Fig. 1: Proposed Rice-Mele Y-coupler for qubits.

The switching of the edge state is done by simply tuning the on-site potential of the qubit site. a Layout of the Rice-Mele coupler where a central site (in white) couples two Rice-Mele chains which have a modulating on-site potential (orange and blue for + V and − V) and modulating tunnel coupling (t₁ and t₂ with t₂ > t₁). The qubit separately couples to the central site via tunnel coupling t_Q with itself having a tunable on-site potential V_Q. We term each strongly coupled pair of sites a ‘unit cell’ and the Rice-Mele chains each have p unit cells. The sites for the effective 4-site model in Eq. (1) are labelled Q, C, L and R. b Energy spectrum of the proposed Rice-Mele Y-model, shown in a with V = V_R = − V_L. The eigenstates producing the leftward and rightward edge-states are \({t}_{{{{\rm{Q}}}}}\left\vert {{{\rm{L}}}}\right\rangle -{t}_{1}\left\vert {{{\rm{Q}}}}\right\rangle\) and \({t}_{{{{\rm{Q}}}}}\left\vert {{{\rm{R}}}}\right\rangle -{t}_{1}\left\vert {{{\rm{Q}}}}\right\rangle\) and occur at V_Q = − V and V_Q = V respectively (shown by the blue and orange circles) as highlighted by sketched population on the two inset diagrams (with white for finite population while black for zero population). The remaining two eigenstates produce a bidirectional population spread as shown in the top-left and bottom-right inset diagrams. c Numeric simulation of the eigenvalues produced by the full coupler design described in Eq. (2). The simulation takes V = 37.5 MHz, t₁ = 120 MHz, t₂ = 150 MHz and t_Q = 62.5 MHz. There are p = 10 unit cells on both Rice-Mele chains. The spectra are plotted for both V_Q = ± V. The non-shaded region indicates the band-gap which contains two gap states. The encircled edge states correspond to the operating points shown in b. d Occupation probabilities exposing the edge-states when taking the respective eigenvectors from the spectrum in c. Note that the occupation probability is zero on one side for both directional edge-states. The qubit site 44 has been omitted for clarity, while the site indices are enumerated from 1 to 43 from the most leftward site to the most righward site (so 22 is the central site). e An example multi-qubit array where multiple edge states can be made to either overlap (finite interaction) or have zero crosstalk by simply switching the qubits’ on-site potentials.