• Open Access

Investigating the exchange of Ising chains on a digital quantum computer

Bassel Heiba Elfeky, Matthieu C. Dartiailh, S. M. Farzaneh, and Javad Shabani
Phys. Rev. Research 3, 033108 – Published 2 August 2021

Abstract

The ferromagnetic state of an Ising chain can represent a twofold degenerate subspace or equivalently a logical qubit that is protected from excitations by an energy gap. Here, we study a braiding-like exchange operation through the movement of the ferromagnetic state in the qubit subspace, which resembles that of the localized edge modes in a Kitaev chain. The system consists of two Ising chains in a one-dimensional geometry where the operation is simulated through the adiabatic time evolution of the ground state. The time evolution is implemented via the Suzuki-Trotter expansion on basic single- and two-qubit quantum gates using IBM's Aer QASM simulator. The fidelity of the system is investigated as a function of the evolution and system parameters to obtain optimum efficiency and accuracy for different system sizes. Various aspects of the implementation, including the circuit depth, Trotterization error, and quantum gate errors pertaining to noisy intermediate-scale quantum (NISQ) hardware, are discussed as well. We demonstrate that the quantum gate errors, i.e., bit-flip, phase errors, are the dominating factor in determining the fidelity of the system as the Trotter error and the adiabatic condition are less restrictive even for modest values of Trotter time steps. We reach an optimum fidelity >99% on systems of up to 11 sites per Ising chain. We show that running such simulations is far beyond the reach of current NISQ hardware with the most efficient implementation of a single braiding-like operation for a fidelity above 90% requiring a circuit depth of the order of 103 restricting the individual gate errors to be less than 106.

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  • Received 9 March 2021
  • Accepted 7 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033108

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Bassel Heiba Elfeky, Matthieu C. Dartiailh, S. M. Farzaneh, and Javad Shabani

  • Department of Physics, New York University, New York, New York 10003, USA

Article Text

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Issue

Vol. 3, Iss. 3 — August - October 2021

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