters and the circuit depth. In the second phase of the project, we systematically investigated the DWave hardware in terms of TSP to achieve better performance. We looked at the asymmetric and symmetric distribution of the cities to see if symmetry helps in finding the correct solution and found that this is indeed the case. We will carry out the calculations in the second project phase with the VQE algorithm instead of QAOA. This was run interactively (as a simulation) for a single example, whereby the optimization parameters and the circuit depth were changed.

#### Optimization of electric vehicle charging schedules

We focus on the execution of application scenarios on real quantum computers, in particular on the IBMQ System One in Ehningen. This allows us to demonstrate the technological status and future potential of quantum computing using a real application example. For this purpose, we provide systematic series of problem instances of different sizes and coupling strengths (i.e. of different degrees of difficulty) and show their implementation -- from the classical model to the post-processing of the quantum computing solution (end-to-end run).

In this demonstration, we present a Quantum Alternating Algorithm designed to address Mixed Integer Linear Problems (MILP). The algorithm's efficacy is showcased through the resolution of an energy use case, employing CPU and GPU quantum simulators, as well as the IBM Quantum System at Ehningen. The demonstrator comprises two parts. The first part delves into the quantum alternating algorithm, explaining the theory and implementation of Variational Quantum Eigensolver (VQE) as a pivotal component. Using a toy example, this notebook illustrates the concept and implementation scheme of the quantum alternating algorithm. The second part is devoted to applying the quantum alternating algorithm to tackle the energy use case problem. The mathematical formulation of the problem is cast in the MILP framework. This notebook not only guides users through the problem-solving process with the alternating algorithm but also demonstrates leveraging benchmarking toolkits for performance enhancement via GPU acceleration. Furthermore, we showcase experimental results, presenting and discussing outcomes obtained from the execution of the algorithm on the IBM Quantum System at Ehningen.

#### Optimization of Charging Schedules for Electric Cars (EMP)

In this demonstrator, we use four Notebooks to show how to solve an energy use case on a quantum computer. In the first notebook, we introduce the use case, show how it can be formulated as a mathematical optimization problem and derive a Python implementation. In the second notebook, we explain both the theory of the quantum algorithm QAOA and its implementation in Qiskit using the energy use case. In the third notebook, we implement a transpilation pipeline with which QAOA circuits can be executed on real IBM quantum computers. We also explain how the results of a quantum computer can be processed with a big data library. In the last notebook, we present and discuss a series of experiments performed on the IBM Quantum System in Ehningen ("ibmq_ehningen").

#### Disclaimer

The interactive demonstrator notebooks have been licensed under the Apache licence (version 2.0). The files may only be used in accordance with the licence. A copy of the licence can be downloaded from http://www.apache.org/licenses/LICENSE-2.0 Except as required by applicable law or agreed to in writing, software distributed under this licence is distributed on an "AS IS" basis, without warranties or conditions of any kind, either express or implied. See the licence for the specific rights and restrictions associated with it.

This is a research prototype. Liability for loss of profit, loss of production, business interruption, loss of use, loss of data and information, financing costs and other financial and consequential damage is excluded, except in cases of gross negligence, intent and personal injury.