The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
arXiv:1607.05256
Abstract
These are lecture notes from a weeklong course in quantum complexity theory taught at the Bellairs Research Institute in Barbados, February 21-25, 2016. The focus is quantum circuit complexity---i.e., the minimum number of gates needed to prepare a given quantum state or apply a given unitary transformation---as a unifying theme tying together several topics of recent interest in the field. Those topics include the power of quantum proofs and advice states; how to construct quantum money schemes secure against counterfeiting; and the role of complexity in the black-hole information paradox and the AdS/CFT correspondence (through connections made by Harlow-Hayden, Susskind, and others). The course was taught to a mixed audience of theoretical computer scientists and quantum gravity / string theorists, and starts out with a crash course on quantum information and computation in general.
111 pages, 10 figures. Includes a special guest lecture by Adam Bouland and Luke Schaeffer. Enormous thanks to them, Anil Ada, Denis Therien, and the scribes, without whom these notes wouldn't have happened. Comments welcome