Anharmonic properties of the vibrational quantum computer

Abstract

We developed an efficient approach to study the coherent control of vibrational state-to-state transitions. The approximations employed in our model are valid in the regime of the low vibrational excitation specific to the vibrational quantum computer. Using this approach we explored how the vibrational properties of a two-qubit system affect the accuracy of subpicosecond quantum gates. The optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The focus was on understanding the effect of the three anharmonicity parameters of the system. In the three-dimensional anharmonicity parameter space we identified several spots of high fidelity separated by low fidelity planar regions. The seemingly complicated picture is explained in terms of interferences between different state-to-state transitions. Very general analytic relationships between the anharmonicity parameters and the frequencies are derived to describe the observed features. Geometrically, these expressions represent planes in the three-dimensional anharmonicity parameter space. Results of this work should help to choose a suitable candidate molecule for the practical implementation of the vibrational two-qubit system.

Comment on “Anharmonic properties of the vibrational quantum computer” [J. Chem. Phys. 126, 204102 (2007)]

“…This finding supports our concern that the range selected in Ref. 1 2 and reflects that the properties favorable for NOT ͑Hadamard͒ gates are unfavorable for CNOT gates and vice versa and must be balanced. The approximate approach based on single point calculations represents, in principle, an interesting alternative to the ab initio based approach, but cannot be regarded as more accurate.…”

“…Furthermore, it is not possible to use a single point calculation of naphthalene combined with an anharmonicity range not at all connected to the molecule like in Ref. 1. It is not surprising that such a short CNOT gate of 0.75 ps can be realized for naphthalene under these assumptions.…”

“…In their article, 1 Zhao and Babikov investigate the relation between anharmonicities and a controlled NOT ͑CNOT͒ gate for quantum computing ͑QC͒ with vibrational qubits. A two-qubit model related to naphthalene is setup.…”

Response to “Comment on ‘Anharmonic properties of the vibrational quantum computer’ ” [J. Chem. Phys. 128, 167101 (2008)]

“…͑8͒ in Ref. 1. Both assumptions are often used in spectroscopy and are known to work well for many molecules when the vibrational excitation is low.…”

“…In our original paper, 1 we used an approximate method to study the optimal control of vibrational qubits in a model system. Two simplified assumptions were used in our approach: A linear approximation for the dipole moment function, Eq.…”