  Current technological advancements of quantum computers highlight the need
for application-driven, practical and well-defined methods of benchmarking
their performance. As the existing NISQ device's quality of two-qubit gate
errors rate is even around one percent and the number of qubits is still
limited to a few or several dozen, naturally, we need to propose rather small
algorithms instances taken from key promising application areas, such as
quantum chemistry, combinatorial optimisation or machine learning. While many
techniques for assessing the performance of logical components, such as gate
fidelity and qubit coherence exist, it is still challenging to extrapolate
those values onto the performance of different quantum algorithms and
subroutines. This work aims to introduce a series of initial quantum
application benchmarks together with a methodology of execution for measuring
the performance and fidelity of the results. The proposed suite refers to
several variational algorithms widely used on available NISQ devices but also
includes examples of quantum circuits designed for a fault-tolerant quantum
computer.
