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Communications in Theoretical Physics

Allowable Generalized Quantum Gates Using Nonlinear Quantum Optics

Chunyan Li, Junlin Li

Published Jan 1, 2010• 6 citations
Publisher

Abstract

In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross-Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.

DOI
10.1088/0253-6102/53/1/17

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In this paper, we give an efficient physical realization of a double-slit duality quantum gate. Weak cross-Kerr nonlinearity is exploited here. The probability of success can reach 1/2. Asymmetrical slit duality control gate also can be constructed conveniently. The special quantum control gate could be realized easily in optical system by our current experimental technology.
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.
The controlled phase gate is one of the most important logic gates in the quantum computation field. In this paper, we proposed a protocol for implementing the two-qubit controlled phase gates with the help of cross-Kerr nonlinearity, optical elements and the conventional photon detectors, which are feasible with existing experimental technology. The protocol also can be applied to implement the controlled phase gates of many different atomic and photonic degrees of freedom with successful probability of 100%, that is, our protocol is efficient and flexible.
We propose a protocol to direct implement the two-qubit controlled phase gate with cross-Kerr nonlinearity by using the interference of polarized photons. The protocol is based on optical elements, single polarization photons, cross-Kerr nonlinearity and the conventional photon detectors, which are feasible with existing experimental technology. Compared with Zou's protocol ( Phys. Rev. 2007 A 75 034302), this protocol is to replace the entangled state resources used by Zou with much simpler single-photon resources and has a higher success probability. All these advantages make this protocol more efficient and more convenient than others in the applications in quantum communication.
Schemes for two-qubit and three-qubit controlled gates based on cross-Kerr nonlinearity are proposed in this paper. The probability of the success of these gates can be increased by quantum nondemolition detectors, which are used to judge which paths the signal photons pass through. These schemes are almost deterministic and require no ancilla photon. The advantages of these gates over the existing ones include less resource consumption and a higher probability of success, which make our schemes more feasible with current technology.
On the basis of the probe coherent state and weak cross-Kerr nonlinearities, we present a scheme of a nearly deterministic Controlled-NOT gate. In this construction, feed-forward methods, quantum nondemolition detectors and several optical elements are applied. It is a potentially practical quantum gate with certain features. First, the lack of auxiliary photons is allowable, which decreases consumption of resources. Secondly, employment of the signal photon from either of target output ports and three quantum nondemolition detectors enable the success probability to approach unit and judge whether the signal photons lose or not. Thirdly, the displacement measurement is adopted, and thus the Controlled-NOT gate works against photon loss of the probe coherent state. Finally, in order to circumvent the effect of dephasing, the monochromatic signal photons are exploited.
We present a realization of two-qubit controlled-phase gate, based on the linear and nonlinear properties of the probe and signal optical pulses in an asymmetric GaAs/AlGaAs double quantum wells. It is shown that, in the presence of cross-phase modulation, a giant cross-Kerr nonlinearity and mutually matched group velocities of the probe and signal optical pulses can be achieved while realizing the suppression of linear and self-Kerr optical absorption synchronously. These characteristics serve to exhibit an all-optical two-qubit controlled-phase gate within efficiently controllable photon-photon entanglement by semiconductor mediation. In addition, by using just polarizing beam splitters and half-wave plates, we propose a practical experimental scheme to discriminate the maximally entangled polarization state of two-qubit through distinguishing two out of the four Bell states. This proposal potentially enables the realization of solid states mediated all-optical quantum computation and information processing.