At the moment of writing, the future evolution of the COVID-19 epidemic is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the COVID-19 epidemic in the Hubei province. The network is composed of the cities in Hubei and their interactions (e.g., traffic flow). However, the precise interactions between cities is unknown and must be inferred from observing the epidemic. We propose the Network-Inference-Based Prediction Algorithm (NIPA) to forecast the future prevalence of the COVID-19 epidemic in every city. Our results indicate that NIPA is beneficial for an accurate forecast of the epidemic outbreak.

Researchers from various scientific disciplines have attempted to forecast the spread of coronavirus disease 2019 (COVID-19). The proposed epidemic prediction methods range from basic curve fitting methods and traffic interaction models to machine-learning approaches. If we combine all these approaches, we obtain the Network Inference-based Prediction Algorithm (NIPA). In this paper, we analyse a diverse set of COVID-19 forecast algorithms, including several modifications of NIPA. Among the algorithms that we evaluated, the original NIPA performed best at forecasting the spread of COVID-19 in Hubei, China and in the Netherlands. In particular, we show that network-based forecasting is superior to any other forecasting algorithm.

We study a classical model for the accumulation of errors in multi-qubit quantum computations. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency between errors in the past and future. By subsequently using techniques from the field of discrete probability theory, we calculate the probability that error quantities such as the fidelity and trace distance exceed a threshold analytically. The formulae cover fairly generic error distributions, cover multi-qubit scenarios, and are applicable to the randomized benchmarking protocol. To combat the numerical challenge that may occur when evaluating our expressions, we additionally provide an analytical bound on the error probabilities that is of lower numerical complexity. Besides this, we study a model describing continuous errors accumulating in a single qubit. Finally, taking inspiration from the field of operations research, we illustrate how our expressions can be used to decide how many gates one can apply before too many errors accumulate with high probability, and how one can lower the rate of error accumulation in existing circuits through simulated annealing.