Designing pretty good state transfer via isospectral reductions

M. Röntgen, N. E. Palaiodimopoulos, C. V. Morfonios, I. Brouzos, M. Pyzh, F. K. Diakonos, and P. Schmelcher
Phys. Rev. A 101, 042304 – Published 1 April 2020

Abstract

We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown that PGST generally arises when a network's eigenvectors and the factors P± of its characteristic polynomial P fulfill certain conditions, where P± correspond to eigenvectors which have ±1 parity on the input and target sites. We combine this result with the so-called isospectral reduction of a network to obtain P± from a dimensionally reduced form of the Hamiltonian. Equipped with the knowledge of the factors P±, we show how a variety of setups can be equipped with PGST by proper tuning of P±. Having demonstrated a method of designing networks featuring pretty good state transfer of single site excitations, we further show how the obtained networks can be manipulated such that they allow for robust storage of qubits. We hereby rely on the concept of compact localized states, which are eigenstates of a Hamiltonian localized on a small subdomain, and whose amplitudes completely vanish outside of this domain. Such states are natural candidates for the storage of quantum information, and we show how certain Hamiltonians featuring pretty good state transfer of single site excitation can be equipped with compact localized states such that their transfer is made possible.

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  • Received 6 August 2019
  • Revised 18 December 2019
  • Accepted 25 February 2020

DOI:https://doi.org/10.1103/PhysRevA.101.042304

©2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

M. Röntgen1, N. E. Palaiodimopoulos2, C. V. Morfonios1, I. Brouzos2,3, M. Pyzh1, F. K. Diakonos2, and P. Schmelcher1,4

  • 1Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
  • 2Department of Physics, University of Athens, 15771 Athens, Greece
  • 3Le Mans University, LAUM UMR CNRS 6613, Av. O. Messiaen, 72085, Le Mans, France
  • 4The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

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Vol. 101, Iss. 4 — April 2020

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