Quantum spatial search on graphs subject to dynamical noise

Marco Cattaneo, Matteo A. C. Rossi, Matteo G. A. Paris, and Sabrina Maniscalco
Phys. Rev. A 98, 052347 – Published 27 November 2018

Abstract

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 N1. 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 speedup 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 indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance for just a few nodes also.

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  • Received 7 September 2018

DOI:https://doi.org/10.1103/PhysRevA.98.052347

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Marco Cattaneo1, Matteo A. C. Rossi2, Matteo G. A. Paris1, and Sabrina Maniscalco2,3

  • 1Quantum Technology Lab, Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, I-20133 Milano, Italy
  • 2QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
  • 3QTF Centre of Excellence, Department of Applied Physics, School of Science, Aalto University, FI-00076 Aalto, Finland

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Issue

Vol. 98, Iss. 5 — November 2018

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