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arXiv:2311.04848 · Physical Review A

Parrondo's effect in continuous-time quantum walks

Jefferson J. Ximenes, Marcelo A. Pires, J. M. Villas-Bôas

Published Mar 19, 2024• 11 citations
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Abstract

We present a manifestation of a Parrondo's effect in a continuous-time quantum walk (CTQW). In our protocol we consider a CTQW in the presence of a time-dependent transition defect. Our results show that the alternation between defects, that individually are detrimental to the wavepacket spreading, can paradoxically enhance overall wavepacket propagation. Our findings pave the way for the exploration of unconventional mechanisms that can potentially harness the adverse effects of defects to enhance quantum transport.

DOI
10.1103/physreva.109.032417

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We present a manifestation of a Parrondo's effect in a continuous-time quantum walk (CTQW). In our protocol we consider a CTQW in the presence of a time-dependent transition defect. Our results show that the alternation between defects, that individually are detrimental to the wavepacket spreading, can paradoxically enhance overall wavepacket propagation. Our findings pave the way for the exploration of unconventional mechanisms that can potentially harness the adverse effects of defects to enhance quantum transport.
We investigate the quantum transport of delocalized states in continuous-time quantum walks (CTQWs) on a one-dimensional lattice containing a single defect. The defect is modeled by assigning complex-valued hopping amplitudes to the edges that connect the site corresponding to the mean position of the delocalized initial state to its nearest neighbors. We find that this single defective site is sufficient to enhance the ballistic spreading of an initially Gaussian wave packet. Extending these results, we implement a time-dependent alternation protocol between two distinct defect configurations, each individually yielding poor propagation of the state. The combination of these two unfavorable configurations improves the transport efficiency of the quantum walker, revealing a manifestation of Parrondo's paradox in CTQWs with delocalized initial states. This study provides insights into the role of complex-phase defects and time-dependent protocols in CTQWs, demonstrating that the interplay between quantum interference and graph engineering can effectively enhance quantum transport in discrete lattices.
Parrondo's paradox, where the alternation of two losing strategies can produce a winning outcome, has recently been demonstrated in continuous-time quantum walks (CTQWs) through periodic defect modulation. We extend this phenomenon to aperiodic protocols. We show that deterministic, non-repetitive defect switching can enhance quantum spreading in CTQWs compared to the defect-free case. Furthermore, we establish that the degree of this enhancement is strongly influenced by the autocorrelation and persistence characteristics of the applied aperiodic sequence. Our findings indicate that aperiodic defect modulation reliably maintains Parrondo's effect and provides new ways to control wavepacket properties in CTQWs.
Parrondo's paradox, a counterintuitive phenomenon in which two losing strategies combine to produce a winning outcome, has been a subject of interest across various scientific fields, including quantum mechanics. In this study, we investigate the manifestation of Parrondo's paradox in discrete-time quantum walks. We demonstrate the existence of Parrondo's paradox using site- and time-dependent coins without the need for a higher-dimensional coin or adding decoherence to the system. Our results enhance the feasibility of practical implementations and provide deeper insights into the underlying quantum dynamics, specifically the propagation constrained by the interference pattern of quantum walks. The implications of our results suggest the potential for more accessible and efficient designs in quantum transport, broadening the scope and application of Parrondo's paradox beyond conventional frameworks.
Parrondo's paradox shows that alternating two losing strategies can yield a net positive outcome—a counterintuitive effect relevant to probabilistic systems and control. We demonstrate a quantum analogue using single-qubit inhomogeneous quantum walk—unlike prior work that required multi-coin or position-dependent constructions. Instead, we apply a local phase gate at the origin and alternate two fixedSU(2)\text{SU}(2)SU(2)coins, with parameters from recent inhomogeneous quantum walks. Sequence ABB yields positive displacement despite no individual bias. This establishes that coherent interference alone can reproduce the Parrondo effect in single-qubit systems, with implications for low-cost quantum algorithms and transport protocols.
The well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones, is called Parrondo's paradox. Here, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of the different periods. Moreover, we also analyze the relationships between Parrondo's games and quantum entanglement in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.
Continuous time quantum walks (CTQWs) do not necessarily perform better than their classical counterparts, the continuous time random walks (CTRWs). For one special graph, where a recent analysis showed that in a particular direction of propagation the penetration of the graph is faster by CTQWs than by CTRWs, we demonstrate that in another direction of propagation the opposite is true. In this case a CTQW initially localized at one site displays a slow transport. We furthermore show that when the CTQW's initial condition is a totally symmetric superposition of states of equivalent sites, the transport gets to be much more rapid.