Generalized GHZ States and Distributed Quantum Computing

Abstract

A key problem in quantum computing is finding a viable technological path toward the creation of a scalable quantum computer. One possible approach toward solving part of this problem is distributed computing, which provides an effective way of utilizing a network of limited capacity quantum computers. In this paper, we present two primitive operations, cat-entangler and cat-disentangler, which in turn can be used to implement non-local operations, e.g. non-local CNOT and quantum teleportation. We also show how to establish an entangled pair, and use entangled pairs to efficiently create a generalized GHZ state. Furthermore, we present procedures which allow us to reuse channel qubits in a sequence of non-local operations. These non-local operations work on the principle that a cat-like state, created by cat-entangler, can be used to distribute a control qubit among multiple computers. Using this principle, we show how to efficiently implement non-local control operations in many situation, including a parallel implementation of a certain kind of unitary transformation. Finally, as an example, we present a distributed version of the quantum Fourier transform.