Abstract
Abstract Continuous-time quantum walks may be exploited to enhance spatial search, i.e., for finding a marked element in a database structured as a complex network. However, in practical implementations, the environmental noise has detrimental effects, and a question arises on whether noise engineering may be helpful in mitigating those effects on the performance of the quantum algorithm. Here we study whether time-correlated noise inducing non-Markovianity may represent a resource for quantum search. In particular, we consider quantum search on a star graph, which has been proven to be optimal in the noiseless case, and analyze the effects of independent random telegraph noise (RTN) disturbing each link of the graph. Upon exploiting an exact code for the noisy dynamics, we evaluate the quantum non-Markovianity of the evolution, and show that it cannot be considered as a resource for this algorithm, since its presence is correlated with lower probabilities of success of the search.
Highlights
There is a close connection between quantum metrological precision bounds and quantum computation speed-up limits, e.g. the search time in a database [1]
We here consider quantum spatial search on the star graph with central node as target, proven to be optimal in [10], where it is shown that the random telegraph noise with fast switching rate μ has almost no effects on the probability of success of the search, while decreasing μ leads to worse and worse results, proving that semi-static noise jeopardizes the performance of the algorithm
We investigate if the presence of nonMarkovianity is a resource for quantum spatial search, i.e if it correlates with better performance of the noisy algorithm
Summary
There is a close connection between quantum metrological precision bounds and quantum computation speed-up limits, e.g. the search time in a database [1]. Quantum spatial search [4] is the generalization of this problem to a database characterized by a complex structure, i.e., a database whose elements are distributed in space and connected by links according to a certain topology Such a database can be described by a graph. The study of non-Markovianity requires higher precision and numerical stability, in this paper we employ a numerically exact technique to obtain the state of the walker at a generic time t This technique, valid for any system subject to classical dynamical noise, was first proposed in [34] and used to study the dynamics of small quantum systems, such as one or two qubits perturbed by random telegraph noise [16, 20].
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