I will survey recent feasibility results on building cryptographic primitives which manipulate quantum data. The focus will be protocols for secure evaluation of quantum circuits. Along the way, I'll discuss earlier results on the authentication and encryption of quantum states, and the relationship between secret sharing and error-correction in quantum information theory.
Based on joint work with subsets of Howard Barnum, Michael Ben-Or, Claude Crepeau, Daniel Gottesman, and Avinatan Hasidim. (STOC '02, FOCS '02, Eurocrypt '05, FOCS '06).