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arXiv:2206.12392 · Physical Review Applied

Controlled-Controlled-Phase Gates for Superconducting Qubits Mediated by a Shared Tunable Coupler

Niklas J. Glaser, Federico Roy, Stefan Filipp

Published Apr 3, 2023• 28 citations
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Abstract

Applications for noisy intermediate-scale quantum computing devices rely on the efficient entanglement of many qubits to reach a potential quantum advantage. Although entanglement is typically generated using two-qubit gates, direct control of strong multiqubit interactions can improve the efficiency of the process. Here, we investigate a system of three superconducting transmon-type qubits coupled via a single flux-tunable coupler. Tuning the frequency of the coupler by adiabatic flux pulses enables us to control the conditional energy shifts between the qubits and directly realize multiqubit interactions. To accurately adjust the resulting controlled relative phases, we describe a gate protocol involving refocusing pulses and adjustable interaction times. This enables the implementation of the full family of pairwise controlled-phase and controlled-controlled-phase gates. Numerical simulations result in fidelities around 99% and gate times below 300 ns using currently achievable system parameters and decoherence rates.

DOI
10.1103/physrevapplied.19.044001

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Applications for noisy intermediate-scale quantum computing devices rely on the efficient entanglement of many qubits to reach a potential quantum advantage. Although entanglement is typically generated using two-qubit gates, direct control of strong multiqubit interactions can improve the efficiency of the process. Here, we investigate a system of three superconducting transmon-type qubits coupled via a single flux-tunable coupler. Tuning the frequency of the coupler by adiabatic flux pulses enables us to control the conditional energy shifts between the qubits and directly realize multiqubit interactions. To accurately adjust the resulting controlled relative phases, we describe a gate protocol involving refocusing pulses and adjustable interaction times. This enables the implementation of the full family of pairwise controlled-phase and controlled-controlled-phase gates. Numerical simulations result in fidelities around 99% and gate times below 300 ns using currently achievable system parameters and decoherence rates.
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
High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.
Controllable interaction between superconducting qubits is desirable for large-scale quantum computation and simulation. Here, based on a theoretical proposal by Yan et al. [Phys. Rev. Appl. 10, 054061 (2018)] we experimentally demonstrate a simply designed and flux-controlled tunable coupler with a continuous tunability by adjusting the coupler frequency, which can completely turn off adjacent superconducting qubit coupling. Utilizing the tunable interaction between two qubits via the coupler, we implement a different type of controlled-phase (cz) gate with ``dynamically decoupled regime,'' which allows the qubit-qubit coupling to be only ``on'' at the usual operating point while dynamically ``off'' during the tuning process of one qubit frequency into and out of the operating point. This scheme not only efficiently suppresses the leakage out of the computational subspace, but also allows for the acquired two-qubit phase being geometric at the operating point. We achieve an average cz gate fidelity of $98.3\ifmmode\pm\else\textpm\fi{}0.6\mathrm{%}$, which is dominantly limited by qubit decoherence. The demonstrated tunable coupler provides a desirable tool to suppress adjacent qubit coupling and is suitable for large-scale quantum computation and simulation.
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.
Despite progress towards achieving low error rates with superconducting qubits, error-prone two-qubit gates remain a bottleneck for realizing large-scale quantum computers. Therefore, a systematic framework to design high-fidelity gates becomes imperative. One type of two-qubit gate in superconducting qubits is the controlled-phase (CPHASE) gate, which utilizes a conditional interaction between higher energy levels of the qubits controlled by a baseband flux pulse on one of the qubits or a tunable coupler. In this work, we study an adiabatic implementation of CPHASE gates and formulate the design of the control trajectory for the gate as a pulse-design problem. We show in simulation that the Chebyshev-based trajectory can, in certain cases, enable gates with gate infidelity lower by an average of 23.3% when compared to the widely used Slepian-based trajectory.
Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancelation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase interaction, the static ZZZZZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance controlled-not (cnot) gates within 40 ns and adiabatic controlled-ZZZ gates within 140 ns. Our architecture is not only ZZZZZZ-free, but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance cnot gate can be reduced to below ${10}^{\ensuremath{-}4}$.