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

量子计算机现在的大小很快就会超过当今最快的经典计算机的能力。为了达到量子计算机的全部功率，量子计算机内部的量子比特应该相互连接得很好，这样才能实现信息的传递，并尽快在任意两个量子比特之间产生纠缠。量子比特相互作用将形成一个复杂的时变网络，它们的动力学将过于复杂，经典计算机无法预测。这个项目将为理解快速增长的复杂程度的量子系统提供关键的一步，并找出如何利用这种复杂性在具有稀疏和简单量子比特连接的系统上大规模加速量子计算。该项目将通过量化量子态的复杂性的具体方法，将量子信息科学和凝聚态物理的领域扩展到复杂性科学的领域。随着量子信息前沿在世界各地催生一场新的技术革命，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学分量子工程研究生证书课程，以满足行业专业人员在获取量子专业知识方面的迫切需求。该项目的前半部分旨在了解如何利用高量子比特连接来加速量子信息处理，重点是类似于Lieb-Robinson边界的数学量子速度限制，非常少量或非常大量的量子比特的最佳纠缠协议，以及使用固态量子比特进行纠缠速度限制的实验演示。这个项目的后半部分将集中在哈密顿人创造的具有密集和复杂相互作用的状态，量化它们的复杂性，并了解它们的纠缠结构。借鉴复杂性科学的各种网络方法，将研究可实验测量的量子互信息网络和最近开发的量子神经网络，以期为量子临界现象、纠缠区定律和非平衡多体动力学带来新的见解。该奖项反映了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。

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.