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PRX Quantum

Tunable Inductive Coupler for High-Fidelity Gates Between Fluxonium Qubits

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

Published May 2, 2024• 63 citations
Publisher

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 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

DOI
10.1103/prxquantum.5.020326

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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 $\sim50$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 $< 0.08\%$.

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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 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
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%.
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.
The path toward practical superconducting quantum processors requires the integration of a large number of high-performance qubits. Modular architectures could offer a way to address the scaling limitations of monolithic designs by partitioning a large quantum processor into physically separated modules, or chiplets, linked through long-range interconnects. In this context, although fluxonium qubits have emerged as a compelling platform for quantum computing due to their long coherence times and high-fidelity gates, existing coupling schemes remain restricted to qubits in close proximity on a single chip. This limitation inherently precludes the long-range interconnects essential for modular integration. In this work, we propose a long-range tunable coupler designed to interconnect fluxonium qubits separated by more than one centimeter, thereby supporting the realization of modular fluxonium quantum processors. Under realistic assumptions, the proposed coupler has the potential to achieve inter-module two-qubit gate performance, specifically sub-100-ns gates with intrinsic errors below 10−410^{-4}10−4, comparable to that of intra-module (intra-chiplet) gates, while enabling modular integration with low quantum crosstalk, a key requirement for scalable systems. We further discuss the integration of this coupler into modular fluxonium lattices and explore its feasibility for achieving the higher connectivity and longer coupling range required for complex quantum error correction codes. This work could contribute to the development of large-scale fluxonium quantum processors by bridging their demonstrated potential with modular scalability.
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.
A superconducting fluxonium circuit is an RF-superconducting quantum interference device-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 couplers 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.
We take a bottom-up first-principles approach to designing a two-qubit gate between fluxonium qubits for minimal error, speed, and control simplicity. Our proposed architecture consists of two fluxoniums coupled via a resonator. The use of a simple linear coupler has many practical benefits, including the possibility of material optimization for suppressing loss, reducing fabrication complexity, and increasing yield by circumventing the need for Josephson junctions. Crucially, a resonator-as-coupler approach also suggests a clear path to increased connectivity between fluxonium qubits, by reducing capacitive loading when the coupler has a high impedance. After performing analytic and numerical analyses of the circuit Hamiltonian and gate dynamics, we tune circuit parameters to destructively interfere sources of coherent error, revealing an efficient fourth-order scaling of coherent error with gate duration. For component properties from the literature, we predict an open-system average controlled- Z () gate infidelity of 1.86 × 10 − 4 in 70 ns. Published by the American Physical Society 2024