Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any random unitaries has consequences on their complexity, expressibility, and trainability. To study this property of random circuits, we develop numerical protocols for estimating the frame potential, the distance between a given ensemble and the exact randomness. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high-performing using CPU and GPU parallelism. We study 1. local and parallel random circuits to verify the linear growth in complexity as stated by the Brown-Susskind conjecture, and; 2. hardware-efficient ans\"atze to shed light on its expressibility and the barren plateau problem in the context of variational algorithms. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.
翻译:随机电路在量子至上演示、 化学和机器学习的变异量子算法 以及黑洞信息 中都使用了随机电路。 随机电路接近任何随机线条的能力对其复杂性、 直观性和 可训练性都有影响。 为了研究随机电路的特性, 我们开发了用于估计框架潜力、 给定组合和确切随机性之间的距离的数值规程。 我们的 抗声网络算法对浅层电路具有多元复杂性, 并且使用 CPU 和 GPU 平行法表现得很高。 我们研究了1. 本地和平行随机电路, 以核实布朗- 苏斯本性电导所显示的复杂线性增长; 2. 硬件高效的电路, 以揭示其可显示性, 以及变式算法背景下的贫瘠高地问题。 我们的工作表明, 大型的 数子网络模拟可以为量子信息科学的开放问题提供重要的提示。