The activities of humans are increasingly influencing the Earth's systems. The climate is changing and the ecosystems are being affected by our actions. If we stay in the same path, the consequences could be catastrophic. For this reason, there is a growing focus on how to minimise our negative impacts on the planets and develop in a more sustainable manner. To aid in this objective, computers are a useful tool. Computational techniques can offer solutions to complex problems in sustainability, which often involve uncertainty, optimisation and decision making. However, the potential of classical computers is expected to reach a barrier, since the size of computer chips is reaching its physical limit. This requires new solutions that can provide better computational results in the future. A promising paradigm that is emerging is quantum computing, which works with quantum bits (or qubits) to make calculations and produce new solutions.

Given the potential of quantum computers, it is interesting to consider how they could help industrial ecology. Up to date, there have been no studies that focus on these two scientific disciplines together. For this reason, the first aim of this work is to identify what industrial ecology problems can benefit from quantum computing. The second aim is to provide a practical case study to illustrate how to work with quantum computers. In particular, the case study focuses on how to optimise vehicle routings in order to minimise emissions. Although routing problems have been extensively studied from the sustainability point of view, there are no such studies done on quantum computing yet. Overall, the main research question is "how can quantum computing benefit industrial ecology and how can it be applied to a relevant problem?'".

Regarding the methodology, it is separated into different parts. Firstly, a literature review is conducted to identify possible applications for industrial ecology. This is done by considering relevant industrial ecology problems and investigating if any gains can be obtained by using quantum computers. The second part of the methodology focuses on the more practical side of quantum computing. It starts by benchmarking two state-of-the-art variational quantum algorithms (Rosalin and LCB CMA-ES) to test the performance and evaluate the produced results. Following the benchmarking, a green routing problem will be encoded and optimised using the mentioned algorithms. All the coding is done in Python with the help of Cirq and Openfermion, which are two packages for quantum computing developed by Google.

After following the methodology, several results were obtained. The literature review highlighted a series of problems that can benefit from quantum computing. Examples are the optimisation of flows in an industrial park and the management of data centres to reduce energy needs. Moreover, the review illustrated different techniques to tackle these problems, such as quantum machine learning and quantum information. Secondly, as for the benchmarking, both algorithms perform well in the test cases and there is no clear advantage of one over the other. One is slightly better for some test cases and the other slightly better in the other cases. In the logistics problem, the problem is encoded into a hamiltonian that is more complex than the test cases. To minimise the expectation of the hamiltonian, the previously mentioned algorithms are tested with different quantum circuits and the results are compared. LCB CMA-ES with circuit of depth 1 gives the best results, while the other LCB CMA-ES experiments do not do as well. This is unexpected because all the LCB CMA-ES experiments are able to optimise successfully the expectation of the hamiltonian. This indicates that it is possible that the encoding of the routing problem is not optimal. Regarding the Rosalin experiments, they are not able to achieve a desirable result due to the adaptive nature of this algorithm, which does not allow a sufficient number of iterations of the optimisation process.

Concluding, although there is potential for using quantum computing in industrial ecology problems, it is clear that for the moment, classical computers produce the best results. However, quantum computing is evolving rapidly, and there may be a point where the tables are turned and quantum computers become the norm. As for now, the obtained results are far from ideal, but these could improve in the coming years.