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Acta Physica Sinica

Realization of quantum fredkin gate in optics

Lin Qing, 福建省华侨大学厦门校区信息科学与工程学院,厦门 361021

Published Jan 1, 2009• 2 citations
Publisher

Abstract

In this article, an experimental scheme of quantum Fredkin gate is proposed. This scheme is based on the cross-Kerr effect between the photons and the ancillary coherent state. Only one coherent state is required, while the single photon detector and the coincidence measurement are not required, so this Fredkin gate is scalable. In addition, this is a nearly deterministic gate with the success probability 1/133, and it is feasible with the current experimental technology in optics.

DOI
10.7498/aps.58.5983

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In this article, an experimental scheme of quantum Fredkin gate is proposed. This scheme is based on the cross-Kerr effect between the photons and the ancillary coherent state. Only one coherent state is required, while the single photon detector and the coincidence measurement are not required, so this Fredkin gate is scalable. In addition, this is a nearly deterministic gate with the success probability 1/133, and it is feasible with the current experimental technology in optics.
A Fredkin gate is an indispensable logic gate for the applications of the scalable quantum network. Weak cross-Kerr nonlinearities serve as the intermediary between photons and coherent states and thus provide the indirect interaction between photons. By means of weak cross-Kerr nonlinearities, we propose a construction scheme of a nearly deterministic Fredkin gate, where polarization modes of photons carry quantum bits. By virtue of an X homodyne measurement on the coherent state, the appropriate classical feed-forward operations are executed according to the different measurement outcomes. Applying one swap gate and two combination gates and other assistant simple optical elements, the nearly deterministic Fredkin gate is successfully constructed. The unique features of photons as quantum information carriers with high velocity and low decoherence, combined with simple elements and mature operation techniques, afford the possibility to the scheme proposed here which takes aim at feasible quantum logic circuits for practical and scalable quantum computation and quantum communication.
In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called controlled-path gate with which the realization of all possible bipartite positive-operator-value measurements of two-photon polarization states may be nearly deterministic. Following the same technique, the realization of quantum control gates, including the controlled-NOT gate, Fredkin gate, Toffoli gate, arbitrary controlled-U gate, and even arbitrary multicontrolled-U gate, are proposed. The corresponding probabilities are 1∕21∕21∕2, 1∕81∕81∕8, 2∕232∕232∕23, etc., respectively. Only the coherent states are required but not any ancilla photons, and no coincidence measurement are required, which results in these gates being scalable. The structures of these gates are very simple, therefore we think they are feasible with the current experimental technology in optics.
A scheme is proposed to implement the optical quantum Fredkin gate with weak nonlinearities and feed-forward. The distinctive feature of the present scheme is that the present Fredkin gate has four sets of possible output ports, and the total success probability for each set of the output ports is near 1/4 without ancillary single-photon. The present scheme requires nonlinear strength of the order of 10−3 and mean photon number of the probe coherent beam of the order of 106 so that the discrimination error probability does not exceed 10−4. These features show that it is still possible to operate in the regime of weak cross-Kerr nonlinearities, and the amplitude of the probe coherent beam is physically reasonable with current technology. These facts make us more confident in the feasibility of the proposed scheme.
We propose a scheme for linear optical quantum Fredkin gate based on the combination of recently experimentally demonstrated linear optical partial-SWAP gate and controlled-Z gates. Both heralded gate and simplified post-selected gate operating in the coincidence basis are designed. The suggested setups have a simple structure and require stabilization of only a single Mach-Zehnder interferometer. A proof-of-principle experimental demonstration of the post-selected Fredkin gate appears to be feasible and within the reach of current technology.