Hardware-Efficient Bosonic Module for Entangling Superconducting Quantum Processors via Optical Networks

Abstract

Scaling superconducting quantum processors beyond single dilution refrigerators requires efficient optical interconnects, yet integrating microwave-to-optical (M2O) transducers poses challenges due to frequency mismatches and qubit decoherence. We propose a modular architecture using SNAIL-based parametric coupling to interface Brillouin M2O transducers with long-lived 3D cavities, while maintaining plug-and-play compatibility. Through numerical simulations incorporating realistic noises, including laser heating, propagation losses, and detection inefficiency, we demonstrate raw entangled bit fidelities of F~0.8 at kHz-level rates over 30 km using the Duan-Lukin-Cirac-Zoller (DLCZ) protocol. Implementing asymmetric entanglement pumping tailored to amplitude damping errors, we achieve purified fidelities F~0.94 at 0.2 kHz rates. Our cavity-based approach outperforms transmon schemes, providing a practical pathway for distributed superconducting quantum computing.

Figures (3)

• Figure 1: (a) Schematic diagram of the superconducting quantum network incorporating the proposed module. A laser pumps the transducers at both distant nodes, where the microwave photons are converted into optical photons and transmitted back for coincidence measurement. By post-selecting single-click detection events, the remote modules become entangled. (b) Schematic of the module: each unit consists of one transducer and one corresponding circuit quantum electrodynamics (cQED) system. (c) Timing diagram illustrating the establishment of microwave-optical photon entanglement via both direct conversion and spontaneous parametric down-conversion (SPDC).
• Figure 2: (a) Raw e-bit distribution performance in both conversion and SPDC schemes. Solid lines represent fidelity $F$, and dashed lines correspond to the heralding rate $R$ (right $y$-axis). For the conversion scheme, $P_e$ is optimized to ensure the highest fidelity $F$ at each pump power. (b) Raw e-bit throughput: the highest-throughput points are marked with stars in corresponding colors. (c) Comparison between transmon and cavity in entanglement distribution. The parameters inside the curly braces represent the operation fidelity $F_{\mathrm{op}}$, energy relaxation time $T_1$, and pure dephasing time $T_{\phi}$, respectively. The node distance $L$ is assumed to be 1 $\mathrm{km}$ in (a) and (b).
• Figure 3: (a) Schematic diagram of the entanglement pumping protocol. In round 0, a raw e-bit is prepared in $C_{3,A}$ and $C_{3,B}$. In each subsequent round, the circuit does not apply bilateral rotations to the e-bits before the CNOT gates Bennett1996; the control pair ($C_{3,A}$, $C_{3,B}$) is preserved only if the target pair ($C_{2,A}$, $C_{2,B}$) is measured in the state $\left|1\right\rangle_{\mu,A}\left|1\right\rangle_{\mu,B}$. The protocol restarts from round 0 if pumping fails. (b) Entanglement pumping performance using the conversion and SPDC schemes. Parameters in the legend denote $T_1$ and $F_{\mathrm{op}}$, respectively. Initial raw e-bits in both scheme are obtained with $P_{\mathrm{on\text{-}chip}}=5~\mathrm{\mu W}$ and $P_e=0.25$. (c) Comparison between raw and purified e-bits after one round of purification, with $T_1=1~\mathrm{ms}$ and $F_{\mathrm{op}}=0.99$. The raw e-bits in round 0 are generated under different pump powers, and the corresponding purified results are plotted for comparison. (d) Comparison between raw and purified e-bits after up to two rounds of purification. The cQED system is idealized with $\eta_{\mathrm{UDT}}=0.9$, $T_1=10~\mathrm{ms}$, and $F_{\mathrm{op}}=0.999$. Similarly, the raw e-bits in round 0 are obtained by varying $P_{\mathrm{laser}}$, as indicated by the colored arrows, and their purification outcomes are evaluated. The $y$-axes in (b)--(d) show infidelity $1-F$ on a logarithmic scale for clarity.