Quantum sensing of noises in one and two dimensional quantum walks

Abstract

Quantum walk (QW) provides a versatile platform for the realization of quantum algorithms. Due to the existence of the inevitable noises in the walk, the different quantum algorithms accommodating to different noises are demanded. Thus, the success of the algorithms based on the QW requires us to sense different noises in the walk. Until now, the way to distinguish different noises in the walk has been discussed rarely. Here, we propose an efficient way to sense the noises in the one and two dimensional QWs. The populations of the coin in the walk with or without decoherence are presented. By only detecting the populations of the coin in the QW, we can determine whether there exists the decoherence in the total QW system. Moreover, the non-Markovianity of the coin in the one and two dimensional QWs is revealed, in which the coin is taken as an open quantum system, and the other components of the QW system is taken as the large environment. With the measured value of the non-Markovianity for the coin, we can conjecture which kinds of noise emerges in the one and two dimensional QWs.

Unusual scaling in a discrete quantum walk with random long range steps

“…Decoherence and subsequent localisation can take place due to several factors like randomness in the environment, defects in the embedding lattice or graphs, measurements of the position or chirality of the walk, inertia, etc. Decoherence has been studied in one dimensional [9,10,11,12,13,14,15,16,17,18,19,20,21,22] and two dimensional [22,23,24,25,26,27] discrete walks as well as in the continuous quantum walk [28,29,30]. Such noisy quantum walks can even be non-unitary [8,31].…”

Parameterization of Translation-Invariant Two-Dimensional Two-State Quantum Walks

“…In this paper, we discuss two-dimensional two-state quantum walks, in which V = Z 2 and H v = C 2 . These have been the subject of some previous studies [1,2,7].…”

Enhanced non-Markovian behavior in quantum walks with Markovian disorder

“…In quantum walks which evolves in position space, the reduced dynamics of the particle obtained after tracing out the position degrees of freedom has * Electronic address: chandru@imsc.res.in been shown to exhibit certain features of quantum non-Markovianity such as information backflow [38,39]. Recently, in [39][40][41] the effect of decoherence caused by the interaction of the particle with an external environment or due to the presence of broken links in position lattice has been shown to reduce the effects of non-Markovianity. Furthermore, in [42] classical non-Markovian random process such as the Elephant random walk has been generalized to the quantum setting.…”

“…In this work we study the intricate connections between quantum interference, entanglement and dynamical properties like non-Markovian quantum effects arising in the time evolution of quantum walks [39][40][41][42]. While quantum interference is understood to be the most fundamental resource that powers quantum walks, the complexity in tracking the changes and measuring it unambiguously has prevented a direct handle for studying it in quantum systems.…”