Transitions in Quantum Complexity

通用量子模拟器需要无限制地访问所谓的通用门集合。然而，万能闸门既昂贵又嘈杂，因此是一种必须在当前技术中节俭使用的资源。了解如何从经济的设计出发，在资源稀少的情况下实现更通用的量子模拟器，对于构建现实的量子计算机，以及从理论上理解量子复杂性、量子混沌，甚至黑洞物理，都是至关重要的。提高我们对量子模拟器和量子计算机的理解是国家当前基础科学和应用科学努力的主要目标之一。走在即将到来的量子信息产业革命的前沿，将为经济带来巨大的好处，特别是为弱势群体创造新的机会，并为各级科学教育的推进提供动力。量子电路的普适性可以通过它对量子演化的一些平均性质的再现来衡量。在这个项目中，该小组的目标是研究如何通过使用非通用Clifford门来掺杂由非通用Clifford门组成的电路，从而驱动量子复杂性的跃迁，并实现对量子电路集合的更普遍的覆盖。他们通过纠缠复杂性、无序关联函数、酉t设计以及在纠缠冷却协议下这类电路的行为来研究量子复杂性的转变。此外，他们计划应用深度神经网络的机器学习技术来检测量子复杂性的转变，并在非Clifford门密度的情况下优化电路架构。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.