There are growing interests to provide telephone services over the Internet. In particular, Internet services providers (ISPs) may become the next generation telephone company especially in providing international telephone services. This paper proposes a novel method called quantum IP (QIP) for transporting international voice traffic over the Internet via QIP routers. Emulating the traditional circuit switching technique, the basic concept of QIP is to pack voice traffic being sent to the same next-hop QIP router as small QIP cells (virtual time slots) into quantum packets (virtual time frames). Quantum packets are then routed to the destined QIP routers over the Internet accordingly. The proposed method shortens packetization delay and facilitates interconnection with existing telephone networks.