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

该提案针对一系列跨学科任务，直接解决新兴的量子信息处理（QIP）领域面临的挑战。特别是，这两个基础工作，旨在加强对基本概念的理解，如量子纠缠，以及应用工作，如设计量子算法，只需要几十个量子比特，同时仍然提供比经典的对手更好的性能，是有针对性的。在拟议的工作中采用的技术方法涵盖了许多不同的领域，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relatedcomputational methods.Intellectual优点：在QIP可以成为一个可行的计算范式之前，需要克服一些根本性的挑战。这个提议以一种新颖的方式解决了其中的几个挑战，包括：（i）在包含数十个量子比特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：一个包含数千个量子位的系统，需要将整数分解成超过现有经典计算机能力的整数，充其量是一个长期目标。相比之下，一个包含数十个量子比特的系统是一个可以想象的目标;然而，是否有任何量子算法可以在这样一个小规模的计算机上实现，而且性能优于经典算法？该方案提出了一种量子算法，可以用来模拟麦克斯韦方程，以确定经典的谐振结构的电磁模式频率，其中完整的模式场分布是不需要的。据估计，50个逻辑量子比特将有助于产生有用的电磁模拟结果。(ii)量子密钥分发之外还有生命吗？该提案提出的结果是，量子密码学的基本工具被用来建立一个多参与者协议，该协议使参与者能够匿名宣布经典信息。该协议对任何攻击都是安全的，这是有史以来第一个使用真正的多体量子纠缠态的多参与者量子协议。(iii)什么是非平凡的新量子算法的例子（即，Shor的分解和Gover的搜索算法该提案报告了使用量子光学模型确定酉矩阵和相关矩阵的永久性的有效量子算法的发展结果。更广泛的影响：（一）本科跨学科计划：在与加州大学洛杉矶分校纳米科学研究所（CNSI）和电气工程系合作，我们正在开发一个纳米科学跨部门计划的过程中。量子信息处理是该计划的一个关键组成部分，NSF赠款将用于支持这一倡议，并培训研究生和本科生。(ii)量子信息处理年度研讨会：与加州大学洛杉矶分校的NSF纯粹与应用数学研究所（IPAM）合作，将举办量子信息处理和计算跨学科年度研讨会。(iii)为面向实现的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组的首席理论家，该实验组致力于基于固态的量子信息处理技术。实验工作目前由DARPA和ARO的赠款支持，NSF的资助将利用现有的计划，并专注于将理论结果转移到实验组。（iv）外展和少数民族学生的参与：IPAM和CNSI都有吸引少数民族学生和K12学生的机构基础设施，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.