Single-Step Hybrid CV-DV Transfer of Multipartite W States Using Cat-State Qubits

TL;DR

This work addresses transferring multipartite entanglement encoded in hybrid CV-DV cat-state qubits across cavities in circuit QED. It introduces a deterministic, single-step protocol wherein a single superconducting flux qutrit mediates dispersive Raman-type interactions to implement simultaneous beam-splitter couplings between resonator pairs, enabling the transfer of an $n$-qubit W state, $|W_n^{\(\mathrm{cat}\)}\rangle$, from odd to even resonators while keeping the qutrit in the $|g\rangle,|e\rangle$ manifold and avoiding population of $|f\rangle$. The key results include the derivation of the effective Hamiltonian $H_{\mathrm{eff}}$ and the decoupled, commuting pairwise evolutions $H_e$, which yield a deterministic transfer at $t=T=\pi/(2|\lambda|)$; numerical Lindblad simulations with realistic losses show a maximum fidelity around $0.92$ for a three-qubit W state, demonstrating experimental feasibility with current circuit QED technology. This approach provides a practical route to scalable, high-fidelity hybrid CV-DV entanglement distribution in superconducting microwave networks without intermediate measurements or complex control sequences.

Abstract

We propose a deterministic hybrid continuous-variable-discrete-variable (CV-DV) scheme for the single-step transfer of an $n$-qubit W state encoded in photonic Schr$\ddot{o}$dinger cat-state qubits within a circuit QED architecture. Logical qubits are encoded in even- and odd-parity cat states of bosonic modes, while effective Raman-type interactions between resonator pairs are mediated by a single superconducting flux qutrit operating in the dispersive regime. The protocol coherently transfers the multipartite W state in a single collective operation without populating higher excited atomic levels, thereby strongly suppressing decoherence. Numerical simulations based on the full Lindblad master equation, including realistic cavity dissipation, qutrit relaxation and dephasing, and inter-cavity crosstalk, show that a three-qubit cat-state W state can be transferred with a maximum fidelity of approximately $0.92$. These results demonstrate the feasibility of scalable hybrid CV-DV entanglement transfer using current circuit QED technology.

Figures (2)

• Figure 1: (a) Diagram of an artificial superconducting qutrit (represented by circle A) and six microwave resonators. For 1D microwave resonator, the qutrit is capacitively coupled to each resonator 59. (b) Illustration of the qutrit-cavity dispersive interaction and the qutrit-pulse resonant interaction.
• Figure 2: Time evolution of the fidelity $F$ for the transfer of the W-type cat-state encoded cavity state as a function of the normalized interaction time $t/T$, where $T=\pi/(2|\lambda_{12}|)$ is the effective swap time. The simulation includes cavity dissipation ($\kappa^{-1}=20~\mu\mathrm{s}$), qutrit energy relaxation and dephasing, inter-cavity crosstalk, and unwanted pulse-induced transitions using experimentally realistic parameters.