Regarding Optical Constructions of CNOT Gate

This post is based on a presentation made by S. Balakrishnan and R. Sankaranarayanan from the Department of Physics, National Institute of Technology, Tiruchirapalli, India, at the recently held APW 2010 in Cochin.

According to the authors, it is known that any n-qubit quantum circuit can be achieved using a sequence of one-qubit and two-qubit gates. However, finding an optimal two-qubit operation using a given family of gates is not easy.

A general two-qubit circuit can be achieved using three controlled NOT (CNOT) gates supplemented with one-qubit gates. In this sense, the CNOT is believed to be a universal gate. It is also important to find gates capable of constructing CNOT. Due to the significance of CNOT, its construction finds the essential part in the study of quantum gates.

In their work, the authors have presented various constructions of CNOTs, wherein three different gates have been employed. They find it worth mentioning that the proposed CNOT constructions are optimal as the number of two-qubit gates used are only two. These constructions may help in finding the experimental feasibility of the CNOT gate.

They conclude that local invariants of all of the above constructions are independent of the parameter 'n', which implies that all gates belong to the three edges that are capable of generating CNOT class. Also, the given constructions are optimal in the sense that the number of the non-logical gates utilized is only two.

In this context, it is worth identifying the suitable physical models for realizing these edges. For example, the anisotropic Heisenberg spin system may realize some of the gates that have been mentioned.

In another context, I must also mention that I was pleasantly surprised to be recently contacted by Mitsubishi's Thomas Tay. Apparently, he has read my earlier post on blue laser diodes. He sent me a message over LinkedIn, saying: “Mitsubishi Electric will be developing and introducing blue laser diode for the new application market.”

This is wonderful news. I've asked him to furnish some more details, which I hope to share with you, once I have those!

Pradeep