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