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Journal of Modern Optics

Counteracting quantum decoherence with optimized disorder in discrete-time quantum walks

Irwin Huang, Yu‐Ping Huang

Published Aug 25, 2019• 2 citations
Publisher

Abstract

Decoherence and disorder are two major difficulties limiting the performance of quantum systems in practical settings. Yet they can potentially counteract each other to partially restore the systems' quantum signatures. We adopt the particle swarm optimization method to find the optimal disorder for mitigating the effects of decoherence in one- and two-dimensional quantum random walks, achieving substantial increase in the mean walking distance for a wide range of decoherence strength. This result suggests a viable approach to constructing practical quantum systems robust against decoherence and disorder.

DOI
10.1080/09500340.2019.1655598

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Decoherence and disorder are two major difficulties limiting the performance of quantum systems in practical settings. Yet they can potentially counteract each other to partially restore the systems' quantum signatures. We adopt the particle swarm optimization method to find the optimal disorder for mitigating the effects of decoherence in one- and two-dimensional quantum random walks, achieving substantial increase in the mean walking distance for a wide range of decoherence strength. This result suggests a viable approach to constructing practical quantum systems robust against decoherence and disorder.
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is contrasted with the decoherence effect of dynamic disorder having strength WWW, where a quantum to classical crossover at time ${t}_{c}\ensuremath{\propto}{W}^{\ensuremath{-}2}$ transforms the quantum walk into an ordinary random walk with diffusive spreading. We demonstrate these localization and decoherence phenomena in quantum carpets of the observed time evolution, we relate our results to previously studied models of decoherence for quantum walks, and examine in detail a dimer lattice which corresponds to a single qubit subject to randomness.
The time evolution of one- and two-dimensional discrete-time quantum walk with increase in disorder is studied. We use spatial, temporal and spatio-temporal broken periodicity of the unitary evolution as disorder to mimic the effect of disordered/random medium in our study. Disorder induces a dramatic change in the interference pattern leading to localization of the quantum walks in one- and two-dimensions. Spatial disorder results in the decreases of the particle and position entanglement in one-dimension and counter intuitively, an enhancement in entanglement with temporal and spatio-temporal disorder is seen. The study signifies that the Anderson localization of quantum state without compromising on the degree of entanglement could be implement in a large variety of physical settings where quantum walks has been realized. The study presented here could make it feasible to explore, theoretically and experimentally the interplay between disorder and entanglement. This also brings up a variety of intriguing questions relating to the negative and positive implications on algorithmic and other applications.
We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four- and two-state particles. By comparing the quantum correlations between the two spatial ( x − y ) degrees of freedom using measurement-induced disturbance, we show that the two schemes using a two-state particle are more robust against decoherence than the Grover walk, which uses a four-state particle. We also show that the symmetries which hold for two-state quantum walks break down for the Grover walk, adding to the various other advantages of using two-state rather than four-state particles.
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence in the quantum ``coin'' which drives the walk. We find exact analytical expressions for the time dependence of the first two moments of position, and show that in the long-time limit the variance grows linearly with time, unlike the unitary walk. We compare this to the results of direct numerical simulation, and see how the form of the position distribution changes from the unitary to the usual classical result as we increase the strength of the decoherence.