[Paper Review] Tunable coupling scheme for implementing two-qubit gates on fluxonium qubits

Ilya N. Moskalenko, Ilya S. Besedin+2 more|arXiv (Cornell University)|Jul 24, 2021

Quantum Information and CryptographyComputer Science30 references34 citations

TL;DR

This paper proposes a tunable coupling scheme for implementing high-fidelity two-qubit gates on fixed-frequency fluxonium qubits by using a fluxonium-based coupler biased at half-flux quantum. The scheme enables iSWAP-like gates via dynamic flux tuning of the coupler, achieving high gate fidelity in a planar on-chip architecture compatible with existing transmon hardware, while benefiting from lower qubit frequencies that reduce control electronics complexity and enhance coherence.

ABSTRACT

The superconducting fluxonium circuit is an RF-SQUID-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, biased at half flux quantum. In this system, both qubits and coupler are coupled capacitively and implemented as fluxonium circuits with an additional harmonic mode. We investigate the performance of the scheme by simulating a universal two-qubit fSim gate. In the proposed approach, we rely on a planar on-chip architecture for the whole device. Our design is compatible with existing hardware for transmon-based devices, with the additional advantage of lower qubit frequency facilitating high-precision gating.

Motivation & Objective

• To develop a tunable coupling scheme for two-qubit gates on fixed-frequency fluxonium qubits.
• To enable high-fidelity two-qubit operations in a planar on-chip architecture compatible with existing transmon hardware.
• To leverage the long coherence times of fluxonium qubits (T1 > 200 µs) while maintaining gate fidelity through dynamic flux control.
• To reduce control electronics complexity by operating at sub-gigahertz frequencies.
• To minimize leakage and coherent errors in two-qubit gates via optimized coupling and tuning protocols.

Proposed method

• The scheme uses three fluxonium qubits: two computational qubits and one tunable coupler, all implemented as modified fluxonium circuits with a harmonic mode.
• Qubit and coupler are capacitively coupled, with interaction strength controlled by tuning the coupler's flux bias.
• The system operates at the flux degeneracy point (Φx = Φ₀/2), where all three qubits are near-resonant, enabling strong XX-type interaction.
• A vacuum Rabi cycle is used to implement an iSWAP-like fSim gate by tuning the coupler through its flux sweet spot.
• The Hamiltonian is modeled using normal mode coordinates (ϑ+ and ϑ−), with the harmonic mode (ϑ+) and nonlinear fluxonium mode (ϑ−) coupled via asymmetries in capacitance and inductance.
• Numerical simulations are used to evaluate gate performance under decoherence, leakage, and coherent errors, with parameters derived from realistic circuit design.

Experimental results

Research questions

• RQ1 Can a tunable coupling scheme be designed for fixed-frequency fluxonium qubits that enables high-fidelity two-qubit gates?
• RQ2 How does dynamic flux tuning of a fluxonium-based coupler enable iSWAP-like gate operations in a planar architecture?
• RQ3 What are the dominant error sources (decoherence, leakage, coherent errors) in the proposed fSim gate, and how can they be mitigated?
• RQ4 To what extent is the proposed scheme compatible with existing transmon-based control hardware and infrastructure?
• RQ5 What is the impact of harmonic mode asymmetries and nonlinear superinductances on qubit coherence and gate fidelity?

Key findings

• The proposed scheme enables a universal fSim gate with θ = π/4 and conditional phase ϕ, achieving high fidelity through dynamic flux tuning of the coupler.
• The gate is implemented by tuning the coupler from the upper to lower flux sweet spot and back, completing a quarter vacuum Rabi cycle.
• The system achieves a dispersive shift of χ = 23 MHz from capacitance and inductance asymmetries (5% relative asymmetry), and χ = 0.5 MHz from superinductor nonlinearity.
• Thermal dephasing is suppressed with Tϕ > 1 s at 10 mK, due to low harmonic mode decay rate (κ = 0.01 MHz) and high χ.
• The design is compatible with existing transmon hardware and enables sub-gigahertz control, reducing cost and complexity of control electronics.
• The scheme maintains low crosstalk, with parasitic ZZ crosstalk ζon_zz < 1 MHz at the flux degeneracy point, and effective coupling gxx ≈ 200 MHz at zero flux bias.