Abstract
In this paper, we present a protocol to generate a W state of three superconducting qubits (SQs) by using multiple Schrödinger dynamics. The three SQs are respective embedded in three different coplanar waveguide resonators (CPWRs), which are coupled to a superconducting coupler (SCC) qubit at the center of the setups. With the multiple Schrödinger dynamics, we build a shortcuts to adiabaticity (STA), which greatly accelerates the evolution of the system. The Rabi frequencies of the laser pulses being designed can be expressed by the superpositions of Gaussian functions via the curves fitting, so that they can be realized easily in experiments. What is more, numerical simulation result shows that the protocol is robust against control parameters variations and decoherence mechanisms, such as the dissipations from the CPWRs and the energy relaxation. In addition, the influences of the dephasing are also resisted on account of the accelerating for the dynamics. Thus, the performance of the protocol is much better than that with the conventional adiabatic passage techniques when the dephasing is taken into account. We hope the protocol could be implemented easily in experiments with current technology.
Highlights
Refs 31 and 36 has shown that, the fidelity for generating of the W state by using adiabatic passage is quite sensitive to the dephasing, which is an ineluctable element of the decoherence mechanisms in the superconducting systems, i.e., a small increase of the dephasing rates causes a large decrease of the fidelity; this will bring challenges to the experiments
To overcome the problem causing by the long evolution time of the adiabatic passage, one should speed up the evolution by using some other techniques
It is proved in ref. 32 that, with resonant interaction, the population of each state changes rapidly when the evolution time increases, and a high fidelity of the target state only appears in very narrow ranges around some certain moments
Summary
We would like to review the multiple Schrödinger dynamics[104,105,106] firstly. If one hopes the transitions between instantaneous eigenstates {|n0(t)〉} are all action picture is diagonal. Interaction picture (Hj(t)), one can obtain the j-th modified Schrödinger Hamiltonian as. As for the SCC qubit, it has an excited state |e〉c and two ground states |g〉cand |f〉c, which has similar structure as the three SQs. The transition |e〉c↔ |f〉c is driven by the laser pulse with Rabi frequency Ωc(t). We assume that the coupling constant for the transition |e〉c ↔|g〉c coupled to CPWRk is νk. The Hamiltonian in the 1-st iteration picture can be solved in basis {|ξ0〉, |ξ+〉, |ξ−〉} as 0 iθ / 2 iθ / 2. The picture transformation for the 2-nd iteration in basis {|ξ0〉, |ξ+〉, |ξ−〉} can be given by.
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