Mathematical synthesis of application and theory in quantum error correction

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As computer chips and transistors shrink in size, engineers will eventually be forced to use objects such as electrons and atoms to encode bits of information, and hence will be forced to deal with the mysterious "quantum world". Scientists have recognized this as a central issue for several decades, but only within the past decade was it shown that quantum effects could be harnessed for a new kind of "quantum computing" that would quite simply revolutionize the world of computing and cryptography, as we know it. The experimental and theoretical progress of recent years has generated tremendous excitement within the scientific community, but there are still many fundamental issues to overcome if the promises of quantum computing and cryptography are to be realized. Extending these successes to large-scale many body quantum systems is one of the most difficult and intriguing problems in modern science.