Fair Sampling Error Analysis on NISQ Devices

We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular IBM Q family backends. Using recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate circuits to solve six problems varying difficulty, each with several optimal solutions, which then run twenty backends across system. For a given circuit evaluated specific set qubits, evaluate: how frequently qubits return an solution problem, fairness sample from all and reported hardware error rate qubits. To quantify fairness, define novel metric based Pearson's $\chi^2$ test. find that is relatively high small large rates, but drops medium rates. This indicates structured errors dominate this regime, while unstructured errors, are random thus inherently fair, noisier longer circuits. Our results show can be powerful tool understanding intricate web affecting current NISQ hardware.