Simulations of complex engineering systems easily require run-times of several weeks even on HPC systems. Any application-relevant subsequent analysis, such as an uncertainty quantification or parameter identification, is hence often computationally impractical, as it requires a large number of simulation runs. Various surrogate modelling strategies have been proposed to tackle this challenge, one being the family of Gaussian process (GP) emulation techniques. GPs have traditionally been used for classification and regression tasks. Their generalization into GP emulators aims at substituting computationally expensive models via a cheap to evaluate, uncertainty-informed alternative. This proves to be a very powerful concept for performing high-throughput tasks and disentangling surrogate-induced uncertainty from other input uncertainty. GPs are by now applied broadly in computational engineering [1, 2, 3]. While GPs are known for their robustness and sound theoretical background, they are limited to a moderate dimension of the design parameter space as their training requires inverting a potentially densely populated covariance matrix (O(N³) complexity). Quantum computing alternatives have been suggested to tackle this limitation, for instance the Harrow-Hassidim-Llyod (HHL) algorithm theoretically predicts an exponential improvement. Unfortunately, any real-world speedups would be lost in an attempt to read the inverted matrix from the quantum computer, due to the long known readout-problem [4, 5]. In this contribution, we go back to the origins of GP emulator training, which consists of optimizing a scalar-valued objective function subject to hyper-parameters and training data. The challenge is then to screen the parameter space efficiently and retrieve only the optimal parameter values. However, screening a large parameter space is a feasible task for quantum computers, as shown recently in another context by the authors and collaborators [6]. In addition, we demonstrate how the multi-dimensional hyper-parameter space can be screened analytically, using a symbolic simulator, in contrast to numerical probing based on established simulators such as Qiskit, Pennylane, etc. Finally, we identify challenges in quantum optimization and extrapolate to other use-cases, such as quantum neural networks (QNNs), or error correction (QEC).