QnTM: Harnessing Quantum Entaglement: Fundamental Studies, Communication Protocols, and Computing

这项提议的目标是一系列跨学科任务，直接应对新兴的量子信息处理(QIP)领域面临的挑战。特别是，旨在加强对量子纠缠等基本基本概念的理解的基础工作，以及诸如设计只需要数十个量子比特的量子算法，同时仍提供比其经典对应部分更好的性能的应用工作，都是目标。拟采用的技术方法涵盖多个不同领域，包括量子力学、量子信息理论和概念、计算理论、组合学、经典电磁场和相关计算方法。智力优势：在QIP成为可行的计算范式之前，需要克服一些根本性的挑战。这一提议以一种新颖的方式解决了其中的几个挑战，包括：(I)在由数十个量子比特组成的系统中，可以实现什么样的量子算法？这是量子计算领域面临的一个非常重要的问题：一个由数千个量子比特组成的系统充其量只是一个长期目标，这些量子比特需要分解整数，而不是现有经典计算机的能力。相反，一个由数十个量子比特组成的系统是一个可以想象的目标；然而，有没有任何量子算法可以在这样一台小规模的计算机上实现，而且性能优于经典算法？该提议提出了一个量子算法，可以用来模拟麦克斯韦方程来确定谐振结构的经典电磁模式频率，其中不需要完整的模场分布。据估计，50个逻辑量子位足以产生有用的电磁模拟结果。(Ii)量子密钥分配之外还有生命吗？该方案给出了使用量子密码学的基本工具来构建一个多参与者协议的结果，该协议使参与者能够匿名宣布经典信息。这个协议被证明是安全的，可以抵抗任何和所有的攻击。这是第一个使用真正的多方量子纠缠态的多参与者量子协议。(Iii)有哪些非平凡的新量子算法的例子(即Shor分解和Gover的搜索算法？该提案报告了利用量子光学模型开发用于确定酉阵和相关矩阵的恒等式的高效量子算法的结果。主要影响：(I)本科生跨学科项目：与加州大学洛杉矶分校纳米科学研究所(CNSI)和加州大学洛杉矶分校电气工程系合作，我们正在开发一个纳米科学跨部门项目。量子信息处理是这一计划的关键组成部分，NSF的拨款将被用来支持这一倡议，并用于培训研究生和本科生。(Ii)量子信息处理年度讲习班：将与加州大学洛杉矶分校的国家科学基金会理论和应用数学研究所(IPAM)合作，举办量子信息处理和计算跨学科年度讲习班。(Iii)为面向实施的DARPA量子计算项目提供支持：Roychowdhury博士是加州大学洛杉矶分校一个大型跨学科实验小组的首席理论家，致力于开发基于固态的量子信息处理技术。实验工作目前得到了DARPA和ARO的拨款支持，NSF的拨款将利用现有的计划，并专注于将理论结果转移到实验小组。(Iv)外展和少数族裔学生参与：IPAM和CNSI都有机构培训名额，以吸引少数族裔和K12学生，我们计划通过研讨会和免费参加我们的讲习班来吸引他们并对他们进行培训。

This proposal targets a set of interdisciplinary tasks that directly address the challenges facingthe burgeoning field of quantum information processing (QIP). In particular, both foundationalwork aimed at enhancing the understanding of fundamental underlying concepts, such as quan-tumentanglement, as well as applied work, such as designing quantum algorithms that wouldrequire only tens of qubits, while still providing better performance than their classical counter-parts,are targeted. The technical approaches to be adopted in the proposed work encompassa number of different fields, including quantum mechanics, quantum information theory andconcepts, theory of computation, combinatorics, and classical electromagnetic fields and relatedcomputational methods.Intellectual Merits: A number of fundamental challenges need to be overcome before QIPcan become a viable computing paradigm. This proposal addresses several of these challengesin a novel fashion, including: (i) What kinds of quantum algorithms can one implement insystems comprising tens of qubits? This is a very important issue facing the field of quantumcomputation: a system comprising the thousands of qubits necessary to factorize integers beyondthe capability of existing classical computers is, at best, a long-term goal. In contrast, a systemcomprising tens of qubits is a conceivable goal; however, would there be any quantum algorithmthat can be implemented on such a small scale computer and yet outperform classical algorithms?The proposal presents a quantum algorithm that can be used to simulate Maxwell's equations todetermine classical electromagnetic mode frequencies of resonant structures, where the completemode field distribution is not required. It is estimated that 50 logical qubits would be sufficientto produce useful electromagnetic simulation results. (ii) Is there life beyond Quantum KeyDistribution? The proposal presents results where the basic tools of quantum cryptography areused to build a multi-participant protocol which gives the participants the ability to anonymouslyannounce classical information. This protocol is shown to be secure against any and all attacks.This is the first ever multi-participant quantum protocol that uses a truly multipartite quantumentangled state. (iii) What are examples of nontrivial new quantum algorithms (i.e., otherthan Shor's factorization and Gover's search algorithms? The proposal reports results on thedevelopment of efficient quantum algorithms for determining the permanent of unitary andrelated matrices using the quantum optical model. A number of such critical open questionsrelated to QIP are addressed.Broader Impacts: (i) Undergraduate Interdisciplinary Program: In collaboration with the Cal-iforniaNano-science Institute (CNSI) and the Department of Electrical Engineering at UCLA,we are in the process of developing a nano-science interdepartmental program. Quantum in-formationprocessing is a key component of this program and the NSF grant will be leveragedto support this initiative, and in training graduate and undergraduate students. (ii) AnnualWorkshops On Quantum Information Processing: In collaboration with the NSF Institute ofPure and Applied Mathematics (IPAM) at UCLA, an interdisciplinary annual workshop onQuantum Information Processing and Computing will be held. (iii) Providing Support forImplementation-Oriented DARPA projects on Quantum Computing: Dr. Roychowdhury is theprincipal theoretician for a large interdisciplinary experimental group at UCLA working on de-velopingsolid-state based quantum information processing technology. The experimental effortis currently supported by grants from DARPA and ARO, and the NSF grant will leverage theexisting program and focus on transferring theoretical results to the experimental groups. (iv)Outreach and Minority Student Participation: Both IPAM and CNSI have institutional infras-tructuresin place to attract minority and K12 students, and we plan to engage them and trainthem through seminars and free access to our workshops.