Evaluating the performance of quantum devices is an important step towards scaling quantum devices and eventually using them in practice. The great number of available quantum metrics and the different hardware technologies used to develop quantum computers complicate this evaluation. In addition, different computational paradigms implement quantum operations in different ways. A prominent quantum metric is given by the Q-score metric of Atos. This metric was originally introduced as a standalone way to benchmark devices using the Max-Cut problem. In this work, we show that the Q-score defines a framework of quantum metrics, which allows benchmarking using different problems, user settings and solvers. To showcase the applicability of the framework, we showcase a second Q-score in this framework, called the Q-score Max-Clique. This yields, to our knowledge, the first application-level metric capable of natively comparing three different paradigms of quantum computing. This metric is evaluated on these computational quantum paradigms - quantum annealing, gate-based quantum computing, and photonic quantum computing - and the results are compared to those obtained by classical solvers.

Much of recent progress in geophysics can be attributed to the adaptation of heterogeneous high-performance computing architectures. It is projected that the next major leap in many areas of science, and hence hopefully in geophysics too, will be due to the emergence of quantum computers. Finding a right combination of hardware, algorithms, and a use case, however, proves to be a very challenging task - especially when looking for a relevant application that scales efficiently on a quantum computer and is difficult to solve using classical means. We find that maximizing stack power for residual statics correction, an NP-hard combinatorial optimization problem, appears to naturally fit a particular type of quantum computing known as quantum annealing. We express the underlying objective function as a quadratic unconstrained binary optimization, which is a quantum-native formulation of the problem. We choose some solution space and define a proper encoding to translate the problem variables into qubit states. We find that these choices can have a significant impact on the maximum problem size that can fit on the quantum annealer and on the fidelity of the final result. To improve the latter, we embed the quantum optimization step in a hybrid classical-quantum workflow, which aims to increase the frequency of finding the global, rather than some local, optimum of the objective function. Finally, we find that a generic, black-box, hybrid classical-quantum solver also could be used to solve stack-power maximization problems proximal to industrial relevance and capable of surpassing deterministic solvers prone to cycle skipping. A custom-built workflow capable of solving larger problems with an even higher robustness and greater control of the user appears to be within reach in the very near future.

In this work, we consider the following problem: given a graph, the addition of which single edge minimises the effective graph resistance of the resulting (or, augmented) graph. A graph’s effective graph resistance is inversely proportional to its robustness, which means the graph augmentation problem is relevant to, in particular, applications involving the robustness and augmentation of complex networks. On a classical computer, the best known algorithm for a graph with N vertices has time complexity (Formula Presented). We show that it is possible to do better: Dürr and Høyer’s quantum algorithm solves the problem in time (Formula Presented). We conclude with a simulation of the algorithm and solve ten small instances of the graph augmentation problem on the Quantum Inspire quantum computing platform.