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

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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.