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arXiv:2106.00725 · Physical Review Applied

Coupler-Assisted Controlled-Phase Gate with Enhanced Adiabaticity

Ji Chu, Fei Yan

Published Nov 9, 2021• 42 citations
arXivHTMLPDF

Abstract

High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502 (2020); Phys. Rev. Lett. 125, 240503 (2020)] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast $ZZ$ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near ${10}^{\ensuremath{-}5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.

DOI
10.1103/physrevapplied.16.054020

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High-fidelity two-qubit entangling gates are essential building blocks for fault-tolerant quantum computers. Over the past decade, tremendous efforts have been made to develop scalable high-fidelity two-qubit gates with superconducting quantum circuits. Recently, an easy-to-scale controlled-phase gate scheme that utilizes the tunable-coupling architecture with fixed-frequency qubits [Phys. Rev. Lett. 125, 240502 (2020); Phys. Rev. Lett. 125, 240503 (2020)] has been demonstrated with high fidelity and attracted broad interest. However, in-depth understanding of the underlying mechanism is still missing, preventing us from fully exploiting its potential. Here we present a comprehensive theoretical study, explaining the origin of the high-contrast ZZZZZZ interaction. Based on improved understanding, we develop a general yet convenient method for shaping an adiabatic pulse in a multilevel system, and identify how to optimize the gate performance from design. Given state-of-the-art coherence properties, we expect the scheme to potentially achieve a two-qubit gate error rate near 10\ensuremath−5{10}^{\ensuremath{-}5}10\ensuremath−5, which would drastically speed up the progress towards fault-tolerant quantum computation.
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-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.
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 ${10}^{\ensuremath{-}4}$.
Achieving fast and high-fidelity qubit operations is crucial for unlocking the potential of quantum computers. In particular, reaching low gate errors in two-qubit gates has been a long-standing challenge in the field of superconducting qubits due to their typically long duration relative to coherence times. To realize fast gates, we use the hybridization between fixed-frequency superconducting qubits with a strongly interacting coupler mode that is tunable in frequency. To reduce population leakage during required adiabatic passages through avoided level crossings, we employ a sensitivity-adaptive closed-loop optimization method to design complex pulse shapes. We compare the performance of Gaussian-square, Fourier-series, and piecewise-constant-slope pulse parametrizations and are able to reach 99.9% controlled- Z -gate fidelity using a 64-ns-long Fourier-series pulse defined by only seven parameters. These high-fidelity values are achieved by analyzing the optimized pulse shapes to identify and systematically mitigate signal-line distortions in the experiment. To improve the convergence speed of the optimization, we implement an adaptive cost function, which continuously maximizes the sensitivity. The demonstrated method can be used for tune-up and recalibration of superconducting quantum processors.
Unlocking a fast adiabatic CZ gate and exact residual ZZZZZZ cancellation between fixed-frequency transmons using a floating tunable coupler
Tunable couplers in superconducting qubit architectures enable strong qubit-qubit interactions for two-qubit gates while suppressing unwanted coupling during single-qubit operations. However, achieving low error rates for fast two-qubit gates remains challenging, as suppressing leakage and non-adiabatic errors typically requires specialized qubit, coupler, or pulse designs, often at the expense of an idling ZZ=0ZZ=0ZZ=0 condition. In this work, we demonstrate that a symmetric floating tunable coupler provides a natural platform for fast, high-fidelity adiabatic controlled-Z (CZ) gates. Its favorable energy-level structure eliminates the conventional trade-off between rapid conditional-phase accumulation and adiabatic evolution while preserving exact cancellation of residual ZZZZZZ interaction at idling. This architecture exhibits intrinsic robustness to non-adiabatic transitions, even under simple flux modulation waveforms. To push performance at short gate durations, where maintaining adiabaticity becomes more challenging despite the favorable level structure, we introduce pulse-shaping techniques based on the instantaneous adiabatic factor that further suppress non-adiabatic errors. We experimentally realize a 24 ns adiabatic CZ gate with fidelity exceeding 99.9% and stable operation over several hours.
A possible building block for a scalable quantum computer has recently been demonstrated [Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a controlled-${\ensuremath{\sigma}}^{z}$ (cz) operation between a qubit and the bus. The cz gate is implemented with the aid of the noncomputational qubit $|2\ensuremath{\rangle}$ state [Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus cz gate with 99.9% (99.99%) fidelity in about 17ns17\phantom{\rule{0.16em}{0ex}}\mathrm{ns}17ns (23ns23\phantom{\rule{0.16em}{0ex}}\mathrm{ns}23ns) with a realistic two-parameter pulse profile, plus two auxiliary zzz rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multiqubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus cz gate as a function of qubit anharmonicity, identify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit cz gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a 99.999.9%99.9 cz gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.