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arXiv:1907.10870 · Physical Review A

Switching effect of the side chain on quantum walks on triple graphs

Yi-Mu Du, Li-Hua Lü, You‐Quan Li

Published Jul 9, 2015• 4 citations
arXivHTMLPDF

Abstract

We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we find that a switching effect appears if there is an odd number of points in the side chain when concrete conditions between the length of the main chain and the position of the side chain are satisfied. However, such an effect does not occur if there is an even number of points in the side chain. We also suggest two proposals for experiments to demonstrate this effect, which may be employed to design a new type of switching device.

DOI
10.1103/physreva.92.012309

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We consider a continuous-time quantum walk on a triple graph and investigate the influence of the side chain on propagation in the main chain. Calculating the interchange of the probabilities between the two parts of the main chain, we find that a switching effect appears if there is an odd number of points in the side chain when concrete conditions between the length of the main chain and the position of the side chain are satisfied. However, such an effect does not occur if there is an even number of points in the side chain. We also suggest two proposals for experiments to demonstrate this effect, which may be employed to design a new type of switching device.
Abstract We consider an continuous-time quantum walk on triple graphs with a potential well in one of the terminal sites on the main chain and study its dynamical properties in the open system by introducing a ‘spontaneous damping’ process between the terminal site and its nearest neighbour one. Calculating the stable probability of the terminal site and the time evolution of probabilities of the other sites on the main chain, we show that the system can manifest the factorization and coherence protection phenomena when the length and position of the side chain satisfy some concrete conditions. Furthermore we investigate the effect of disorder on the hopping strength and show that the existence of the disorder can destroy the coherence protection phenomena and increase the stable probability of the terminal site on the main chain.
Quantum walks are a useful platform for studying high-efficiency energy transport. In this paper, we study the probability transfer in the discrete-time quantum walk (DTQW) in detail. With intricate design of the initial state, the probability transfer in the DTQW system can exhibit similar behaviors to those in continuous-time quantum walks (CTQWs). Furthermore, without the assumption of a biased initial state and coupling to the environment in the DTQW system, we explore how to achieve directed probability transfer in the DTQW and find that it is closely connected to the time-reversal symmetry of the effective Hamiltonian of the walk. We find that regardless of whether the number of vertices in the DTQW is even or odd, we can control the probability transfer in the DTQW by modulating the time-reversal symmetry of the system. Such control of directed probability transfer can only work well in a CTQW with odd vertices. Even when temporal or spatial disorder emerges in the DTQW, the connection between the probability transfer and the symmetry of the walk still exists. Experimental proposals for observing the probability distributions in the DTQW are discussed.
The continuous-time quantum walk on a one-dimensional graph of odd number of sites with an on-site potential at the center is studied. We show that such a quantum-walk system can construct an X-gate of a single qubit as well as a control gate for two qubits, when the potential is much larger than the hopping strength. We investigate the decoherence effect and find that the coherence time can be enhanced by either increasing the number of sites on the graph or the ratio of the potential to the hopping strength, which is expected to motivate the design of the quantum gate with long coherence time. We also suggest several experimental proposals to realize such a system.
Abstract We investigate novel transport properties of chiral continuous-time quantum walks (CTQWs) on graphs. By employing a gauge transformation, we demonstrate that CTQWs on chiral chains are equivalent to those on non-chiral chains, but with additional momenta from initial wave packets. This explains the novel transport phenomenon numerically studied in (Khalique et al 2021 New J. Phys. 23 083005). Building on this, we delve deeper into the analysis of chiral CTQWs on the Y-junction graph, introducing phases to account for the chirality. The phase plays a key role in controlling both asymmetric transport and directed complete transport among the chains in the Y-junction graph. We systematically analyze these features through a comprehensive examination of the chiral CTQW on a Y-junction graph. Our analysis shows that the CTQW on Y-junction graph can be modeled as a combination of three wave functions, each of which evolves independently on three effective open chains. By constructing a lattice scattering theory, we calculate the phase shift of a wave packet after it interacts with the potential-shifted boundary. Our results demonstrate that the interplay of these phase shifts leads to the observed enhancement and suppression of quantum transport. The explicit condition for directed complete transport or 100 % efficiency is analytically derived. Our theory has applications in building quantum versions of binary tree search algorithms.
Searching efficiency, which biologists and roboticists are ever concerned about, has become important in physics and information science nowadays. In classical probability-based searching problems, as stigmergy, the increase in graph complexity will decrease the searching efficiency. Here we study the searching efficiency based on the first-passage probability and find a counterintuitive phenomenon in quantum walk on a graph with floating vertices. Connecting one vertex in the floating layer to that in the base layer will speed up the searching rapidity, but such a speed-up effect will be suppressed at once if one more vertex is connected to the already connected vertex in the floating layer. This is a counterintuitive phenomenon in comparison to its classical counterpart, where additional vertices at the side chain will retard the searching rapidity. We also propose an ancillary model that bridges the measurement of the probability and the first-passage probability, which is expected to provide new ideas for quantum simulation by means of qubit chips.