  We propose a new concept, oblivious quantum computation, which requires
performing oblivious transfer with respect to the computation outcome of the
quantum computation, where the secrecy of the input qubits and the program to
identify the quantum gates are required. Exploiting quantum teleportation, we
propose a two-server protocol for this task, which realizes an exponential
improvement for the communication complexity over the simple application of
two-server (quantum) oblivious transfer to the sending of the computation
result. Also, we discuss delegated multiparty quantum computation, in which,
several users ask multiparty quantum computation to server(s) only using
classical communications. We propose a two-server protocol for the latter task
as well.
