# The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes

@article{Aaronson2016TheCO, title={The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes}, author={Scott Aaronson}, journal={Electron. Colloquium Comput. Complex.}, year={2016}, volume={TR16} }

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…

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