Robust quantum state transfer via topological edge states in superconducting qubit chains

Robust quantum state transfer (QST) is an indispensable ingredient in scalable quantum information processing. Here we present an experimentally feasible mechanism for realizing robust QST via topologically protected edge states in superconducting qubit chains. Using superconducting Xmon qubits with tunable couplings, we construct generalized Su-Schrieffer-Heeger models and analytically derive the wave functions of topological edge states. We find that such edge states can be employed as a quantum channel to realize robust QST between remote qubits. With a numerical simulation, we show that both single-qubit states and two-qubit entangled states can be robustly transferred in the presence of sizable imperfections in the qubit couplings. The transfer fidelity demonstrates a wide plateau at the value of unity in the imperfection magnitude. This approach is general and can be implemented in a variety of quantum computing platforms.

Figure 1

(a) The transfer of unknown single-qubit or entangled states from the qubits inside the left box to the qubits inside the right box through the intermediate qubit chain. Each circle represents a qubit. (b) The implementation of the qubit chain with superconducting Xmon qubits. The qubits $Q_x$ and $Q_{x+1}$ are inductively coupled by the tunable coupler $CP$ with the coupling strength $J_x$.

Figure 2

The energy spectra of the $p=2$ SSH model vs $\theta$ for the imperfection strength (a) $W=0$, (c) $W=0.6g_1$, and (d) $W=0.8g_1$. The total qubit number is 9. (b) The fidelity of the QST vs the imperfection strength. The total qubit number is 9 (the solid line), 15 (the dashed line), and 21 (the dash-dot line), with $\mathrm{\Omega }=\{0.04g_1,0.02g_1,0.01g_1\}$. The other parameter is $g_0=g_1$.

Figure 3

(a) The energy spectra of the $p=3$ generalized SSH model vs $\theta$ with a chain of 8 qubits and $g_0=0$. (b) The fidelities of entanglement transfer vs the imperfection strength. The total qubit numbers are 8 (the solid line), 14 (the dashed line), and 20 (the dash-dot line) with $\mathrm{\Omega }=\{0.01g_1,0.004g_1,0.001g_1\}$, respectively.

Figure 4

(a) The bulk-edge energy gap vs qubit number for the $p=2$ (point) and $p=3$ (circle) SSH models. (b) The fidelities of the QST vs $lg[W/\mathrm{\Delta }]$. Blue: The $p=2$ SSH model with 9 (circle), 15 (star), and 21 (square) qubits. Red: The $p=3$ generalized SSH model with 8 (diamond), 14 (pentagram), and 20 (triangle) qubits. Other parameters are the same as those in Figs. 2 and 3.