The notable claim of quantum supremacy presented by Google's team in 2019 consists of demonstrating the ability of a quantum circuit to generate, albeit with considerable noise, bitstrings from a distribution that is considered hard to simulate on classical computers. Verifying that the generated data is indeed from the claimed distribution and assessing the circuit's noise level and its fidelity is a purely statistical undertaking. The objective of this paper is to explain the relations between quantum computing and some of the statistical aspects involved in demonstrating quantum supremacy in terms that are accessible to statisticians, computer scientists, and mathematicians. Starting with the statistical analysis in Google's demonstration, which we explain, we study various estimators of the fidelity, and different approaches to testing the distributions generated by the quantum computer. We propose different noise models, and discuss their implications. A preliminary study of the Google data, focusing mostly on circuits of 12 and 14 qubits is discussed throughout the paper.
翻译:Google团队在2019年提出的量子至上这一引人注目的主张,包括展示量子电路能够生成(尽管噪音很大)从古典计算机上难以模拟的分布中生成的比特字符串。核实生成的数据的确是来自声称的分布,并评估电路的噪音水平及其忠诚度,这纯粹是一项统计工作。本文的目的是解释量子计算与以统计人员、计算机科学家和数学家可以使用的方式展示量子至上的某些统计方面之间的关系。从谷歌演示中的统计分析开始,我们解释,我们研究各种忠实性的估测者,以及测试量子计算机产生的分布的不同方法。我们提出了不同的噪音模型,并讨论它们的影响。对谷歌数据的初步研究,主要侧重于12和14公尺的电路,整个文件都讨论了。