AF: Large: Collaborative Research: Reliable Quantum Communication and Computation in the Presence of Noise

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Quantum information science has yielded deep theoretical insights into the nature of information and communication, while raising the hope of dramatically more capable computers and communication networks. But the achievement of these practical goals is hindered by the inherent fragility of quantum information. Traditional approaches for obtaining reliability through simple redundancy do not work; instead, fault tolerance must, and can, in principle, be obtained through subtler techniques that contrive to measure and correct errors without learning anything about the encoded data.Unfortunately present methods for fault-tolerant quantum computation require significant overhead, and present understanding of quantum channel capacities remain very limited. For example, no quantum code is known on which arbitrary fault-tolerant quantum computation can be performed without leaving the code space. And only very recently was it discovered that classical information can be sent at rates exceeding the long-conjectured Holevo bound.This project will attempt to develop new methods for reliable quantum communication and computation in the presence of noise. First, the research will push the capabilities and boundaries of quantum error-correction techniques, both by extending and delineating the types of correctable errors, and by determining the scenarios under which such error correction is or is not possible. The second goal is to develop the deep but heretofore largely unexplored connections between quantum codes, entanglement, and many-body physics, complexity theory, cryptography and high-dimensional geometry. The objective is to advance our understanding both of quantum codes as well as the related areas of mathematics, physics and computer science. Finally the team will seek to elucidate the subtle differences between quantum communication and its closest classical analog---private communication.This research endeavors to contribute definitively to realistic embodiments of large-scale quantum computers, which would dramatically improve mankind's ability to process and communicate information. And the research program itself is deeply interdisciplinary, bringing together physicists, computer scientists and mathematicians from industry and academia, and training students and postdocs.