  One of the central themes in classical cryptography is multi-party
computation, which performs joint computation on multiple participants' data
while maintaining data privacy. The extension to the quantum regime was
proposed in 2002, but despite two decades of research, the current
state-of-the-art multi-party quantum computation protocol for a fixed number of
parties (even 2 parties) requires unbounded rounds of communication, which
greatly limit its practical usage. In this work, we propose the first
constant-round multi-party quantum computation protocol for a fixed number of
parties against specious adversaries, thereby significantly reducing the
required number of rounds. Our work constitutes a key step towards practical
implementation of secure multi-party quantum computation, and opens the door
for practitioners to be involved in this exciting field. The result of our work
has wide implications to quantum fidelity evaluation, quantum machine learning,
quantum voting, and distributed quantum information processing.
