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Physical Review Letters

Quantum optical Fredkin gate

Gerard J Milburn

Published May 1, 1989• 437 citations
Publisher

Abstract

A simple optical model to realize a reversible, potentially error-free logic gate---a Fredkin gate---is discussed. The device dissipates no energy and makes use of the Kerr nonlinearity to produce intensity-dependent phase shifts. The analysis shows that quantum mechanics permits the operation of error-free logic gates which dissipate no energy. However, even though the device is nondissipative, error-free performance only occurs under particular operating conditions.

DOI
10.1103/physrevlett.62.2124

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A simple optical model to realize a reversible, potentially error-free logic gate---a Fredkin gate---is discussed. The device dissipates no energy and makes use of the Kerr nonlinearity to produce intensity-dependent phase shifts. The analysis shows that quantum mechanics permits the operation of error-free logic gates which dissipate no energy. However, even though the device is nondissipative, error-free performance only occurs under particular operating conditions.
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.
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.
Quantum phase slip junction (QPSJ) can offer very low power switching operation and represent near adiabatic switching operation for using in designing of the reversible logic gates. The reversible gates have logical reversibility, where the inputs can be logically reconstructed from the outputs and no data is lost, and physical (adiabatic) reversibility, where the energy dissipation can be decreased even below the Landauer limit. In this manuscript, for the first time, designing of the QPSJ-based basic reversible gates, namely Feynman, Toffoli, Peres and Fredkin, from the logical reversibility point of view is represented. The main logic function in these gates is the XOR function. First, a new two-input QPSJ-based XOR gate with simple circuit is designed in which the outputs of the previous gate can be connected directly to its inputs without the need for splitter lines. Second, the proposed XOR gate is used to design the Feynman and Toffoli gates. Further, the Peres and Fredkin gates are designed by using the proposed Feynman and Toffoli gates. Proper operation of the proposed gates are verified by simulation results. Logical reversibility of the Feynman and Toffoli gates is verified by cascading them and operating their logical function two times, i.e.f(f(x))=x.
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.
Abstract Reversible gate has been one of the emerging research areas that ensure continual process of innovation trends that explore and utilizes the resources. Due to the increasing power consumption of electronic circuits, it has been observed that quantum computing is one of its latest applications. This technology can be utilized by reducing the energy consumption by preserving the bits of information that are still useful. A photon has zero rest mass, while an electron has a nonzero rest mass. These characteristics inspired the researchers to develop an all-optical Fredkin gate. The proposed gate design overcomes the shortcomings of conventional Fredkin gates and provides better performance.