Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm

We propose a protocol for complete Bell-state analysis for two superconducting-quantum-interference-device qubits. The Bell-state analysis could be completed by using a sequence of microwave pulses designed by the transitionless tracking algorithm, which is a useful method in the technique of shortcut to adiabaticity. After the whole process, the information for distinguishing four Bell states will be encoded on two auxiliary qubits, while the Bell states remain unchanged. One can read out the information by detecting the auxiliary qubits. Thus the Bell-state analysis is nondestructive. The numerical simulations show that the protocol possesses a high success probability of distinguishing each Bell state with current experimental technology even when decoherence is taken into account. Thus, the protocol may have potential applications for the information readout in quantum communications and quantum computations in superconducting quantum networks.

Figure 1

The level configuration of a single SQUID qubit.

Figure 2

(a) The auxiliary qubits $A_1$, $A_2$ and the information carriers $B_1$, $B_2$ placed in a microwave cavity. (b) The level configuration of SQUID qubit $A_j$ ($j=1,2$). (c) The level configurations of SQUID qubits $B_1$ and $B_2$.

Figure 3

Microwave pulses for the Bell-state analysis.

Figure 4

Success probabilities vs $g$. $P\left({\mathrm{\Psi }}_{+}\right)$ (solid blue line), $P\left({\mathrm{\Psi }}_{-}\right),P\left({\mathrm{\Phi }}_{+}\right)$ (dotted green line), and $P\left({\mathrm{\Phi }}_{-}\right)$ (dashed red line).

Figure 5

(a) $P\left({\mathrm{\Psi }}_{+}\right)$, (b) $P\left({\mathrm{\Psi }}_{-}\right)$, (c) $P\left({\mathrm{\Phi }}_{+}\right)$, and (d) $P\left({\mathrm{\Phi }}_{-}\right)$ vs $\kappa /{\mathrm{\Omega }}_{max}$ (solid red line), $\gamma /{\mathrm{\Omega }}_{max}$ (dashed green line), and $10{\gamma }_{\varphi }/{\mathrm{\Omega }}_{max}$ (dotted blue line).