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Implementation of a two-dimensional quantum walk using cross-Kerr nonlinearity

Wei‐Chao Gao, Cong Cao, Xiaofei Liu, Tie-Jun Wang, Chuan Xi Wang

Published Apr 24, 2019• 4 citations

Abstract

A quantum walk is the quantum analog of the classical random walk, which provides a powerful tool for quantum computation and quantum simulation. However, the current experimental realization of the quantum walk based on photonic systems has been restricted to evolution in one dimension or small scale in two dimensions so far, and the growing demands cannot be fulfilled for further application of certain quantum computation tasks. Here, we theoretically propose a feasible scheme of a two-dimensional quantum walk with infinite steps by exploiting the orbital angular momentum of the photons and the phase information of the auxiliary coherent state induced by cross-Kerr nonlinearity. The numerical simulation shows that a proper parameter setting guarantees the walking for infinite steps in a two-dimensional grid with nearly $100\%$100% success probability.

DOI: 10.1364/osac.2.001667

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A quantum walk is the quantum analog of the classical random walk, which provides a powerful tool for quantum computation and quantum simulation. However, the current experimental realization of the quantum walk based on photonic systems has been restricted to evolution in one dimension or small scale in two dimensions so far, and the growing demands cannot be fulfilled for further application of certain quantum computation tasks. Here, we theoretically propose a feasible scheme of a two-dimensional quantum walk with infinite steps by exploiting the orbital angular momentum of the photons and the phase information of the auxiliary coherent state induced by cross-Kerr nonlinearity. The numerical simulation shows that a proper parameter setting guarantees the walking for infinite steps in a two-dimensional grid with nearly

100\%

100% success probability.

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.

Quantum random walks have attracted special interest because they could lead to new quantum algorithms. Photons can carry orbital angular momentum (OAM) thereby offering a practical realization of a high-dimensional quantum information carrier. By employing OAM of photons, we experimentally realized the one-dimensional discrete-time quantum random walk. Three steps of a one-dimensional quantum random walk were implemented in our protocol showing the obvious difference between quantum and classical random walks.

Photons can carry spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used to realize a qubit system and a high-dimension system, respectively. This spin-orbital system is very suitable for implementing one-dimensional discrete-time quantum random walks. We propose a simple scheme of quantum walks on the spin-orbital angular momentum space of photons, where photons walk on the infinite OAM space controlled by their SAM. By employing the recent invention of an optical device, the so-called ``

q

-plate,'' our scheme is more simple and efficient than others because there is no Mach-Zehnder interferometer in the scheme.

Quantum walks in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged as a versatile platform to implement various quantum information tasks and a promising candidate to perform large-scale quantum walks. Both extending physical dimensions and involving more particles will increase the complexity of the evolving systems and the desired quantum resources. Pioneer works have demonstrated single particle walking on two-dimensional (2D) lattices and multiple walkers interfering on a one-dimensional structure. However, 2D multi-particle quantum walk, genuinely being not classically simulatable, has been a vacancy for nearly ten years. Here, we present a genuine 2D quantum walk with correlated photons on a triangular photonic lattice, which can be mapped to a state space up to 37X37 dimensions. This breaks through the physically restriction of single-particle evolution, which can encode information in a large space and constitute high-dimensional graphs indeed beneficial to quantum information processing. A site-by-site addressing between the chip facet and the 2D fanout interface enables an observation of over 600 non-classical interferences simultaneously, violating a classical limit up to 57 standard deviations. Our platform offers a promising prospect for multi-photon quantum walks in a large-scale 2D arrangement, paving the way for practical quantum simulation and quantum computation beyond classical regime.