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Optical implementation of quantum random walks using weak cross-Kerr media

Chuan Xi Wang, Yansong Li, Liang Hao

Chinese Science BulletinJun 30, 201118 citations

Implementing arbitrary coined two-dimensional quantum walks via bulk optical interferometry

Peng Xue, Xin Zhang, Kunkun Wang +2 more

Optics CommunicationsJun 22, 20182 citations

Physical Implementation of Quantum Walks

Kia Manouchehri, Jingbo B. Wang

Springer eBooksAug 21, 2013249 citations

Asymptotics of a quantum random walk driven by an optical cavity

Demosthenes Ellinas, Ioannis Smyrnakis

We investigate a novel quantum random walk (QRW) model, of possible use in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behaviour expressed in the form of a limit probability distribution of a double-horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes–Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin–field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behaviour of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by an enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental set-up that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.We investigate a novel quantum random walk (QRW) model, of possible use in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behaviour expressed in the form of a limit probability distribution of a double-horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes–Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin–field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behaviour of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by an enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental set-up that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.

arXiv:quant-ph/0510112Journal of Optics B Quantum and Semiclassical OpticsJun 30, 20059 citations

Asymptotics of Quantum Random Walk Driven by Optical Cavity

Demosthenes Ellinas, Ioannis Smyrnakis

We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior expressed in the form of a limit probability distribution of a double horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes-Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin-field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behavior of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental setup that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.We investigate a novel quantum random walk (QRW) model, possibly useful in quantum algorithm implementation, that achieves a quadratically faster diffusion rate compared to its classical counterpart. We evaluate its asymptotic behavior expressed in the form of a limit probability distribution of a double horn shape. Questions of robustness and control of that limit distribution are addressed by introducing a quantum optical cavity in which a resonant Jaynes-Cummings type of interaction between the quantum walk coin system realized in the form of a two-level atom and a laser field is taking place. Driving the optical cavity by means of the coin-field interaction time and the initial quantum coin state, we determine two types of modification of the asymptotic behavior of the QRW. In the first one the limit distribution is robustly reproduced up to a scaling, while in the second one the quantum features of the walk, exemplified by enhanced diffusion rate, are washed out and Gaussian asymptotics prevail. Verification of these findings in an experimental setup that involves two quantum optical cavities that implement the driven QRW and its quantum to classical transition is discussed.

Jan 1, 20059 citations

Implementation of two-dimensional quantum walks

João Fernando Doriguello Diniz

Jun 17, 20160 citations

Optical cavity implementations of the quantum walk

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