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The Journal of Chemical Physics

Implementation of quantum gate operations in molecules with weak laser fields

Yoshiaki Teranishi, Yukiyoshi Ohtsuki, Kouichi Hosaka, H. Chiba, Hiroyuki Katsuki, Kenji Ohmori

Published Mar 17, 2006• 24 citations
Publisher

Abstract

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.

DOI
10.1063/1.2172605

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We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.
For practical realization of quantum information processing we need a quantum system that provides reliable preparation of the initial state, high-fidelity quantum gate operations, error tolerance, readout of the result of quantum computation and scalability of the system to increase the number of qubits. In this dissertation we show how these requirements can be addressed for molecular quantum computer. For computational study of quantum information processing with molecules we employ thiophosgene (SCCl2) molecule that has been used as a test system for quantum control experiments [Mol. Phys. 105, 1999 (2007)]. We investigate the gateway scheme of control in which transitions between the vibrational states that encode qubits are only allowed through the intermediate “gateway” state in the B electronic state. This scheme of control provides reliable preparation of the initial qubit state and allows using UV/vis laser pulses. We demonstrate that high-fidelity quantum gates are possible to achieve in molecular quantum computer. The optimal control theory is employed to obtain a shape of laser pulse that performs CNOT gate with ~0.9999 fidelity. Analysis of frequency profile of the optimal pulse shows that preparation of the high-fidelity computational pulse requires only 64 frequency channels. Error tolerance of the computational pulse is studied by modifying amplitudes and phases of frequency components. It is shown that gate fidelity remains high after small modifications are introduced to the optimal pulse. The scheme of readout of quantum information using quantum beat spectroscopy is proposed. The quantum beat signal is obtained from excitation of the final superposition of the qubit states to a readout state in the B electronic state with a time-delayed pulse. We find that fitting the quantum beat signal with a standard fitting expression produces a phase error and propose a new accurate expression that includes phase correction term. The system of two atomic ions trapped in a double-well potential is also studied as a first step towards scalable quantum computation with trapped molecular ions. The rigorous computational treatment of the system provides explanation of the vibrational energy transfer between the ions in terms of wave packet dynamics in the accurate asymmetric potential.
Within the scope of molecular quantum computing with vibrational qubits, we analyse the impact of phases that are present during the quantum computation processes. While the phase relation in superposition states and its temporal evolution are crucial to any implementation of quantum computing, we elucidate the special challenge that emerges for phase control of qubits encoded in molecular vibrational eigenstates. Phase correctly prepared superposition states in general exist only for a finite time and with the inherent entanglement in molecular vibrational qubit systems their development displays a complex pattern. We show that the free relative phase evolution in such qubit systems can be utilized for the implementation of quantum phase gates. Moreover, a practical experimental realization of phase correct quantum gates acting on molecular vibrational qubits could be accomplished by a decomposition into laser-induced population transfer and free evolution phase gates. This concept adds to the flexibility in the implementation of quantum gate sequences and algorithms. A modification, where only a reduced number of selected relative phases needs to be adjusted, will make this scheme more robust and versatile. Finally, we also disclose and discuss another key feature for the implementation of phase correct quantum gates, i.e. the dependence of the quantum gate fidelity on the absolute or carrier-envelope phase of the driving femtosecond laserfield.
A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.
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In order to use molecular vibrations for quantum information processing one should be able to shape infrared laser pulses so that they can play the role of accurate quantum gates and drive the required vibrational transitions. In this paper we studied theoretically how the relative phase of the optimized transitions affects accuracy of the quantum gates in such a system. Optimal control theory and numerical propagation of laser-driven vibrational wave packets were employed. The dependencies observed for one-qubit gates NOT, pi-rotation, and Hadamard transform are qualitatively similar to each other. The results of the numerical tests agree well with the analytical predictions.