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arXiv:2309.05720

Tunable Inductive Coupler for High-Fidelity Gates Between Fluxonium Qubits

Helin Zhang, Chunyang Ding, D. K. Weiss, Ziwen Huang, Yuwei Ma, Charles R. Guinn, Sara Sussman, Sai Pavan Chitta, Danyang Chen, Andrew Houck, Jens Koch, David Schuster

Published Sep 11, 2023• 0 citations
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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 $\textit{XX}$ coupling strengths ($-35$ to $75$ MHz). The $\textit{ZZ}$ coupling strength is $<3$kHz across the entire coupler bias range, and $<100$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 ($2 σ$) $< 0.02\%$ and $\sqrt{i\mathrm{SWAP}}$ drift $< 0.08\%$.

DOI
10.48550/arxiv.2309.05720

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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 ∼50\sim50∼50MHz frequencies and ∼5\sim5∼5 GHz anharmonicities. The coupler enables the qubits to have a large tuning range of XX\textit{XX}XX coupling strengths (−35-35−35 to 757575 MHz). The ZZ\textit{ZZ}ZZ coupling strength is <3<3<3kHz across the entire coupler bias range, and <100<100<100Hz 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 iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gate in 258258258ns with fidelity 99.72%99.72\%99.72%, and by driving at the sum frequency of the two qubits, we achieve a bSWAP\sqrt{b\mathrm{SWAP}}bSWAP​ gate in 102102102ns with fidelity 99.91%99.91\%99.91%. This latter gate is only 5 qubit Larmor periods in length. We run cross-entropy benchmarking for over 202020 consecutive hours and measure stable gate fidelities, with bSWAP\sqrt{b\mathrm{SWAP}}bSWAP​ drift (2σ2 σ2σ) <0.02%< 0.02\%<0.02% and iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ drift <0.08%< 0.08\%<0.08%.
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 approximately 50 -MHz frequencies and approximately 5 -GHz anharmonicities. The coupler enables the qubits to have a large tuning range of X X coupling strengths ( − 35 to 75 MHz). The Z Z coupling strength is < 3 kHz across the entire coupler bias range and < 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 i SWAP gate in 258 ns with fidelity 99.72%, and by driving at the sum frequency of the two qubits, we achieve a b SWAP gate in 102 ns with fidelity 99.91%. This latter gate is only five qubit Larmor periods in length. We run cross-entropy benchmarking for over 20 consecutive hours and measure stable gate fidelities, with b SWAP drift ( 2 σ ) < 0.02 % and i SWAP drift < 0.08 % . Published by the American Physical Society 2024
Abstract Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.
Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.
Two qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have previously been implemented in different ways with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2πππ rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of 10−210^{-2}10−2 for gate times below 60~ns. At longer durations, our gate is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency selective entangling gates.
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 10−410^{-4}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.
We propose and demonstrate an architecture for fluxonium-fluxonium two-qubit gates mediated by transmon couplers (FTF, for fluxonium-transmon-fluxonium).Relative to architectures that exclusively rely on a direct coupling between fluxonium qubits, FTF enables stronger couplings for gates using noncomputational states while simultaneously suppressing the static controlled-phase entangling rate (ZZ) down to kilohertz levels, all without requiring strict parameter matching.Here, we implement FTF with a flux-tunable transmon coupler and demonstrate a microwave-activated controlled-Z (CZ) gate whose operation frequency can be tuned over a 2-GHz range, adding frequency allocation freedom for FTFs in larger systems.Across this range, state-of-the-art CZ gate fidelities are observed over many bias points and reproduced across the two devices characterized in this work.After optimizing both the operation frequency and the gate duration, we achieve peak CZ fidelities in the 99.85%-99.9%range.Finally, we implement model-free reinforcement learning of the pulse parameters to boost the mean gate fidelity up to 99.922% Æ 0.009%, averaged over roughly an hour between scheduled training runs.Beyond the microwave-activated CZ gate we present here, FTF can be applied to a variety of other fluxonium gate schemes to improve gate fidelities and passively reduce unwanted ZZ interactions.