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arXiv:quant-ph/0212149

Implement Quantum Random Walks with Linear Optics Elements

Zhi Zhao, Jiangfeng Du, Hui Li, Tao Yang, Zeng‐Bing Chen, Jian-Wei Pan

Published Dec 29, 2002• 6 citations
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Abstract

The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line using only linear optics elements. With current single-photon interference technology, the steps that could be experimentally implemented can be extended to very large numbers. We also show that, by decohering the quantum states, our scheme for quantum random walk tends to be classical.

DOI
10.48550/arxiv.quant-ph/0212149

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The quantum random walk has drawn special interests because its remarkable features to the classical counterpart could lead to new quantum algorithms. In this paper, we propose a feasible scheme to implement quantum random walks on a line using only linear optics elements. With current single-photon interference technology, the steps that could be experimentally implemented can be extended to very large numbers. We also show that, by decohering the quantum states, our scheme for quantum random walk tends to be classical.
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Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The number of optical elements required scales linearly with the number of steps. We measure walks with up to 6 steps and explore the quantum-to-classical transition by introducing tunable decoherence. Finally, we also investigate the effect of absorbing boundaries and show that decoherence significantly affects the probability of absorption.
Quantum random walks have received much interest due to their nonintuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable and not limited to special connectivity criteria. We present a scheme for walking on arbitrarily complex graphs, which can be realized using a variety of quantum systems such as a Bose-Einstein condensate trapped inside an optical lattice. This scheme is particularly elegant since the walker is not required to physically step between the nodes; only flipping coins is sufficient.
We discuss quantum random walk of two photons using linear optical elements. We analyze the quantum random walk using photons in a variety of quantum states including entangled states. We find that for photons initially in separable Fock states, the final state is entangled. For polarization entangled photons produced by type-II downconverter, we calculate the joint probability of detecting two photons at a given site. We show the remarkable dependence of the two photon detection probability on the quantum nature of the state. In order to understand the quantum random walk, we present exact analytical results for small number of steps such as five. We present in detail numerical results for a number of cases and supplement the numerical results with asymptotic analytical results.
We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing different initial coin states, we observe non-Gaussian distribution of the walkers' finial position, which characterizes a quadratic enhancement of the spread of photon wavepackets compared to a classical random walk. By introducing controllable decoherence, we observe the quantum-to-classical transmission in a quantum walk architecture.