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arXiv:1810.06850 · PLoS ONE

A versatile quantum walk resonator with bright classical light

Bereneice Sephton, Angela L. Dudley, Gianluca Ruffato, Filippo Romanato, Lorenzo Marrucci, Miles J. Padgett, Sandeep K. Goyal, Filippus Stefanus Roux, Thomas Konrad, Andrew Forbes

Published Apr 9, 2019• 35 citations
arXivHTMLPDF

Abstract

In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the searching of problem solution spaces faster than with classical random walks, and holds promise for advances in dynamical quantum simulation, biological process modelling and quantum computation. Here we employ a versatile and scalable resonator configuration to realise quantum walks with bright classical light. We experimentally demonstrate the versatility of our approach by implementing a variety of QWs, all with the same experimental platform, while the use of a resonator allows for an arbitrary number of steps without scaling the number of optics. This paves the way for future QW implementations with spatial modes of light in free-space that are both versatile and scalable.

DOI
10.1371/journal.pone.0214891

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In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the searching of problem solution spaces faster than with classical random walks, and holds promise for advances in dynamical quantum simulation, biological process modelling and quantum computation. Here we employ a versatile and scalable resonator configuration to realise quantum walks with bright classical light. We experimentally demonstrate the versatility of our approach by implementing a variety of QWs, all with the same experimental platform, while the use of a resonator allows for an arbitrary number of steps without scaling the number of optics. This paves the way for future QW implementations with spatial modes of light in free-space that are both versatile and scalable.
In the avid search for means to increase computational power in comparison to that which is currently available, quantum walks (QWs) have become a promising option with derived quantum algorithms providing an associated speed up compared to what is currently used for implementation in classical computers. It has additionally been shown that the physical implementation of QWs will provide a successful computational basis for a quantum computer. It follows that considerable drive for finding such means has been occurring over the 20+ years since its introduction with phenomena such as electrons and photons being employed. Principal problems encountered with such quantum systems involve the vulnerability to environmental influence as well as scalability of the systems. Here we outline how to perform the QW due to interference characteristics inherent in the phenomenon, to mitigate these challenges. We utilize the properties of vector beams to physically implement such a walk in orbital angular momentum space by manipulating polarization and exploiting the non-separability of such beams.
A quantum walk is the quantum analog of the classical random walks. Despite their simple structure they form a universal platform to implement any algorithm of quantum computation. However, it is very hard to realize quantum walks with a sufficient number of iterations in quantum systems due to their sensitivity to environmental influences and subsequent loss of coherence. Here we present a scalable implementation scheme for one-dimensional quantum walks for arbitrary number of steps using the orbital angular momentum modes of classical light beams. Furthermore, we show that using the same setup with a minor adjustment we can also realize electric quantum walks.
Random processes are ubiquitous in the natural world as well as in man-made environments. While classical random walks may behave highly complex or even chaotic, there outcome can, in principle, always be predicted from the parameters of the system and the initial conditions. In the realm of quantum mechanics, however, this is not possible as the underlying wave mechanics leads to intrinsically indeterministic outcomes. Moreover, if multiple indistinguishable particles are subjected to such a quantum random walk, their exchange symmetry causes quantum interference, thereby enriching the dynamics of the system even further. \nIn this work, quantum random walks of pairs of indistinguishable photons, the quanta of light, are investigated. Networks of coupled optical waveguides are chosen as the experimental platform of choice, offering a high degree of coherence and versatility. In these photonic lattices, light propagates along one spatial dimension, whereas the individual waveguides are connected by evanescent coupling in the transverse dimensions. \nIn particular, it is investigated how the various degrees of freedom, which are available in such photonic lattices, affect the trajectories in the quantum walks and their complexity. It is shown how the facilitation of both transverse dimensions allows for much richer quantum walks with properties unencountered in planar arrangements. But even if just a single transverse dimension is available, the coupling properties of the lattice along this dimension are a potent degree of freedom, which can be used to manipulate the quantum walk. Finally, an experimental technique is developed which enables a convenient characterisation of the expected quantum walk in an arbitrary waveguide lattice by classical light. \nThe thesis concludes with a summary of the results and an outlook onto further developments in the field.
The quantum walk (QW) has proven to be a valuable testbed for fundamental inquiries in quantum technology applications such as quantum simulation and quantum search algorithms. Many benefits have been found by exploring implementations of QWs in various physical systems, including photonic platforms. Here, we propose a platform to perform quantum walks based on ultrafast time-bin encoding (UTBE) and all-optical Kerr gating. This platform supports the scalability of quantum walks to a large number of steps and walkers while retaining a significant degree of programmability. More importantly, ultrafast time bins are encoded at the picosecond time scale, far away from mechanical fluctuations. This enables the scalability of our platform to many modes while preserving excellent interferometric phase stability over extremely long periods of time without requiring active phase stabilization. Our 18-step QW is shown to preserve interferometric phase stability over a period of 50 h, with an overall walk fidelity maintained above 95%.
We put forward a versatile and highly scalable experimental setup for the realization of discrete two-dimensional quantum random walks with a single-qubit coin and tunable degree of decoherence. The proposed scheme makes use of a small number of simple optical components arranged in a multipath Mach-Zehnder-like configuration, where a weak coherent state is injected. Environmental effects (decoherence) are generated by a spatial light modulator, which introduces pure dephasing in the transverse spatial plane perpendicular to the direction of propagation of the light beam. By controlling the characteristics of this dephasing, one can explore a great variety of scenarios of quantum random walks: pure quantum evolution (ballistic spread), fast fluctuating environment leading to a diffusive classical random walk, and static disorder resulting in the observation of Anderson localization.
Classical optics can be used to efficiently implement certain quantum information processing tasks with a high degree of control, for example, one-dimensional quantum walks through the space of orbital angular momentum of light directed by its polarization. To explore the potential of quantum information processing with classical light, we here suggest a method to realize ddd-dimensional quantum walks with classical optics---an important step towards robust implementation of certain quantum algorithms. In this scheme, different degrees of freedom of light, such as frequency, orbital angular momentum, and time bins, represent different directions for the walker while the coin to decide which direction the walker takes is realized by employing the polarization combined with different light paths.