Quantum-based Computational Fluid Dynamics

Current quantum computers are characterized by small and error-prone systems. The search for algorithms that can be used advantageously under these conditions has attracted a lot of attention in recent years. Promising candidates in this context are variational quantum algorithms, where only part of the algorithm is executed on the quantum computer. Therefore, they usually require fewer qubits and qubit gates and can deal with the errors of a real quantum computer. An important example of variational quantum algorithms is the so-called quantum circuit learning algorithm (QCL), which can approximate arbitrary functions. It is particularly interesting because it can be combined with the parameter shift rule to solve non-linear differential equations. This demonstrator aims to explain the basics of QCL and uses an example to show how different functions can be approximated. It also shows how the multi-qubit character of QCL can be utilized in a targeted manner. Thus, several functions can be approximated simultaneously with the same QCL circuit by measuring multiple qubits. Finally, it is described how arbitrary differential equations can be solved in combination with the parameter shift rule.