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arXiv:1704.03108 · Physical Review A

Quantum simulation of discrete-time Hamiltonians using directionally unbiased linear optical multiports

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

Published Apr 10, 2017• 18 citations
arXivHTMLPDF

Abstract

Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

DOI
10.1103/physreva.95.042109

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Recently, a generalization of the standard optical multiport was proposed [Phys. Rev. A 93, 043845 (2016)]. These directionally unbiased multiports allow photons to reverse direction and exit backwards from the input port, providing a realistic linear optical scattering vertex for quantum walks on arbitrary graph structures. Here, it is shown that arrays of these multiports allow the simulation of a range of discrete-time Hamiltonian systems. Examples are described, including a case where both spatial and internal degrees of freedom are simulated. Because input ports also double as output ports, there is substantial savings of resources compared to feed-forward networks carrying out the same functions. The simulation is implemented in a scalable manner using only linear optics, and can be generalized to higher dimensional systems in a straightforward fashion, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.
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].
It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states of nonzero winding number and has topologically protected boundary states. In the large-system limit this approach uses quadratically fewer resources to carry out quantum simulations than previous linear-optical approaches and can be readily generalized to higher-dimensional systems. The basic optical units that implement this simulation consist of combinations of optical multiports that allow photons to reverse direction.
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.
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call “directionally-biased”. Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated.
All existing optical quantum walk approaches are based on the use of beamsplitters and multiple paths to explore the multitude of unitary transformations of quantum amplitudes in a Hilbert space. The beamsplitter is naturally a directionally biased device: the photon cannot travel in the reverse direction. This causes rapid increases in the optical hardware resources required for complex quantum walk applications, since the number of options for the walking particle grows with each step. Here we present the experimental demonstration of a directionally-unbiased linear-optical multiport, which allows reversibility of the photon direction. An amplitude-controllable probability distribution matrix for a unitary three-edge vertex is reconstructed with only linear-optical devices. Such directionally-unbiased multiports allow direct execution of quantum walks over a multitude of complex graphs and in tensor networks. This approach would enable simulation of complex Hamiltonians of physical systems and quantum walk applications in a more efficient and compact setup, substantially reducing the required hardware resources.