One-step generation of continuous-variable quadripartite cluster states in a circuit QED system

We propose a dissipative scheme for one-step generation of continuous-variable quadripartite cluster states in a circuit QED setup consisting of four superconducting coplanar waveguide resonators and a gap-tunable superconducting flux qubit. With external driving fields to adjust the desired qubit-resonator and resonator-resonator interactions, we show that continuous-variable quadripartite cluster states of the four resonators can be generated with the assistance of energy relaxation of the qubit. By comparison with the previous proposals, the distinct advantage of our scheme is that only one step of quantum operation is needed to realize the quantum state engineering. This makes our scheme simpler and more feasible in experiment. Our result may have useful application for implementing quantum computation in solid-state circuit QED systems.

Figure 1

A possible setup for four-resonator circuit QED with a gap-tunable flux qubit. Four superconducting coplanar waveguide resonators are linearly coupled with each other via SQUIDs, and a gap-tunable superconducting flux qubit is coupled to resonator modes $a_1$ and $a_2$ via the mutual inductance. The qubit has a low-inductance dc SQUID loop which is used to realize energy gap tunability, denoted by a red circle.

Figure 2

Schematic of CV quadripartite cluster states: (a) linear cluster state, (b) square cluster state, and (c) T-shaped cluster state.

Figure 3

Time evolution of variances (a) $V_1$, (b) $V_2$, (c) $V_3$, and (d) $V_4$ for different values of the resonator decay rate. The parameters are chosen as $g/2\pi =50$ MHz, ${\xi }_2=0.2$, ${\xi }_1=0.16$, and $\mathrm{\Omega }/2\pi =5$ MHz, $\mathrm{\Gamma }/2\pi =10\text{MHz},\mathrm{\Delta }g=0$.

Figure 4

Time evolution of variances (a) $V_1$, (b) $V_2$, (c) $V_3$, and (d) $V_4$ for various values of the qubit-resonator coupling-strength difference. The parameters are chosen as $g/2\pi =50$ MHz, ${\xi }_2=0.2$, ${\xi }_1=0.16$, and $\mathrm{\Omega }/2\pi =5$ MHz, $\mathrm{\Gamma }/2\pi =10$ MHz.