Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines thekey-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.

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.