Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction

TL;DR

This work addresses realizing fast, high-fidelity two-qubit gates in fluxonium-based quantum processors by modulating the plasmon interaction with a tunable coupler. The authors derive an effective plasmon–plasmon Hamiltonian and show that driving the coupler at the sum frequency of the plasmon transitions activates a bSWAP-type interaction, enabling a controlled-phase gate via occupation of noncomputational plasmon states. They identify three parametric pathways (bSWAP between plasmon modes, blue-sideband couplings, and coupler squeezing) and demonstrate that, despite potential spurious transitions, the target $|11\rangle\rightarrow|22\rangle$ transition can be harnessed with sub-100 ns gate times and intrinsic errors below $10^{-4}$ under realistic conditions. Sensitivity analyses reveal robustness to drive and bias fluctuations, while leakage and spectator interactions are analyzed and mitigated through synchronization strategies and circuit design. Overall, the approach provides a scalable, versatile framework for fluxonium quantum processors with potential extensions to multi-qubit gates, contingent on advances in plasmon coherence and leakage control.

Abstract

In superconducting quantum processors, exploring diverse control methods could offer essential versatility and redundancy to mitigate challenges such as frequency crowding, spurious couplings, control crosstalk, and fabrication variability, thus leading to better system-level performance. Here we introduce a control strategy for fast entangling gates in a scalable fluxonium architecture, utilizing parametric modulation of the plasmon interaction. In this architecture, fluxoniums are coupled via a tunable coupler, whose transition frequency is flux-modulated to control the inter-fluxonium plasmon interaction. A bSWAP-type interaction is activated by parametrically driving the coupler at the sum frequency of the plasmon transitions of the two fluxoniums, resulting in the simultaneous excitation or de-excitation of both plasmon modes. This strategy therefore allow the transitions between computational states and non-computational plasmon states, enabling the accumulation of conditional phases on the computational subspace and facilitating the realization of controlled-phase gates. By focusing on a specific case of these bSWAP-type interactions, we show that a simple drive pulse enables sub-100ns CZ gates with an error below $10^{-4}$. Given its operational flexibility and extensibility, this approach could potentially offer a foundational framework for developing scalable fluxonium-based quantum processors.

Figures (15)

• Figure 1: (a) A two-dimensional (2D) square qubit lattice comprising fluxoniums (circles) coupled via couplers (squares). The inset depicts the fluxonium architecture featuring tunable plasmon interactions, where fluxoniums are coupled via a frequency-tunable transmon coupler. (b) The energy levels of the unit cell comprising two coupled fluxonium qubits (i.e., $Q_{0}$ and $Q_{1}$), with emphasis on the computational subspace spanned by $\{|000\rangle, |001\rangle, |100\rangle, |101\rangle\}$ (shaded region) and the fluxonium's plasmon mode $|1\rangle \rightarrow |2\rangle$. The full system state is labeled as $|Q_0, C, Q_1\rangle$. Solid orange arrows indicate direct plasmon-coupler couplings, while dashed orange arrows represent coupler-mediated plasmon-plasmon interactions. In addition to blue sideband transitions between each fluxonium and the coupler (red arrows), parametric modulation of the coupler can also activate a bSWAP-type interaction ($|101\rangle \rightarrow |202\rangle$, black arrow) between the plasmon modes of the two fluxoniums.
• Figure 2: (a) Coupler-mediated interactions for the plasmon transition $|1\rangle\rightarrow|2\rangle$, characterized by state-dependent plasmon frequency shifts as a function of coupler flux bias. Discontinuities and abrupt jumps in the curves result from state labeling ambiguities near avoided crossings. Solid and dashed lines represent results for coupled fluxonium systems with distinct parameter sets, including coupling strengths and coupler frequencies, as specified in Table \ref{['tab:circuit_parameters']}. Black arrows indicate the coupler idle point (where state-dependent frequency shifts are minimized) and interaction point for the system with $J_{ck}/2\pi=500\,{\rm MHz}$, while gray arrows mark the corresponding points for the system with $J_{ck}/2\pi=300\,{\rm MHz}$. (b) In the context of implementing parametric gates, these parameter sets lead to two distinct operational configurations: the left panel illustrates the combination of a parametric drive with a dynamic flux bias, while the right panel shows the combination of a parametric drive with a static flux bias.
• Figure 3: Population within the computational (qubit) subspace as a function of parametric drive frequency and evolution time, for the coupled fluxonium system initialized in the state $(|00\rangle+|01\rangle+|10\rangle+|11\rangle)/2$. (a) System with $J_{ck}/2\pi=500\,{\rm MHz}$. The static coupler bias is set to $\Phi_{s}/\Phi_{0}=0.35$, and the parametric drive amplitude is $\delta_{\Phi}/\Phi_{0}=0.045$. (b) System with $J_{ck}/2\pi=300\,{\rm MHz}$. The static coupler bias is set to $\Phi_{s}/\Phi_{0}=0.30$, and and the drive amplitude is $\delta_{\Phi}/\Phi_{0}=0.075$. The pink dashed boxes highlight the parametric-activated transition $|11\rangle\rightarrow|22\rangle$, while the pink label $S$ indicates an example of a spurious transition induced by the parametric drive, specifically $|000(100)\rangle\leftrightarrow|004(104)\rangle$.
• Figure 4: Population versus the parametric drive frequency around the $|11\rangle\rightarrow|22\rangle$ transition and the evolution time, presented as an enlarged view of the region within the pink dashed box in Fig. \ref{['fig3']}. Here, $P_{ij\rightarrow ij}$ represents the population in state $|ij\rangle$ when the system is initially prepared in $|ij\rangle$. The circuit parameters used in (a-d) and (e-h) are the same as those in Fig. \ref{['fig3']}(a) and Fig. \ref{['fig3']}(b), respectively. The vertical dashed lines indicate the ideal transition frequency for $|11\rangle\rightarrow|22\rangle$ without accounting for drive-induced frequency shifts.
• Figure 5: Population in $|11\rangle$ in the parametric-driven system as a function of the parametric drive frequency around the $|11\rangle\rightarrow|22\rangle$ transition and the drive amplitude, with the evolution time fixed at 100 ns and the initial state of $|11\rangle$. The circuit parameters used in (a) and (b) correspond to those in Fig. \ref{['fig3']}(a) and Fig. \ref{['fig3']}(b), respectively. The orange square in (a) and the teal circle in (b) mark the transition frequencies of $|11\rangle\rightarrow|22\rangle$ obtained using the Floquet numerical method. The corresponding transition strengths are shown in the insets, with grey lines indicating the results from the approximate model.