Crosstalk in Multi-Qubit Fluxonium Architectures with Transmon Couplers

Abstract

In recent years, several architectures have been proposed for implementing two-qubit operations on fluxonium superconducting qubits. A particularly promising approach, which was demonstrated experimentally by Refs. [1,2], employs a transmon superconducting qubit as a tunable coupler between the fluxonium qubits. These experiments have shown that the transmon coupler enables fast, high-fidelity two-qubit operations while suppressing unwanted ZZ crosstalk between the fluxonium qubits. In this work, we numerically study the scalability of this architecture. We find that, when trivially scaling this architecture, crosstalk from spectator qubits limits the gate fidelity to below 90%. We show that these spectator errors can be reduced to below $10^{-4}$ by reducing the coupling strength and by dynamically tuning transmons that are not used for a two-qubit operation to an off position. We further investigate the resilience of the operation to direct capacitive coupling between the transmon couplers and to microwave crosstalk.

Figures (10)

• Figure 1: Schematic drawing of the systems studied in this work. The numbers indicate the site numbering used throughout the main text. (a) 1D system, (b) 2D grid system and (c) 2D system for the $\llbracket 4,2,2 \rrbracket$ error correcting code with two auxiliary qubits.
• Figure 2: (a) Schematic circuit diagram of the three node FTF system. (b) Fluxonium and transmon energy levels as a function of $E_{J}^\text{T}$. The green-shaded and red-shaded lines correspond to states with the transmon in its ground state and first excited state respectively. (c) Transition energies of the transmon's qubit level as a function of $E_{J}^\text{T}$. (d) Residual ZZ coupling between the fluxonium qubits with the transmon in the ground or excited state. (e) Minimum frequency separation of the transmon's qubit transition. The vertical dashed line in panels (c) and (e) indicate the $E_{J}^\text{T}$ experimentally realized in Ref. sidd_eugene.
• Figure 3: Spectator errors in a 1D chain consisting of six fluxoniums and five transmon couplers as a function of the gate duration $t_g$. For each system, the two-qubit operation is calibrated with all spectators in $\ket{0}$ (solid lines), and then the error is averaged over the four spectator states with $s_l,s_r \in \{0,1\}$ (dashed lines). In red and blue, we plot the errors for the parameters inspired (Insp.) by Refs. mit_cz and sidd_eugene respectively, and in green we plot the results for the parameters proposed in this work. For the parameters inspired by Refs. mit_czsidd_eugene all transmons are statically positioned at their on point, while for the parameters proposed in this work the frequencies of inactive transmons are dynamically tuned to an off position.
• Figure 4: Spectator errors for the 2D qubit architectures illustrated in Fig. \ref{['fig:grid1d']}. For each system, the two-qubit operation is calibrated with all spectators in $\ket{0}$ (solid lines), and then the error is averaged over all spectator configurations (dashed lines).
• Figure 5: (a) Total error $E_\text{tot}$ averaged over all spectator configurations for the 2D grid system as a function of the gate duration $t_g$ and the capacitive coupling between neighboring transmons $g_\text{TT}$. (b) Total error $E_\text{tot}$ of the bare center FTF pair as a function of the gate duration $t_g$ and the microwave (MW) crosstalk strength $\gamma$.