Transitions in Quantum Complexity

通用量子模拟器需要无限访问所谓的通用门集合。 然而，通用门是昂贵且有噪声的，因此必须在当前技术中节约使用。理解如何从经济的设计出发，以稀疏的资源实现更通用的量子模拟器，对于现实量子计算机的构建以及量子复杂性，量子混沌甚至黑洞物理的理论理解都具有根本的重要性。推进我们对量子模拟器和量子计算机的理解是该国目前在基础科学和应用科学方面奋进的主要目标之一。站在即将到来的量子信息工业革命的最前沿将为经济带来巨大利益，特别是为来自不利背景的人创造新的机会，并为各级科学教育的发展提供动力。量子电路的通用性可以通过它再现量子演化的某些平均性质的程度来衡量。在这个项目中，该小组的目标是研究如何通过非Clifford门掺杂由非通用Clifford门制成的电路，可以驱动量子复杂性的转变，并实现量子电路系综的更普遍覆盖。 他们通过纠缠复杂性，无序相关函数，酉t设计以及这种电路在纠缠冷却协议下的行为来研究量子复杂性的转变。此外，他们计划通过深度神经网络应用机器学习技术，以检测量子复杂性的转变，并在非克利福德门密度的情况下优化电路架构。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

A universal quantum simulator needs unlimited access to a so-called universal set of gates. Universal gates, however, are expensive and noisy and therefore a resource that must be used sparingly with current technology. Understanding how starting from economical designs one can achieve more universal quantum simulators with sparse resources is of fundamental importance in both the construction of realistic quantum computers and in the theoretical understanding of quantum complexity, quantum chaos, and even black hole physics. Advancing our understanding of quantum simulators and quantum computers is one of the main goals of the country's current endeavor in both fundamental and applied science. Being at the forefront of the upcoming quantum information industrial revolution will bring enormous benefits for the economy, in particular creating new opportunities for people from disadvantageous backgrounds and provide an impulse for the advancement of scientific education at all levels. How universal a quantum circuit is can be captured by how well it reproduces some average properties of quantum evolutions. In this project the group aims at studying how by doping circuits made of non-universal Clifford gates by means of non-Clifford gates one can drive transitions in quantum complexity and achieve a more universal coverage of the ensemble of quantum circuits. They study the transitions in quantum complexity by entanglement complexity, out-of-time-order correlation functions, unitary t-designs, and the behavior of such circuits under an entanglement cooling protocol. Moreover, they plan to apply techniques of machine learning by a deep neural network to both detect the transitions in quantum complexity and to optimize the circuit architecture given the density of non-Clifford gates.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.