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arXiv:1604.06476 · Physical Review A

Group transformations and entangled-state quantum gates with directionally unbiased linear-optical multiports

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

Published Apr 25, 2016• 32 citations
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Abstract

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.

DOI
10.1103/physreva.93.043845

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•Jan 1, 2021•0 citations
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.
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.
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.
The progress in modern quantum information processing (QIP) strongly depends on new algorithms and on the development of novel quantum entanglement processing elements enabling to perform quantum computation and quantum simulation effectively. Several examples of quantum information processing applications based on freshly designed linear-optics devices are presented. A beam splitter (BS) is a central device in linear-optical quantum information processing because it can split the incoming photon amplitudes into spatially distinct modes to establish conditions for quantum superposition. The BS naturally possesses directional-bias in a sense that incoming photons can only propagate in a forward manner. When the execution of certain quantum information tasks would require multiple operations, this directionality condition becomes a serious obstacle by creating significant overhead in the number of needed elements and other supporting devices. We introduce a family of amplitude-controllable fully-reversible linear-optical quantum information processors, called directionally-unbiased linear-optical multiports, in order to achieve significant reduction in the number of required hardware. The theoretical analysis of the device design as well as the experimental realization of three-port unit using bulk linear optics is demonstrated. These devices offer several fresh approaches in quantum-walk-based applications such as quantum simulation of solid-state Hamiltonians, topological protection of polarization qubits against errors, and quantum communication. Topological photonics is an emerging and actively developing field because of its capability to stabilize and protect some quantum states from perturbation errors by ensuring the environment carries a distinct topological signature. Topology-dependent quantum information processing is globally stable due to the entire system being engaged in the information manipulation. We demonstrate suppression of quantum amplitude transfer between two distinct bulk regions of a system. This results in error avoidance for a two-photon polarization-entangled state under specific conditions. The goal of modern quantum communication is a reliable distribution of quantum entanglement between multiple nodes performing quantum operations such as quantum memories and quantum computers. We demonstrated that local quantum information processing using new fully-reversible four-port linear-optical structures could find an immediate application in quantum communication. A quantum information routing device is introduced based on the use of four-dimensional Grover matrices and beam splitters. Several multiport-based units are developed to demonstrate new higher-dimensional Hong-Ou-Mandel (HOM) effect and directionally-controllable entangled state distribution while changing only phases in a waveguided unit. Several such operational elements could be linked to form a reconfigurable network of quantum users without losing control of quantum amplitudes. This allows controllable routing of entangled photons and sharing entanglement between any designated users in the future quantum computational networks.