[Paper Review] Tunable inductive coupler for high fidelity gates between fluxonium qubits

Helin Zhang, Chunyang Ding+10 more|arXiv (Cornell University)|Sep 11, 2023

Neural Networks and Reservoir ComputingComputer Science3 citations

TL;DR

This paper presents a tunable inductive coupler that enables high-fidelity two-qubit gates between heavy-fluxonium qubits by achieving strong, controllable XX coupling (−35 to 75 MHz) with minimal ZZ crosstalk (<3 kHz). The coupler supports a √bSWAP gate in 102 ns with 99.91% fidelity and stable performance over 20+ hours, demonstrating high-fidelity, fast operations essential for scalable quantum computing.

ABSTRACT

The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with $\sim50$MHz frequencies and $\sim5$ GHz anharmonicities. The coupler enables the qubits to have a large tuning range of $ extit{XX}$ coupling strengths ($-35$ to $75$ MHz). The $ extit{ZZ}$ coupling strength is $&lt;3$kHz across the entire coupler bias range, and $&lt;100$Hz at the coupler off-position. These qualities lead to fast, high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a $\sqrt{i\mathrm{SWAP}}$ gate in $258$ns with fidelity $99.72\%$, and by driving at the sum frequency of the two qubits, we achieve a $\sqrt{b\mathrm{SWAP}}$ gate in $102$ns with fidelity $99.91\%$. This latter gate is only 5 qubit Larmor periods in length. We run cross-entropy benchmarking for over $20$ consecutive hours and measure stable gate fidelities, with $\sqrt{b\mathrm{SWAP}}$ drift ($2 σ$) $&lt; 0.02\%$ and $\sqrt{i\mathrm{SWAP}}$ drift $&lt; 0.08\%$.

Motivation & Objective

• Develop a tunable inductive coupler to enable high-fidelity two-qubit gates between low-frequency fluxonium qubits.
• Minimize unwanted ZZ coupling to preserve gate fidelity and avoid leakage outside the computational subspace.
• Achieve fast, high-fidelity single- and two-qubit gates by leveraging strong, controllable XX coupling.
• Demonstrate stable gate performance over extended operation times to validate scalability potential.
• Enable high-fidelity entangling gates using flux-tunable inductive coupling without populating higher excited states.

Proposed method

• Implement a tunable inductive coupler based on a small Josephson junction and a short array of large junctions, enabling flux-tunable inductive coupling between two heavy-fluxonium qubits.
• Use the coupler's flux bias to tune the XX coupling strength from −35 MHz to 75 MHz, enabling fast gate operations.
• Design the coupler to allow both XX and ZZ couplings to be turned off at the coupler's off-position, enabling single-qubit gate operations.
• Drive the system at the difference frequency (|ω_b − ω_a|) to implement a √iSWAP gate and at the sum frequency (ω_b + ω_a) to implement a √bSWAP gate.
• Apply a rotating wave approximation (RWA) to derive the effective Hamiltonian, isolating the desired XX interaction and minimizing unwanted terms.
• Use numerical simulations of the Lindblad master equation to model decoherence effects and quantify error contributions from decay, dephasing, and crosstalk.

Experimental results

Research questions

• RQ1 Can a tunable inductive coupler achieve strong, controllable XX coupling between low-frequency fluxonium qubits while suppressing ZZ crosstalk?
• RQ2 What is the achievable gate fidelity and speed for two-qubit entangling gates using this inductive coupling scheme?
• RQ3 How stable are the gate fidelities over extended operation times, and what are the dominant error sources?
• RQ4 Can the coupler enable high-fidelity gates without populating higher excited states outside the computational subspace?
• RQ5 How do factors like RF flux crosstalk and carrier-envelope phase variation affect gate infidelity, and can they be mitigated?

Key findings

• The tunable inductive coupler achieves a wide XX coupling range of −35 MHz to 75 MHz, enabling fast two-qubit gates.
• ZZ coupling is suppressed to <3 kHz across the entire coupler bias range and <100 Hz at the coupler off-position, minimizing unwanted interactions.
• A √bSWAP gate is realized in 102 ns with a fidelity of 99.91%, corresponding to only 5 qubit Larmor periods.
• A √iSWAP gate is implemented in 258 ns with a fidelity of 99.72%, demonstrating high-fidelity operation at the difference frequency.
• Cross-entropy benchmarking over 20+ hours shows minimal drift: √bSWAP drift <0.02% (2σ) and √iSWAP drift <0.08% (2σ), indicating long-term stability.
• Decoherence is the dominant error source, contributing about half of the total infidelity, with numerical simulations showing excellent agreement with analytical estimates.