**Optical
generation of non-classical states**

**toward universal quantum computation**

**
**

A quantum computer, which uses nature of quantum mechanics for computing, is a promising device to efficiently solve some problems beyond present classical computers [1]. Univesal quantum computing requires certain quantum gates as well as classical computers consist of NAND gates. In the field of continuous variable quantum information processing, it is known that we can build the quantum computer by exploiting only five optical-quantum gates in principle [2]. In our laboratory, four of them have been already implemented [3]. Our present challenge is to realize the last fifth gate. This is called “cubic phase gate”, a key block of universal quantum computing.

It is theoretically shown that the cubic phase gate can be realized by combining quantum teleportation technologies and one highly-nonclassical quantum state [4], represented by a superposition of zero- to three-photon-number states. Although some experiments of generating superpositions of photon-number states have been reported [5, 6], they were limited up to two-photon level. Furthermore, the generated states in their experiments undergo a nearly fifty percent loss in the process of generation and measurement. This is probably because they exploited the pulsed scheme so that they couldn’t get high measurement efficiency. Since the quantum teleportation circuit for the cubic phase gate requires high measurement efficiency, the systems of the previous experiments are not suitble for our purpose.

In 2013, based on the continuous wave scheme, we achieved generation of arbitrary superpositions of zero- to three-photon-number states with 80% high-efficiency [7]. In the same scheme we also generated the state required for the cubic phase gate, whose non-classicality has been verified [8]. With this scheme, together with quantum teleportation technologies, we are now trying to implement the cubic phase gate.

Fig. 1. Experimental schematic of non-classical superposition state generation. When we get simultaneous clicks of three APDs in the Trigger mode, we immediately know that we have the desired non-classical state in the Signal mode.

Fig. 2. Experimentally obtained density matricies and Wigner functions of photon-number superposition states (hbar = 1). The state (c) is the very one for the cubic phase gate.

**Bibliography**

[1] M. A. Nielsen and I. L. Chuang, *Quantum Computation and Quantum Information*,
Cambridge University Press, Cambridge (2004).

[2] A. Furusawa and P. van Loock, *Quantum Teleportation and Entanglement*,
Wiley-VCH, Berlin (2011)

[3] R. Ukai *et al*., Phys. Rev. Lett. **106**,
240504 (2011).

[4] P. Marek *et al*., Phys. Rev. A **84**,
053802 (2011).

[5] A. I. Lvovsky and J. Mlynek, Phys.
Rev. Lett. **88**, 250401 (2002).

[6] E. Bimbard *et al*., Nat. Photon. **4**,
243 (2010).

[7] M. Yukawa *et al*., Opt. Express **21**,
5529 (2013).

[8] M. Yukawa *et al*., Phys. Rev. A **88**,
053816 (2013).