Stability of longitudinal coupling for Josephson charge qubits

For inductively coupled superconducting quantum bits, we determine the conditions when the coupling commutes with the single-qubit terms. We show that in certain parameter regimes such longitudinal coupling can be stabilized with respect to variations of the circuit parameters. In addition, we analyze its stability against fluctuations of the control fields.

Figure 1

Charge qubits coupled to an $LC$ circuit. Earlier proposals with either longitudinal (Ref. 15) or transverse (Refs. 12, 14) coupling can be considered as particular cases of this design. The fluxes shown here are applied in the loops between the qubits, such that the total flux bias between the inductance and a qubit $j$ is given as ${\Phi }_{\mathrm{x}}^j={\sum }_{k=1}^j{\tilde{\Phi }}_{\mathrm{x}}^k$. The junctions may be replaced by SQUID loops to achieve tunable Josephson energies.

Figure 2

(Color online) Stability diagram for a Josephson charge qubit. In region I, tuning to longitudinal coupling by applied magnetic fluxes is possible. In region II, the coupling always has a transverse component.