  We investigate definitions of and protocols for multi-party quantum computing
in the scenario where the secret data are quantum systems. We work in the
quantum information-theoretic model, where no assumptions are made on the
computational power of the adversary. For the slightly weaker task of
verifiable quantum secret sharing, we give a protocol which tolerates any t <
n/4 cheating parties (out of n). This is shown to be optimal. We use this new
tool to establish that any multi-party quantum computation can be securely
performed as long as the number of dishonest players is less than n/6.
