Benjamin Zanger

To localize and quantify greenhouse gas emissions from cities, gas concentrations are typically measured at a small number of sites and then linked to emission fluxes using atmospheric transport models. Solving this inverse problem is challenging because the system of equations often has no unique solution and the solution can be sensitive to noise. A common top–down approach for solving this problem is Bayesian inversion with the assumption of a multivariate Gaussian distribution as the prior emission field. However, such an assumption has drawbacks when the assumed spatial emissions are incorrect or not Gaussian distributed. In our work, we investigate sparse reconstruction (SR), an alternative reconstruction method that can achieve reasonable estimations without using a prior emission field by making the assumption that the emission field is sparse. We show that this assumption is generally true for the cities we investigated and that the use of the discrete wavelet transform helps to make the urban emission field even more sparse. To evaluate the performance of SR, we created concentration data by applying an atmospheric forward transport model to CO₂ emission inventories of several major European cities. We used SR to locate and quantify the emission sources by applying compressed sensing theory and compared the results to regularized least squares (LSs) methods. Our results show that SR requires fewer measurements than LS methods and that SR is better at localizing and quantifying unknown emitters.

To localize and quantify greenhouse gas emissions from cities, gas concentrations are typically measured at a small number of sites and then linked to emission fluxes using atmospheric transport models. Solving this inverse problem is challenging because the system of equations is usually underdetermined. A common top-down approach to solving this problem is Bayesian inversion that uses a given Gaussian prior emission field. However, such an approach has drawbacks when the assumed spatial emission distribution is incorrect. In our work, we investigate sparse reconstruction (SR), an alternative reconstruction method that does not require a prior emission field, but only the assumption that the emission field is sparse. We show that this assumption is mostly true for the cities we investigated and that the use of the discrete wavelet transform helps to make the urban emission field even more sparse. To evaluate the performance of SR, we created concentration data by applying an atmospheric forward transport model to CO₂ emission inventories of several major European cities. We used SR to locate and quantify the emission sources by applying compressed sensing theory and compared the results to regularized least squares (LS) methods. Our results show that SR requires fewer measurements than LS methods and that SR provides better localization and quantification of unknown emitters.

Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6$^{\mathrm{th}}$ order Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good agreement with the reference solution. We find that the quantum annealing approach exhibits the largest potential for high-order implicit integration methods. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.

As quantum internet technologies develop, the need for simulation software and education for quantum internet rises. QuNetSim aims to fill this need. QuNetSim is a Python software framework that can be used to simulate quantum networks up to the network layer. The goal of QuNetSim is to make it easier to investigate and test quantum networking protocols over various quantum network configurations and parameters. The framework incorporates many known quantum network protocols so that users can quickly build simulations and beginners can easily learn to implement their own quantum networking protocols.