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Journal of the Optical Society of America B

Scheme for implementing linear optical quantum iSWAP gate with conventional photon detectors

Hong‐Fu Wang, Xiao‐Qiang Shao, Yongfang Zhao, Shou Zhang, Kyu-Hwang Yeon

Published Dec 11, 2009• 8 citations
Publisher

Abstract

A simple scheme is proposed to implement a two-qubit linear optical quantum iSWAP gate that is a universal gate in quantum computation and quantum information processing. By the interference effect of the polarized photons, a quantum iSWAP gate can be achieved with a low success probability (η4/32, with η being the quantum efficiency of photon detectors). The scheme is based only on simple linear optical elements, a pair of two-photon polarization entangled states, and conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states, which greatly decreases the experimental difficulty of implementing linear optical quantum computation.

DOI
10.1364/josab.27.000027

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A simple scheme is proposed to implement a two-qubit linear optical quantum iSWAP gate that is a universal gate in quantum computation and quantum information processing. By the interference effect of the polarized photons, a quantum iSWAP gate can be achieved with a low success probability (η4/32, with η being the quantum efficiency of photon detectors). The scheme is based only on simple linear optical elements, a pair of two-photon polarization entangled states, and conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states, which greatly decreases the experimental difficulty of implementing linear optical quantum computation.
We propose a linear optical scheme to implement the nondeterministic two-qubit controlled phase gate with the certain success probability. The proposed setup involves simple linear optical elements, a pair of the two-photon polarization entangled states, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This can greatly simplify the experimental realization of a linear optical quantum computer.
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.
We propose a protocol to controlled implement the two-photon controlled phase gate within a network by using interference of polarized photons. The realization of this protocol is appealing due to the fact that the quantum state of light is robust against the decoherence, and photons are ideal carriers for transmitting quantum information over long distances. The proposed setup involves simple linear optical elements and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. This can greatly simplify the experimental realization of a linear optical quantum computer.
We present a linear optical scheme for implementing two-bit discrete quantum Fourier transform based only on simple linear optical elements, a pair of two-photon polarization entangled states, and the conventional photon detectors that only distinguish between the presence and absence of the photons. The scheme can be implemented with a certain success probability, and the implementation of the scheme in experiment would be an important step towards more complex linear optical quantum computation.
Optical quantum computation was limited to a few photon applications such as quantum cryptography and partial teleportation until 2001. Then the possibility of performing arbitrary logic conditional on certain detection outcomes was introduced by Knill, Laflamme and Milburn ( Nature 2001 409 46). Simple circuits consisting of single photon sources, entangled pair sources, linear optical elements and high efficiency photon counting detectors can be used to develop probabilistic two-photon logic gates. Initially such gates show a low probability of success but can approach the success rate of deterministic (non-linear) logic at the cost of added complexity. These developments have led to the emergence of a novel field of research aimed at improving the efficiency of linear logic and developing the efficient sources and detectors for its implementation. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is devoted to recent advances in this field. Key to all linear optics gates is the interference effect between separate photons that have no previous history. In this issue we include the first experiment to show such an effect (Rarity et al ), on which many later experiments are based. These interference effects can then be used to entangle separate pairs of particles into higher order entangled states (Zou et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 119–121) and also to establish entanglement between matter qubits (Kok et al ). Quantum dot single photon sources suitable for linear optics quantum logic are discussed in the paper by Unitt et al while a waveguide source of pair photons is presented by Ducci et al . The difficulties in scaling linear optics quantum computing arise from the low success probabilities of the gates. Introducing a small amount of non-linearity could allow unit efficiency gates to be designed (Munro et al ) while large non-linearities generated by the collective effects in EIT could be used to implement a wide variety of quantum logic functions (Petrosyan). The development of algorithms suitable for optical implementation is addressed by Ellinas et al . Key contributors to this issue are collaborating in the project IST:38864 RAMBOQ which has a primary goal of developing linear optics computation tools and techniques.