FET: CIF: Small: Distributed Quantum Information Processing using Structured Operators

许多量子通信/计算算法需要量子计算机对足够多的量子比特同时执行逻辑运算，这些量子比特已组合成叠加态。不幸的是，当前最先进的量子计算机只能在数十个量子位上运行来存储和处理任务。构建可扩展量子系统的最大障碍之一是退相干，这个术语涵盖了导致量子寄存器中编码信息衰减的所有过程。随着量子比特数量的增加，退相干率增加，因此量子信息变得更加脆弱。克服这一挑战的一种方法是采用分布式范式，其中通过经典链路和量子链路连接的有限量子位容量的量子计算机网络用于通过将已知的集中式算法转换为分布式版本来以分布式方式解决问题。这可能会对社会在高级计算和通信平台方面产生重大影响。该项目的目标之一是在量子力学、信息论和抽象代数等不同学科之间架起桥梁，从而促进社区之间的进一步合作。 我们共同努力让女性和代表性不足的少数族裔学生参与该项目，该项目旨在开发一种基本方法，从量子信息理论的角度解决分布式量子信息处理、通信和计算中的一些挑战。 该项目的研究工作基于两个相互关联但互补的研究主旨。 该项目的一个主旨是基于一种新颖的马尔可夫结构量子测量和随机分箱技术来解决分布式测量压缩问题。强调了这种方法的其他影响，包括基本问题和实际应用。在该项目的第二个重点中，考虑了一种研究量子源的分布式可靠（无损）压缩和计算的新方法。作为第二个推力的一部分，通过探索量子通道上的量子纠错问题与量子源的率失真压缩之间的对偶联系，从新的角度解决了量子到量子的率失真问题。 该项目还解决了量子到经典率失真编码背景下的分布式函数计算问题。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Many quantum communication/computing algorithms require quantum computers performing logical operations simultaneously on a sufficiently large number of quantum bits which have been combined into a superposition state. Unfortunately, the current state-of-the-art quantum computers can only operate on tens of qubits for storing and processing tasks. One of the biggest obstacles toward building a scalable quantum system is decoherence, a term that encompasses all the processes contributing to the decay of information coded in a quantum register. As the number of qubits is increased, the decoherence rate increases, and hence quantum information becomes more fragile. One way to overcome this challenge is to employ the distributed paradigm, where a network of limited qubit-capacity quantum computers, connected through classical and quantum links, are used to solve problems in a distributed manner by casting known centralized algorithms into their distributed versions. This may have significant impact on the society in terms of superior computing and communication platforms. One of the goals of this project is to provide bridge among different disciplines such as quantum mechanics, information theory, and abstract algebra, and thereby contribute to furthering collaborations between communities. A concerted effort is made to involve women and under-represented minority students in this project,This project aims to develop a foundational approach to address some of the challenges in distributed quantum information processing, communication, and computation from a quantum information-theoretic perspective. The research effort of this project is based on two interconnected yet complementary research thrusts. In one thrust of the project, the problem of distributed measurement compression is addressed based on a novel Markov structured quantum measurements and the technique of random binning. Other implications of this approach, both concerning fundamental problems and practical applications are highlighted. In the second thrust of the project, a novel approach for studying distributed reliable (lossless) compression and computation of quantum sources is considered. As a part of the second thrust, the quantum-to-quantum rate distortion problem is addressed from a new perspective -- by exploring the duality connection between the problem of quantum error correction over a quantum channel and rate-distortion compression of a quantum source. This project also addresses problem of distributed function computation in the context of quantum-to-classical rate-distortion coding.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.