[Paper Review] Demonstration of the Two-Fluxonium Cross-Resonance Gate

Ebru Doğan, Dario Rosenstock+8 more|arXiv (Cornell University)|Apr 25, 2022

Atomic and Subatomic Physics Research4 citations

TL;DR

This paper demonstrates a fast, all-microwave cross-resonance (CR) CNOT gate between two fluxonium qubits, operating entirely within the computational subspace at the half-flux quantum sweet spot. The gate achieves a fidelity of 99.49(6)% in 70 ns, preserving coherence and avoiding flux tuning or population of non-computational states, marking a key step toward high-fidelity, coherence-optimized two-qubit operations in superconducting quantum processors.

ABSTRACT

The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half flux quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the non-computational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively-coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct CNOT gate in 70 ns with fidelity up to $\mathcal{F}=0.9949(6)$ despite the limitations of a sub-optimal measurement setup and device coherence. Our results project a possible pathway towards reducing the two-qubit error rate below $10^{-4}$ with present-day technologies.

Motivation & Objective

• To develop a two-qubit gate for fluxonium qubits that maintains high coherence by avoiding flux tuning away from the half-flux quantum sweet spot.
• To implement a cross-resonance gate using only microwave drives, eliminating the need for dynamic flux control or tunable couplers.
• To achieve high-fidelity two-qubit operations while confining qubit dynamics strictly to the computational subspace.
• To demonstrate that fluxonium's strong anharmonicity enables fast, high-fidelity gates without compromising coherence.
• To project a pathway toward two-qubit error rates below 10⁻⁴ using existing technology.

Proposed method

• The two fluxonium qubits are capacitively coupled and operated at the half-flux quantum sweet spot to maximize coherence.
• A control qubit is driven at the target qubit's transition frequency to induce a cross-resonance interaction, enabling a CNOT operation.
• The gate is implemented using microwave pulses with minimal pulse shaping, leveraging the large anharmonicity and hierarchy of matrix elements in fluxonium.
• The gate operates without populating non-computational states or detuning qubit frequencies from the sweet spot.
• Pulse ramp times were reduced to 2 ns without fidelity degradation, demonstrating robustness to fast pulses.
• Numerical simulations were used to model gate error sources, including unitary and incoherent errors, to guide optimization.

Experimental results

Research questions

• RQ1 Can a high-fidelity two-qubit gate be implemented in fluxonium qubits without detuning from the half-flux quantum sweet spot?
• RQ2 Can the cross-resonance gate mechanism be effectively applied to fluxonium qubits due to their strong anharmonicity and selection rules?
• RQ3 What is the achievable gate fidelity and speed when the gate is confined to the computational subspace and uses only microwave drives?
• RQ4 How do coherence times and error sources such as relaxation and dephasing limit gate performance in this configuration?
• RQ5 Can the gate fidelity be improved to below 10⁻⁴ error rate with current device parameters and modest improvements?

Key findings

• A direct CNOT gate was realized in 70 ns with a fidelity of 99.49(6)%, demonstrating high-performance operation within the computational subspace.
• The gate fidelity is close to the free-evolution coherence limit, indicating no hidden control errors or decoherence at the 10⁻³ level.
• Pulse ramp times as short as 2 ns had no measurable impact on fidelity, highlighting robustness to fast pulses.
• Numerical simulations suggest that gate speeds of 40 ns could be optimal if pulse reflection issues were resolved.
• With improved coherence times (e.g., T₂ > 200 μs), a coherence-limited error rate of 2×10⁻⁴ at 50 ns gate time is projected.
• The system is expected to support parameterized controlled unitary operations, including CYπ and arbitrary single-qubit rotations, enabling broader quantum algorithm applications.