RAISE-TAQS: Entanglement and information in complex networks of qubits

量子计算机现在正在接近一个尺寸，它将很快执行超过当今最快的经典计算机的任务。为了获得量子计算机的全部功率，量子计算机内部的量子比特应该彼此很好地连接，以便可以传输信息，并且可以尽可能快地在任何两个量子比特之间产生纠缠。量子比特的相互作用将形成一个复杂的、时变的网络，它们的动力学将过于复杂，经典计算机无法预测。该项目将为理解复杂性迅速增加的量子系统提供关键一步，并找出如何利用这种复杂性来大规模加速具有稀疏和简单量子位连接的系统的量子计算。该项目将通过量化量子态复杂性的具体方法，将量子信息科学和凝聚态物理学领域扩展到复杂性科学领域。随着量子信息前沿正在全球范围内孕育一场新的技术革命，该项目将培养新一代具有量子技术专业知识的本科生和研究生，并开发新的12-量子工程的学分研究生证书课程，以满足行业专业人士在获得量子专业知识方面的迫切需求。该项目的前半部分旨在找出量子比特连接的高度可用于加速量子信息处理，专注于类似于Lieb-Robinson边界的数学量子速度限制，非常小或非常大数量量子位的最佳纠缠协议，以及使用固态量子位的纠缠速度限制的实验演示。该项目的第二部分将专注于由具有密集和复杂相互作用的哈密顿量创建的状态，量化其复杂性并理解其纠缠结构。从复杂性科学中借用的各种网络测度将被用来研究实验可测的量子互信息网络和最近发展起来的量子神经网络，以便对量子临界现象、纠缠区定律、而非平衡态该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准。

Quantum computers are now approaching a size that will soon perform tasks surpassing the power of today's fastest classical computers. To attain the full power of a quantum computer, qubits inside the quantum computer should be well connected with each other, so that information can be transferred, and entanglement can be generated between any two qubits as fast as possible. The qubit interactions will form a complex and time-varying network and their dynamics will be too complicated for classical computers to predict. This project will provide a key step in understanding quantum systems of a rapidly increasing level of complexity and find out how such complexity can be employed to massively speed up quantum computing over systems with sparse and simple qubit connections. The project will expand the fields of quantum information science and condensed matter physics into the territory of complexity science, via concrete ways to quantify complexity of quantum states. As the quantum information frontier is fostering a new technological revolution around the world, the project will train a new generation of undergraduate and graduate students with expertise in quantum technologies and develop a new 12-credit graduate certificate program in quantum engineering to accommodate the pressing need from industry professionals in obtaining quantum expertise.The first half of this project aims to find out how high qubit connectivity can be used to speed up quantum information processing, focusing on mathematical quantum speed limits akin to Lieb-Robinson bounds, optimal entangling protocols for very small or very large number of qubits, and experimental demonstrations of entangling speed limit using solid-state qubits. The second half of this project will focus on states created by Hamiltonians with dense and complex interactions, quantifying their complexity and understanding their entanglement structure. Various network measures borrowed from complexity science will be employed to study the experimentally measurable quantum mutual information network and the recently developed quantum neural network, in order to bring new insight to quantum critical phenomena, entanglement area laws, and nonequilibrium many-body dynamics.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.