Application Performance Benchmarks for Quantum Computers

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 often 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 performance and fidelity of the results. The proposed suite refers to several variational algorithms, widely-used on current NISQ devices, but also includes examples of quantum circuits designed for a fault-tolerant quantum computer.