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Physics of Particles and Nuclei Letters

Possible implementation of CNOT and CCNOT gates

I. Yu. Popov, George P. Miroshnichenko, Alexander Trifanov

Published Nov 19, 2009• 0 citations
Publisher

Abstract

The quantum optical gate CCNOT based on five level atomic scheme is discussed. The qubits are encoded in polarization properties of three optical beams. The nonlinear cross Kerr effect is used for getting nonlinear phase shifts in these beams. A way of CNOT implementation using coupled double quantum wells is suggested. The device is described in the framework of the model based on the operator extensions theory.

DOI
10.1134/s1547477109070218

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The quantum optical gate CCNOT based on five level atomic scheme is discussed. The qubits are encoded in polarization properties of three optical beams. The nonlinear cross Kerr effect is used for getting nonlinear phase shifts in these beams. A way of CNOT implementation using coupled double quantum wells is suggested. The device is described in the framework of the model based on the operator extensions theory.
Possible optical implementation of CCNOT gate based on the M-configuration system of atomic levels is discussed. The semiclassical estimations of summary conditional phase shift for the corresponding Controlled Phase Shift (CPS) operator are got. To this end the nonlinear optical phenomena (such as EIT) connected with resonant interaction of electromagnetic field acting on the four transients of five level atomic system with M-configuration (in stationary operating mode) is investigated. It is shown that the M-scheme may be used for implementation of CCNOT gate.
It is known that photons are the ideal carriers of quantum information and ensemble of atoms can be acted as the long lived storage and processing units. In the coherently prepared atomic ensemble with the light resonantly interacting with the atoms, various schemes have been proposed to implement quantum state transfer and storage, quantum phase gate, generation of entangled photons, and the long-distance quantum communication [1]. We first proposed the dark-state polaritons in a five-level M-type atomic ensemble in the electro magnetically induced transparency (EIT) [2], Under conditions of the low excitation limit and adiabatic following, the quantum field can be mapped onto the atomic polarization states, forming the shape preserving quantum states of polaritons. Two channels for robust quantum memory are provided. Then, we investigated the nonlinear optical response of a five-level tripod atomic system in the EIT, and proposed a three-qubit phase gate protocol based on the fifth-order nonlinearity [3]. The cross phase modulation among three weak fields induced by the fifth-order nonlinearity in EIT can produce the phase shift of order n, which can be used to realize the three-qubit polarization phase gate. Finally, we proposed a cavity-QED scheme that can effectively generate EPR polarization-entangled photon pairs [4], A four-level tripod atom successively couples to two high-Q optical cavities possessing polarization degeneracy, assisted by a classical π-polarized pump field. The stimulated Raman adiabatic passage process in the atom-cavity system is used to produce the polarization-entangled photon pairs. The proposal is particularly robust against atomic spontaneous decay. The above protocols should have potential applications in quantum information processing.
We first investigate the nonlinear optical response of a five-level tripod atomic system in electromagnetically induced transparency and then propose a 3-qubit phase gate protocol based on the fifth-order nonlinearity. The cross-phase modulation among the three weak fields induced by the fifth-order nonlinearity in electromagnetically induced transparency can produce the phase shift of order π, which can be used to realize the 3-qubit polarization phase gate. This protocol should have potential applications in quantum information processing.
Quantum logic operations can be implemented using nonlinear phase shifts (the Kerr effect) or the quantum Zeno effect based on strong two-photon absorption. Both approaches utilize three-level atoms, where the upper level is tuned on resonance for the Zeno gates and off-resonance for the nonlinear phase gates. The performance of nonlinear phase gates and Zeno gates are compared under conditions where the parameters of the resonant cavities and three-level atoms are the same in both cases. It is found that the expected performance is comparable for the two approaches, despite the apparent differences in the way they are implemented.
The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.