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Frontiers in Optics

Entangled-State Quantum Gates With Directionally Unbiased Linear-Optical Multiports

Alexander V. Sergienko, David S. Simon, Casey A. Fitzpatrick

Published Jan 1, 2016• 0 citations
Publisher

Abstract

The concept of directionally unbiased optical multiport is introduced, in which photons may reflect back out the input direction. It acts as universal Bell-state processor to implement probabilistic quantum gates acting on state symmetries.
DOI
10.1364/fio.2016.ff5d.3

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The concept of directionally unbiased optical multiports is introduced, in which photons may reflect back out the input direction. A linear-optical implementation is described, and the simplest three-port version studied. Symmetry arguments demonstrate potential for unusual quantum information processing applications. The devices impose group structures on two-photon entangled Bell states and act as universal Bell-state processors to implement probabilistic quantum gates acting on state symmetries. These multiports allow optical scattering experiments to be carried out on arbitrary undirected graphs via linear optics and raise the possibility of linear-optical information processing using group structures formed by optical qudit states.
Summary form only given. Quantum computers have been shown to be capable of performing certain kinds of tasks exponentially faster than classical computers. As a result, an enormous amount of effort has gone into their development. Although advances have been made, the ultimate goal of a large-scale programmable, general-purpose quantum computer still seems to be a relatively long way off. Therefore it is useful to consider returning to Feynman's original motivation for discussing quantum computers: using simple quantum systems to simulate the behavior of more complicated physical systems.Here we introduce a linear-optical arrangement that restores the symmetry: it is directionally unbiased. This arrangement, which can be thought of from multiple viewpoints (as a directionally unbiased multiport BS, as a resonant cavity with three or more exit directions, or as a scattering vertex for an undirected graph), is generalizable to any number of ports n = 3; we focus on the simplest case of n = 3. Despite its simplicity, the high degree of symmetry and the ability of photons to reverse direction lead to interesting properties that allow it to be used as the basis for a variety of applications related to quantum information processing [1].
A particular type of linear optical multiport, the Grover four-port, has previously been shown to couple the spatial symmetry of a photon to its direction of travel. It is shown here that use of a nonstandard choice of qubit, based on symmetry, allows Grover four ports to act as compact, low-resource deterministic linear optical controlledNOTgates, with no post-selection or ancilla measurements required. This approach allows programmable devices, made from Grover multiports in combination with other standard optical components, that can implement multiple different one-, two-, and three-qubit gates, including the Fredkin and Toffoli gates.
Linear optical multiports are widely used in photonic quantum information processing. Naturally, these devices are directionally-biased since photons always propagate from the input ports toward the output ports. Recently, the concept of directionally-unbiased linear optical multiports was proposed. These directionally-unbiased multiports allow photons to propagate along a reverse direction, which can greatly reduce the number of required linear optical elements for complicated linear optical quantum networks. Here, we report an experimental demonstration of a 3 × 3 directionally-unbiased linear optical fiber multiport using an optical tritter and mirrors. Compared to the previous demonstration using bulk optical elements which works only with light sources with a long coherence length, our experimental directionally-unbiased 3 × 3 optical multiport does not require a long coherence length since it provides negligible optical path length differences among all possible optical trajectories. It can be a useful building block for implementing large-scale quantum walks on complex graph networks.