Dispersive coupling between the superconducting transmission line resonator and the double quantum dots

Realization of controllable interaction between distant qubits is one of the major problems in scalable solid-state quantum computing. We study a superconducting transmission line resonator (TLR) as a tunable dispersive coupler for the double-dot molecules. A general interaction Hamiltonian of $n$ two-electron spin-based qubits and the TLR is presented, where the double-dot qubits are biased at the large detuning region and the TLR is always empty and virtually excited. Our analysis of the main decoherence sources indicates that various major quantum operations can be reliably implemented with current technology.

Figure 1

(Color online) Coupled system of a TLR and $n$ double-dot molecules. The length of the TLR is $L$ (about ten millimeters). $C_0$ is the wiring capacitor between TLR and external input or output. The double-dot qubits are connected to the TLR via the coupling capacitors $C_{ci}$. The TLR acts as a data bus between the double-dot qubits.

Figure 2

(Color online) Circuit representation of a TLR. The TLR consists of a full-wave section of superconducting coplanar waveguide. The red line represents the full-wave mode. The coupling capacitors connected to the input or output wiring slightly modify the frequency and phase of the TLR’s modes.

Figure 3

Micrograph of a double-dot sample. This figure is reproduced from Fig. 1 of Ref. 4. The $L$ and $R$ gates represent the left and right gates, respectively, in the text, and the $T$ gate can be used to adjust the tunneling coupling strength between two dots.

Figure 4

(Color online) Lowest-energy states of the double-dot molecule. The gray region is the “saddle” point in the text.

Figure 5

(Color online) Dependence of the error probability $D$ in entanglement generation on dissipation factors ${\gamma }_{\phi }$ and $\gamma$.