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The Journal of Chemical Physics

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

C. Gollub, Regina de Vivie‐Riedle

Published Apr 25, 2008• 6 citations
Publisher

Abstract

Suitable molecules for quantum computing cannot be discussed in terms of anharmonicity and CNOT gates alone. The validity of the approximate approach [M. Zhao and D. Babikov, J. Chem. Phys.126, 204102 (2007)] is limited. Frequencies and anharmonicities cannot be used independent from the molecule. Hermite polynomials with the linear approximation for the dipole moment lead to oversimplified gates with potentially low intensities.

DOI
10.1063/1.2907728

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Suitable molecules for quantum computing cannot be discussed in terms of anharmonicity and CNOT gates alone. The validity of the approximate approach [M. Zhao and D. Babikov, J. Chem. Phys.126, 204102 (2007)] is limited. Frequencies and anharmonicities cannot be used independent from the molecule. Hermite polynomials with the linear approximation for the dipole moment lead to oversimplified gates with potentially low intensities.
My thesis focuses on theoretical studies in the molecular quantum computing with vibrational qubits. We studied how the molecular vibrational properties affect the fidelity of the logic gates. Our approach is to encode states of the quantum information register into the vibrational eigenstates of a molecule and use the shaped laser pulse (femtosecond, infrared) to control the vibrational state-to-state transition. By using the Optimal Control Theory to shape a femtosecond laser and numerical propagation of laser-driven vibrational wave packets, we analyzed how the vibrational properties of a two-qubit system affect the accuracy of the quantum gates and how to effectively control the vibrational state-to-state transitions. From these studies, we found the anharmonicities are very important for the control of the vibrational state-to-state transitions and an intricate interplay between the frequencies and anharmonicities in the two-qubit system leads to the occurrence of resonances between different transitions in the vibrational manifold. Such resonances cause "leakage" of population into other vibrational states and hinder the control. From theoretical analysis of resonances, we formulate several criteria for selection of molecule for implementation of the vibrational two-qubit system. These criteria can help experimentalists to choose the best molecules to achieve accurate qubit transformations in the experiment.
A benchmark study of the approximate approach to the optimal control of vibrational qubits, which was used in the original paper [J. Chem. Phys.126, 204102 (2007)], is presented. Two simplified assumptions are used in this method: A linear approximation for the dipole moment function and a harmonic approximation for the vibrational wave functions. Both assumptions are often used in spectroscopy and are known to work well for many molecules when the vibrational excitation is low. Here, we show that our method works well for the OH molecule, which exhibits a very anharmonic spectrum of vibrational eigenstates and a complicated dipole moment function.
In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates.