Overcoming efficiency constraints on blind quantum computation

Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraints only hold in limited scenarios and show how to overcome it using a method based on iterated gate-teleportations. We present our results as a family of protocols, with varying degrees of computational-ability requirements on the client. Certain protocols in this family exponentially outperform previously known schemes in terms of total communication. The approach presented here can be adapted to other distributed computing protocols to reduce communication requirements.