Continuous-time quantum walks on spatially correlated noisy lattices

Rossi, Matteo A. C.; Benedetti, Claudia; Borrelli, Massimo; Maniscalco, Sabrina; Paris, Matteo G. A.

doi:10.1103/physreva.96.040301

Cited by 27 publications

(27 citation statements)

References 33 publications

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“…Our choice for the noise is motivated by its relevance in systems of interest for quantum information processing [17][18][19][20][21], and by the fact that RTN is at the root of the 1/ f noise affecting superconducting qubits [22]. In recent years some works have addressed the properties of CTQWs on the one-dimensional lattice subject to random telegraph noise [23][24][25][26], also in the presence of spatial correlations [27]. In this paper we analyze the effects of RTN on spatial search on graphs with generic topology.…”

Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order N, also proving that noiseless spatial search shows optimal quantum speedup in the latter, in the computational limit N 1. The noise is modeled by independent sources of random telegraph noise (RTN), dynamically perturbing the links of the graph. We observe two different behaviors depending on the switching rate of RTN: fast noise only slightly degrades performance, whereas slow noise is more detrimental and, in general, lowers the success probability. In particular, we still find a quadratic speed-up for the average running time of the algorithm, while for the star graph with external target node we observe a transition to classical scaling. We also address how the effects of noise depend on the order of the graphs, and discuss the role of the graph topology. Overall, our results suggest that realizations of quantum spatial search are possible with current technology, and also indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance also for just few nodes.

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Section: Introductionmentioning

confidence: 99%

Quantum spatial search on graphs subject to dynamical noise

et al. 2018

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“…The behavior of a quantum walk is fundamentally different from a classical walk since in a quantum walk there is interference between different trajectories of the walk. Two kinds of quantum walks have been introduced in the literature; namely, continuous time quantum walks (Farhi and Gutmann 1998;Rossi et al 2017) and discrete time quantum walks (Lovett et al 2010). Quantum walks have recently received much attention because they have been shown to be a universal model for quantum computation (Childs 2009).…”

Section: Graph Quantum Walksmentioning

confidence: 99%

Quantum walk neural networks with feature dependent coins

et al. 2019

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Recent neural networks designed to operate on graph-structured data have proven effective in many domains. These graph neural networks often diffuse information using the spatial structure of the graph. We propose a quantum walk neural network that learns a diffusion operation that is not only dependent on the geometry of the graph but also on the features of the nodes and the learning task. A quantum walk neural network is based on learning the coin operators that determine the behavior of quantum random walks, the quantum parallel to classical random walks. We demonstrate the effectiveness of our method on multiple classification and regression tasks at both node and graph levels.

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“…Uchiyama et al [17] have analyzed the effect of spatial and temporal correlations on EET in a multi-site model by using a Ornstein-Uhlenbeck noise process to describe the environment, and observe that negative spatial correlation of the noise is the most effective in helping the EET. The effect of RTN on transport via continuous-time quantum walks has been studied on lattices [30,31], also in presence of spatial correlations [32]. Its effect on the non-Markovianity of the dynamics of the spin-boson model has also been considered [33].…”

Section: Introductionmentioning

confidence: 99%

Efficient quantum transport in a multi-site system combining classical noise and quantum baths

2020

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We study the population dynamics and quantum transport efficiency of a multi-site dissipative system driven by a random telegraph noise (RTN) by using a variational polaron master equation for both linear chain and ring configurations. By using two different environment descriptions-RTN only and a thermal bath+RTN-we show that the presence of the classical noise has a non-trivial role on quantum transport. We observe that there exist large areas of parameter space where the combined bath+RTN influence is clearly beneficial for populating the target state of the transport, and for average trapping time and transport efficiency when accounting for the presence of the reaction center via the use of the sink. This result holds for both of the considered intra-site coupling configurations including a chain and ring. In general, our formalism and achieved results provide a platform for engineering and characterizing efficient quantum transport in multi-site systems both for realistic environments and engineered systems.

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Continuous-time quantum walks on spatially correlated noisy lattices

Cited by 27 publications

References 33 publications

Quantum spatial search on graphs subject to dynamical noise

Quantum spatial search on graphs subject to dynamical noise

Quantum walk neural networks with feature dependent coins

Efficient quantum transport in a multi-site system combining classical noise and quantum baths

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