Abstract
We study the preparation of topologically ordered states by interpolating between an initial Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate ground state space. By simulating the dynamics for small systems, we numerically observe a certain stability of the prepared state as a function of the initial Hamiltonian. For small systems or long interpolation times, we argue that the resulting state can be identified by computing suitable effective Hamiltonians. For effective anyon models, this analysis singles out the relevant physical processes and extends the study of the splitting of the topological degeneracy by Bonderson (2009 Phys. Rev. Lett. 103 110403). We illustrate our findings using Kitaev’s Majorana chain, effective anyon chains, the toric code and Levin–Wen string-net models.
Highlights
Ordered phases of matter have attracted significant interest in the field of quantum information, following the seminal work of Kitaev [Kit03]
They study an adiabatic evolution where a Hamiltonian having a trivial product ground state is interpolated into a toric code Hamiltonian having a four-fold degenerate ground state space
Such a case was considered by Hamma and Lidar [HL08], who showed that certain ground states of the toric code can be prepared efficiently
Summary
Original content from this work may be used under the terms of the Creative Abstract. We study the preparation of topologically ordered states by interpolating between an initial. Any further distribution of Hamiltonian with a unique product ground state and a Hamiltonian with a topologically degenerate this work must maintain attribution to the ground state space. By simulating the dynamics for small systems, we numerically observe a certain author(s) and the title of stability of the prepared state as a function of the initial Hamiltonian. For small systems or long the work, journal citation and DOI. Interpolation times, we argue that the resulting state can be identified by computing suitable effective. We illustrate our findings using Kitaev’s Majorana chain, effective anyon chains, the toric code and Levin–Wen string-net models
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
