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arXiv:1811.04482 · International Conference on Micro- and Nano-Electronics (ICMNE)

Hitting time for quantum walks of identical particles

Alexey A. Melnikov, Aleksandr P. Alodjants, Leonid Evgenevich Fedichkin

Published Mar 15, 2019• 7 citations

Abstract

Quantum particles are known to be faster than classical when they propagate stochastically on certain graphs. A time needed for a particle to reach a target node on a distance, the hitting time, can be exponentially less for quantum walks than for classical random walks. It is however not known how fast would interacting quantum particles propagate on different graphs. Here we present our results on hitting times for quantum walks of identical particles on cycle graphs, and relate the results to our previous findings on the usefulness of identical interacting particles in quantum information theory. We observe that interacting fermions traverse cycle graphs faster than non-interacting fermions. We show that the rate of propagation is related to fermionic entanglement: interacting fermions keep traversing the cycle graph as long as their entanglement grows. Our results demonstrate the role of entanglement in quantum particles propagation. These results are of importance for understanding quantum transport properties of identical particles.

DOI: 10.1117/12.2521982

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Quantum walks on graphs play an important role in the field of quantum algorithms. Fast hitting is one of the properties that quantum walk algorithms can utilize to outperform classical random walk algorithms. Fast hitting refers to a particle starting from the entrance node on a graph and trying to hit the exit node quickly. Especially, continuous-time quantum walks on random glued binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and laser-written waveguide arrays to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graph’s branching rate from 2 to 5, revealing that quantum walks can exhibit more superiority over classical random walks as the branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.

We study a continuous-time quantum walk of interacting fermions on a cycle graph. By finding analytical solutions and simulating the dynamics of two fermions we observe a diverse structure of entangled states of indistinguishable fermions. The relation between entanglement of distinguishable qutrits and indistinguishable electrons is observed. Restrictions imposed by the symmetry of a cycle graph are derived. Possible realization of a quantum walk in an array of semiconductor quantum dots is discussed.

Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In this work quantum walks of electrons on a graph are studied. The graph is composed of semiconductor quantum dots arranged in a circle. Electrons can tunnel between adjacent dots and interact via Coulomb repulsion, which leads to entanglement. Fermionic entanglement dynamics is obtained and evaluated.

Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In this work quantum walks of electrons on a graph are studied. The graph is composed of semiconductor quantum dots arranged in a circle. Electrons can tunnel between adjacent dots and interact via Coulomb repulsion, which leads to entanglement. Fermionic entanglement dynamics is obtained and evaluated.

Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on central-random glued binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and waveguide arrays written by femtosecond laser to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graph's branching rate from 2 to 5, revealing that quantum walks exhibit more superiority over classical random walks as branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.