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.
翻译:我们研究Noisy中层量子(NISQ)装置的公平取样状况,特别是IBM Q 后端组。我们利用最近推出的用于离散优化的 Grover Mixer-QAOA算法,产生公平的采样电路,以解决不同困难的6个问题,每个问题都有若干最佳解决办法,我们随后在IBM Q 系统中的20个后端运行。对于在特定方位上评估的某一电路,我们评估:qubits 如何经常返回问题的最佳解决办法,所有最佳解决方案的qubits样本的公平性,以及所报告的qubits硬件错误率。为了量化公平性,我们根据Pearson的$\chi2$的测试,定义了一个新的新型指标。我们发现,对中、大误率的电路路的公平性相对较高,但对中差率的电路路的下降率则比较高。这说明,这个系统的结构错误主导着一个系统,而非结构错误是随机的,因此内在公平的,在 nosier qual qubits rough ral rough rough rough 。我们的结果显示一个影响着网络的稳性。