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arXiv:2404.08328

Realization of two-qubit gates and multi-body entanglement states in an asymmetric superconducting circuits

Tao Zhang, Chao Zhao

Published Apr 12, 2024• 0 citations
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Abstract

In recent years, the tunable coupling scheme has become the mainstream scheme for designing superconducting quan tum circuits. By working in the dispersive regime, the ZZ coupling and high-energy level leakage can be effectively suppressed and realize a high fidelity quantum gate. We propose a tunable fluxonium-transmon-transmon (FTT) cou pling scheme. In our system, the coupler is a frequency tunable transmon qubit. Both qubits and coupler are capacitively coupled. The asymmetric structure composed of fluxonium and transmon will optimize the frequency space and form a high fidelity two-qubit quantum gate. By decoupling, the effective coupling strength can be easily adjusted to close to the net coupling between qubits. We numerical simulation the master equation to reduce the quantum noise to zero. We study the performance of this scheme by simulating the general single-qubit Xπ/2 gate and two-qubit (iSWAP) gate. In the bias point of the qubits, we achieve a single qubit gate with 99.99% fidelity and a two-qubit gate with 99.95% fidelity. By adjusting the nonlinear Kerr coefficient of fluxonium to an appropriate value, we can achieve a multi-body entanglement state. We consider the correlation between the two qubits and the coupler, and the magnetic flux passing through one qubit has an effect on the other qubit and the coupler. Finally, we analyze the quantum correlation of the two-body entanglement state.

DOI
10.48550/arxiv.2404.08328

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In recent years, the tunable coupling scheme has become the mainstream scheme for designing superconducting quan tum circuits. By working in the dispersive regime, the ZZ coupling and high-energy level leakage can be effectively suppressed and realize a high fidelity quantum gate. We propose a tunable fluxonium-transmon-transmon (FTT) cou pling scheme. In our system, the coupler is a frequency tunable transmon qubit. Both qubits and coupler are capacitively coupled. The asymmetric structure composed of fluxonium and transmon will optimize the frequency space and form a high fidelity two-qubit quantum gate. By decoupling, the effective coupling strength can be easily adjusted to close to the net coupling between qubits. We numerical simulation the master equation to reduce the quantum noise to zero. We study the performance of this scheme by simulating the general single-qubit Xπ/2 gate and two-qubit (iSWAP) gate. In the bias point of the qubits, we achieve a single qubit gate with 99.99% fidelity and a two-qubit gate with 99.95% fidelity. By adjusting the nonlinear Kerr coefficient of fluxonium to an appropriate value, we can achieve a multi-body entanglement state. We consider the correlation between the two qubits and the coupler, and the magnetic flux passing through one qubit has an effect on the other qubit and the coupler. Finally, we analyze the quantum correlation of the two-body entanglement state.
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.
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.
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.
Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within 25ns25 \mathrm{ns}25ns, with an average gate fidelity exceeding 99.99%99.99\%99.99% and leakage below 10−510^{-5}10−5. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately 99.9%99.9\%99.9%. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below 10−410^{-4}10−4 in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.
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. [L. Ding , S. Singh ], 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 Z Z 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 − 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.
High-fidelity two-qubit gates are essential for scalable quantum computing. We present a scheme based on superconducting transmon qubits and a control pulse delivery protocol that enables arbitrary controlled-phase gates modulated solely by an independent arbitrary waveform generator pulse. We combined a tunable coupler design with bipolar flux-pulsing to demonstrate a high-fidelity gate with a peak performance of 99.5%99.5\%99.5%. Our gates inherit the advantages of both approaches: minimal residual ZZ coupling, built-in echo-like low-frequency noise protection, and time-scale control pulse reproducibility, while remaining easy to calibrate. We optimize the system energy levels to mitigate leakage to the coupler and suppress residual interactions. Numerical simulations of the scheme as three qutrits indicate that an error below 1×10−31 \times 10^{-3}1×10−3 is achievable. We confirm the scalability potential of the proposed scheme on high-fidelity 4-qubit and 8-qubit quantum processors