Superconducting qubits have seen a tremendous progress in the last two decades, and yet they remain unable to extract quantum advantage for application scenarios. While algorithms like Shor’s demonstrate quantum advantage in theory, they do not seem to fit modern noisy quantum processors. Then, in order to achieve quantum advantage either modern quantum processors catch up to their expected behaviour, or modern algorithms are tailored to fit the expected behaviour of modern chips. This thesis focuses on the second approach, which is to explore the implementation of algorithms on modern quantum processors. Along all these implementations, we study the errors that cause these algorithms to derail from their ideal results. We attempt to understand, quantify and control these errors, in the hope that this provides useful insights into how to design algorithms for the modern hardware. This thesis starts by introducing the topic of superconducting quantum processors and modern algorithms in the first two chapters. Then we move onto the three experiments, one chapter each, detailing our findings. The first experiment cover an digital-analog implementation of a quantum simulation of light-matter interaction. We present the implementation that makes use of both digital (gates) and analog (evolution) blocks. The accuracy of the Trotterization technique is studied in detail, as well as the capability to study the photon population in the resonator. We manage to implement up to 90 Trotter steps and reproduce the behaviour in the ultra-strong coupling regime. The second experiment presents an error mitigation technique, on an application of great interest to the field (molecular simulations). This application is a fully digital one, within the hot topic of variational algorithms for ground-state preparation. The mitigation technique, which is an invention of our own team (see referenced theoretical works) manages to reduce the algorithm error over an order of magnitude. In order to demonstrate this level of control, we quantify the error through accurate simulations of the quantum process and independent quantification of the parameters involved. The third experiment presents another variational algorithm, this time to produce thermal states rather than ground states. Again, we pursue a detailed study of the many error mechanisms involved, in order to quantify and match the results obtained. We go beyond incoherent errors and add a coherent error mechanism common to our hardware architecture, the residual ZZ coupling. Finally, we reflect on the final chapters about how to continue towards implementations that make the most out of modern, noisy, hardware.@en