Quantum Machine Learning in a World of Uncertainty: Towards Practical Applications with Quantum Neural Networks

When computers learn to recognize, predict and generate patterns from data without explicit programming we call it machine learning (ML). Although we are starting to see the first glimpses of ML becoming an integral part of society, there exists many mathematical problems requiring extensive computational resources. Meanwhile, Quantum Computers (QCs), which holds great promise for speedups and increased capacity, are being built with the ambition of revolutionizing specific areas of the information technology industry; ML being one of the "killer applications". While building large, scalable and fault-tolerant quantum computers is a difficult job likely to finish decades from now, we already today have access to noisy intermediate-scale quantum (NISQ) computers. In this exciting NISQ-era, the interface between QC and ML—referred to as quantum machine learning (QML)—has been born as a rich and fast-moving research field which studies how a QC and ML can assist each other. Despite practical applications of current QML is widely debated, at least three core questions are considered important regardless of current practicality. The first question is, if there are useful tasks NISQ computers which can be used to accelerate ML. The second question is, given the noisy nature of NISQ hardware can one find key characteristics in the accumulated noise that leads us closer to practical applications. And lastly, can we expand our ML toolbox working together with the quantum computer in order to solve more general problem classes in QML. In order to approach these questions, this thesis offers four scientific papers aiming at delivering results that gets us closer to relevant answers. The first paper develops a quantum algorithm that approximates a specific quantum state which can be used in one of the most computationally hard ML tasks: sampling from complicated high dimensional probability distributions. The second contribution proposes metrics that evaluate noise characteristics in NISQ hardware such that algorithms running on the hardware can be paired with appropriate error mitigation strategies which is paramount to achieve practical NISQ protocols. The third article develops a meta-learning protocol exploiting similarity between key problems in quantum physics and thus enables one to learn across problems in minimum energy eigenstate estimation; a problem very relevant to machine learning as well. The fourth and last paper studies how uncertainty calibration affects the aforementioned meta-learner, and hence this thesis also provides ML investigation with applicability in QML. In the end, the thesis aims both at drawing connections between all contributions as well as giving an introduction to QML for computer scientists. While the marriage of NISQ and ML is still bumpy and their combined future is hard to predict, we end on a positive and optimistic note on the progress of QML in the near term.