Decoherence of a two-qubit system away from perfect symmetry

The decoherence of an asymmetric two-qubit system that is coupled via a variable interaction term to a common bath or two individual baths of harmonic oscillators is examined. The dissipative dynamics are evaluated using the Bloch-Redfield formalism. It is shown that the behavior of the decoherence effects is affected mostly by the symmetries between the qubit operator that is coupled to the environment and the temperature, whereas the differences between the two bath configurations are very small. Moreover, it is elaborated that small imperfections of the qubit parameters do not necessarily lead to a drastic enhancement of the decoherence rates.

Figure 1

Dependence of the gate quality factors on the bath coupling angle $\theta$ defined in Eq. (10) for the CNOT and CPHASE operation at $T\approx 0⪡T_S$. Here, the behavior of the gate quality factors for both the single bath and two bath case is shown. The characteristic energy scale for the gate operation is $E_S∕h=1\mathrm{GHz}$ [15]. The lines are provided as guides to the eye.

Figure 2

Dependence of the gate quality factors on the bath coupling angle $\theta$ defined in Eq. (10) for the CNOT operation at large temperatures $T=2T_S$ and $T=200T_S$. The characteristic energy scale for the gate operation is $E_S∕h=1\mathrm{GHz}$ [15]. The lines are provided as guides to the eye.

Figure 3

(Color online) Dependence of the decoherence rates on the qubit asymmetry. Here, we set $K=0$, ${ϵ}_i=0$, ${\Delta }_2=E_S$, and vary ${\Delta }_1$. The single and two bath cases behave identically, thus only the single bath case is shown. The strength of the decoherence effects is set to $\alpha ={10}^{-3}$ and $T\approx 0.5T_S$. We set the bath coupling angles (24) to ${\theta }_1=0$ and ${\theta }_2=0$, i.e., the bath coupling operator and the Hamiltonian are perpendicular. The decoherence rates are scaled by $\alpha {\nu }_S$, with ${\nu }_S=E_S∕h$. The lines are provided as guides to the eye.

Figure 4

(Color online) Dependence of the decoherence rates on the qubit asymmetry at $T\approx 0.5T_S$. Here, the case of one common bath is investigated. The tunnel matrix element of the second qubit and the interqubit coupling are set to ${\Delta }_2=K=E_S$ and ${\Delta }_1$ is varied. For comparison with experiments, large asymmetry in the tunnel matrix elements of the individual qubits is investigated. The bath coupling angles are set to ${\theta }_1=0$ and ${\theta }_2=0$. The strength of the dissipative effects is $\alpha ={10}^{-3}$. The lines are provided as guides to the eye.

Figure 5

Temperature dependence of selected decoherence rates for $K=0$, ${ϵ}_i=0$, ${\Delta }_1=E_S$, ${\Delta }_2=0.9{\Delta }_1$, for the single bath case. Here, temperature and the bath coupling angles are varied. The strength of the dissipative effects is set to $\alpha ={10}^{-3}$. The decoherence rates are scaled by $\alpha {\nu }_S$, where ${\nu }_S=E_S∕h$. The lines are provided as guides to the eye.