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arXiv:1604.03076 · Physical Review Applied

Universal Gate for Fixed-Frequency Qubits via a Tunable Bus

David C. McKay, Stefan Filipp, Antonio Mezzacapo, Easwar Magesan, Jerry M. Chow, Jay M. Gambetta

Published Dec 12, 2016• 320 citations
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Abstract

The authors address a critical scalability issue in quantum computer design by activating a resonant exchange interaction. They achieve this by coupling two fixed-frequency superconducting qubits with a bus that is modulated at the frequency difference between the qubits. This yields a high-fidelity iSWAP entangling gate, which is sought as an important component for fault-tolerant quantum circuits in the surface-code architecture. The general nature of the interaction also suggests applications in quantum simulation, annealing, and bath engineering.

DOI
10.1103/physrevapplied.6.064007

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The authors address a critical scalability issue in quantum computer design by activating a resonant exchange interaction. They achieve this by coupling two fixed-frequency superconducting qubits with a bus that is modulated at the frequency difference between the qubits. This yields a high-fidelity iSWAP entangling gate, which is sought as an important component for fault-tolerant quantum circuits in the surface-code architecture. The general nature of the interaction also suggests applications in quantum simulation, annealing, and bath engineering.
A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity two-qubit gates in the presence of many resonant elements. As more elements are added to the architecture, and as the multiplicity of their couplings grows, the design's frequency space becomes crowded, and performance suffers. The authors present a way to address this difficulty: selective activation of interactions between transmon qubits of fixed frequency and those of tunable frequency. This activation depends on both the amplitude and frequency of modulation, and using the amplitude as an additional condition for resonance alleviates frequency crowding.
High-fidelity parametric gates have been demonstrated with superconducting qubits via rf flux modulation of the qubit frequency. The modulation however leads to renormalization of the bare qubit-qubit coupling, thereby reducing the gate speed. Here, we realize a parametric-resonance gate, which is activated by bringing the average frequency of the modulated qubit in resonance with a static-frequency qubit while approximately retaining the bare qubit-qubit coupling. The activation of parametric-resonance gates does not depend on the frequency of modulation, allowing us to choose the modulation frequencies and avoid frequency collisions. Moreover, we show that this approach is compatible with tunable coupler architectures, which reduce always-on residual couplings. Using these techniques, we demonstrate iswap and controlled-ZZZ gates between two qubits coupled via a tunable coupler with average process fidelities as high as $99.3\mathrm{%}$ and $97.9\mathrm{%}$, respectively. The flexibility in activating parametric-resonance gates combined with a tunable coupler architecture provides a pathway for building large-scale quantum computers.
High-fidelity quantum interconnection remains a critical challenge for scaling up superconducting quantum chips. Here, we realize a simple fixed coupling scheme to achieve high-fidelity two-qubit gate operation across separate superconducting quantum chips. In this scheme, qubit-qubit coupling between separate chips can be realized via exchange interaction mediated by a bus resonator. By merely tuning the frequency of a single qubit, the resonant mode of the bus resonator can be modulated, enabling high-quality and stable quantum interconnection across different chips. Consequently, the experimentally implemented two-qubit gate operations between separate chips exhibit excellent performance, with a maximum two-qubit CZ gate fidelity reaching 99.57%. This work lays a technical foundation for the realization of high-fidelity chip-to-chip quantum interconnection, which facilitates the development of large-scale superconducting quantum chips with high fidelity.
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.
Implementation of high-fidelity 2-qubit operations is a key ingredient for scalable quantum error correction. In superconducting qubit architectures, tunable buses have been explored as a means to higher-fidelity gates. However, these buses introduce new pathways for leakage. Here we present a modified tunable bus architecture appropriate for fixed-frequency qubits in which the adiabaticity restrictions on gate speed are reduced. We characterize this coupler on a range of 2-qubit devices, achieving a maximum gate fidelity of 99.85%. We further show the calibration is stable over one day.
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 ${10}^{\ensuremath{-}5}$, which would drastically speed up the progress towards fault-tolerant quantum computation.