  Existing protocols for benchmarking current quantum co-processors fail to
meet the usual standards for assessing the performance of
High-Performance-Computing platforms. After a synthetic review of these
protocols -- whether at the gate, circuit or application level -- we introduce
a new benchmark, dubbed Atos Q-score (TM), that is application-centric,
hardware-agnostic and scalable to quantum advantage processor sizes and beyond.
The Q-score measures the maximum number of qubits that can be used effectively
to solve the MaxCut combinatorial optimization problem with the Quantum
Approximate Optimization Algorithm. We give a robust definition of the notion
of effective performance by introducing an improved approximation ratio based
on the scaling of random and optimal algorithms. We illustrate the behavior of
Q-score using perfect and noisy simulations of quantum processors. Finally, we
provide an open-source implementation of Q-score that makes it easy to compute
the Q-score of any quantum hardware.
