Quantum-Classical Tradeoffs for Information-Processing Tasks

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Quantum information science investigates the use of quantum mechanics to performinformation-processing tasks more efficiently than could be done using only classicalresources. To assess the efficacy of quantum information, it is crucial to compare thequantum and classical resources required for particular tasks. The funding climate in theUnited States, dominated by security and defense agencies, has favored investigationsof two particular tasks, quantum computation and quantum key distribution. Thoughthese are important applications of quantum information, focusing on them is perhapsnot the best strategy for assessing quantum-classical tradeoffs or discovering newapplications. This proposal addresses this question by suggesting research on twotopics where quantum-classical tradeoffs can be investigatedrigorously: Clifford and post-Clifford circuits and classical restricted-coordinateproblems.