Fast quantum transfer mediated by topological domain walls

Juan Zurita1,2, Charles E. Creffield2, and Gloria Platero1

1Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, E-28049 Madrid, Spain
2Departamento de Física de Materiales, Universidad Complutense de Madrid, E-28040 Madrid, Spain

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The duration of bidirectional transfer protocols in 1D topological models usually scales exponentially with distance. In this work, we propose transfer protocols in multidomain SSH chains and Creutz ladders that lose the exponential dependence, greatly speeding up the process with respect to their single-domain counterparts, reducing the accumulation of errors and drastically increasing their performance, even in the presence of symmetry-breaking disorder. We also investigate how to harness the localization properties of the Creutz ladder---with two localized modes per domain wall---to choose the two states along the ladder that will be swapped during the transfer protocol, without disturbing the states located in the intermediate walls between them. This provides a 1D network with all-to-all connectivity that can be helpful for quantum information purposes.

Topological insulators are materials that have special quantum states localized at their boundaries. Thanks to the symmetries of the system, these states are highly robust against some kinds of disorder and noise, and so can be useful for quantum information tasks. For instance, in a one-dimensional topological insulator, a particle placed on one side of the chain will be transported robustly to the other without going through all the points in the middle.

However, the duration of this process depends exponentially on transfer distance, making it extremely slow in large chains, like those needed for long-range quantum information transmission. Additionally, this also causes the fidelity of the protocols to drop dramatically when disorder breaks the protecting symmetry.
In this work, we show that, if we instead consider a chain composed of many small pieces with different topological properties, the boundaries between these regions act as amplifiers and greatly speed up the transfer. We show this process is much more robust than the single-region alternative in the case with broken symmetry.

Finally, we also consider another topological model made with two cross-linked chains threaded by a magnetic field. In it, the transfers can take place between any two region boundaries, not only between the ends, without disturbing the states located between them. This can be used to obtain complete connectivity between the nodes in a quantum network, which is fundamental for quantum communication and computing.

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