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arXiv:1310.0420 · Scientific Reports

Quantum walks of interacting fermions on a cycle graph

Alexey A. Melnikov, Leonid Evgenevich Fedichkin

Published Sep 29, 2016• 40 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep34226

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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.
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 are fundamentally different from random walks due to the quantum superposition property of quantum objects. Quantum walk process was found to be very useful for quantum information and quantum computation applications. In this paper we demonstrate how to use quantum walks as a tool to generate high-dimensional two-particle fermionic entanglement. The generated entanglement can survive longer in the presence of depolorazing noise due to the periodicity of quantum walk dynamics. The possibility to create two distinguishable qudits in a system of tunnel-coupled semiconductor quantum dots is discussed.
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.
In this thesis, we present a study of quantum walks with an open quantum system formalism. In this way we allow the walkers to interact with a surrounding environment, and by doing so we are able to add directionality to the paths that the walkers take on a given graph. A theoretical and mathematical framework for performing a directed quantum walk is established, which works for general continuous-time quantum walks on any weighted and/or directed graphs. Since quantum correlations, such as entanglement and quantum discord, play an important role in quantum computation and quantum information processing, a detailed study is also carried out on their dynamical change while two quantum particles walk through specified graphs. Finally the electron transport process in molecules is simulated using quantum walks, in particular in the Titanium dioxide (TiO2) electrode as well as the Fenna-Matthews-Olson protein complex. Quantum correlations are measured in these two systems, showing some evidence of entanglement assisted transport of the excitons in the Fenna-Matthews-Olson protein complex, but not in the TiO2 electrode.