Modern NISQ devices are subject to a variety of biases and sources of noise that degrade the solution quality of computations carried out on these devices. A natural question that arises in the NISQ era, is how fairly do these devices sample ground state solutions. To this end, we run five fair sampling problems (each with at least three ground state solutions) that are based both on quantum annealing and on the Grover Mixer-QAOA algorithm for gate-based NISQ hardware. In particular, we use seven IBM~Q devices, the Aspen-9 Rigetti device, the IonQ device, and three D-Wave quantum annealers. For each of the fair sampling problems, we measure the ground state probability, the relative fairness of the frequency of each ground state solution with respect to the other ground state solutions, and the aggregate error as given by each hardware provider. Overall, our results show that NISQ devices do not achieve fair sampling yet. We also observe differences in the software stack with a particular focus on compilation techniques that illustrate what work will still need to be done to achieve a seamless integration of frontend (i.e. quantum circuit description) and backend compilation.

中文翻译：

---

在 NISQ 设备上采样：“谁是最公平的一个？”

现代 NISQ 设备受到各种偏差和噪声源的影响，这些偏差和噪声源会降低在这些设备上执行的计算的解决方案质量。NISQ 时代出现的一个自然问题是，这些设备对基态解决方案进行采样的公平性如何。为此，我们运行了五个公平采样问题（每个问题都有至少三个基态解决方案），这些问题基于量子退火和基于门的 NISQ 硬件的 Grover Mixer-QAOA 算法。特别是，我们使用了七个 IBM~Q 设备、Aspen-9 Rigetti 设备、IonQ 设备和三个 D-Wave 量子退火器。对于每个公平采样问题，我们测量基态概率、每个基态解决方案相对于其他基态解决方案的频率的相对公平性，以及每个硬件供应商给出的总误差。总体而言，我们的结果表明 NISQ 设备尚未实现公平采样。我们还观察了软件堆栈中的差异，特别关注编译技术，这些技术说明了仍需要完成哪些工作才能实现前端（即量子电路描述）和后端编译的无缝集成。