Among various methods for constructing the quantum bits (qubits) required to perform the quantum computing, there is the concept to use the exciton in nano-structured material such as semiconductor quantum dot (QD), colloidal nanocrystal, or molecule. When the presence/absence of exciton is associated with two-level system of |1>/|0>, the Rabi oscillation of exciton serves as a basis for one-qubit operation. In order to realize the controlled-NOT (CNOT) gate which is essential for the quantum computing, one needs four-level system consisting of two qubits (i.e., |0>|0>, |1>|0>, |0>|1>, and |1>|1>). The construction of exciton CNOT gate is theoretically possible, however, the experimental demonstration has not been conducted. The optical processes of carbon nanotubes are governed by excitons. We attempted to realize the exciton CNOT gate by using the coupled QDs formed in a carbon nanotube.

We fabricated two QDs by terminating both ends of a single-walled carbon nanotube (SWNT) with the collagen model peptides via peptide bonds. The scanning tunneling microscopy and spectroscopy measurements revealed that two QDs of ~ 3.1 nm and ~ 3.9 nm in widths, respectively, were formed in that SWNT with the inter-dot spacing of ~ 5.4 nm. It was confirmed by observing the Rabi oscillations that each QD acted as the exciton two-level system. When the excitons were produced in both QDs, additional exciton emission lines appeared, which may be originating from the coupled state of excitons across two QDs. We define the exciton four-level system as follows; |0>|0> when both QDs are empty, |1>|0>/|0>|1> when exciton is present in either of two QDs, and |1>|1> when excitons coupled across two QDs are generated. |1>|0>, |0>|1>, or |1>|1> could be prepared by irradiating the corresponding π pulse determined from the Rabi oscillation.

The CNOT gate consists of a control qubit and a target qubit, and the logic of the target qubit is flipped only if the control qubit is in logic |1>. When we regard two QDs in our sample as a pair of control qubit and target qubit, the conditional flip of the target qubit corresponds to the π pulse-induced transition between |1>|1> and |1>|0> or between |1>|1> and |0>|1> depending on which QD we choose for the target qubit. The exciton CNOT gate operations were executed by irradiating that π pulse onto the states prepared as inputs. The input/output relations were measured in both ZZ and XX bases, which allowed us to estimate the quantum process fidelity. Our exciton CNOT gate actualized the expected operations whichever QD we used as the target qubit. By executing the CNOT gate operations three times, logic exchange is made between |1>|0> and |0>|1>, which is called the SWAP gate. It was also ascertained that the exchange of the exciton population took place between two QDs when conducting the SWAP operation by applying our CNOT gate.