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International Journal of Quantum Information

IMPLEMENTATION OF SWAP GATE AND FREDKIN GATE USING LINEAR OPTICAL ELEMENTS

Meng-Zheng Zhu, Ye Liu

Published Apr 1, 2013• 9 citations
Publisher

Abstract

A scheme is proposed to directly implement the optical swap gate and quantum Fredkin gate based on the Mach–Zehnder interferometer (MZI). The distinct advantage of the present scheme is that ancilla single-photons are not needed. The optical swap gate is deterministic and does not need the photon number resolving detectors. The total success probability of the present Fredkin gate can reach 1/16 by using basic linear-optics elements.

DOI
10.1142/s0219749913500317

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A scheme is proposed to directly implement the optical swap gate and quantum Fredkin gate based on the Mach–Zehnder interferometer (MZI). The distinct advantage of the present scheme is that ancilla single-photons are not needed. The optical swap gate is deterministic and does not need the photon number resolving detectors. The total success probability of the present Fredkin gate can reach 1/16 by using basic linear-optics elements.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only ddd PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.
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.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to their relatively easy manipulation and realization. We present efficient schemes to implement controlled-not (cnot) gates and controlled-swap (Fredkin) gates by using solely linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd level), respectively. On the basis of the hybrid encoding, cnot and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a cnot gate has been reduced to one polarizing beam splitter, while only ddd polarizing beam splitters are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to 1 and and are dimension independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7% under realistic conditions, which is higher than in previous schemes.
We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.
The majority of linear-optical nondestructive implementations of universal quantum gates are based on single-photon resolving detectors. We propose two implementations, which are nondestructive (i.e., destroying only ancilla states) and work with conventional detectors (i.e., those which do not resolve a number of photons). Moreover, we analyze a recently proposed scheme of Wang [J. Opt. Soc. Am. B27, 27 (2010)] of an optical iSWAP gate based on two ancillae in Bell’s states, classical feedforward, and conventional detectors with the total probability of success equal to η4/32, where η is detector’s efficiency. By observing that the iSWAP gate can be replaced with the controlled NOT gate with additional deterministic gates, we list various possible linear-optical implementations of the iSWAP gate: (i) assuming various ancilla states (unentangled, two-photon, and multiphoton-entangled states) or no ancillae at all, (ii) with or without classical feedforward, (iii) destructive or nondestructive schemes, and (iv) using conventional or single-photon detectors. In particular, we show how the nondestructive iSWAP gate can be implemented with the success probability of η4/8 assuming the same ancillae, classical feedforward, and a fewer number of conventional detectors than those in the scheme of Wang et al. We discuss other schemes of the nondestructive universal gates using conventional detectors and entangled ancillae in a cluster state, and Greenberger–Horne–Zeilinger and Bell’s states giving the success probabilities of η4/4, η6/8, and η4/8, respectively. In the latter scheme, we analyze how detector imperfections (dark counts in addition to finite efficiency and no photon-number resolution) and imperfect sources of ancilla states deteriorate the quantum gate operation.