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Quantum error correction of a qubit encoded in grid states of an oscillator

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Listed:
  • P. Campagne-Ibarcq

    (Yale University)

  • A. Eickbusch

    (Yale University)

  • S. Touzard

    (Yale University)

  • E. Zalys-Geller

    (Yale University)

  • N. E. Frattini

    (Yale University)

  • V. V. Sivak

    (Yale University)

  • P. Reinhold

    (Yale University)

  • S. Puri

    (Yale University)

  • S. Shankar

    (Yale University)

  • R. J. Schoelkopf

    (Yale University)

  • L. Frunzio

    (Yale University)

  • M. Mirrahimi

    (Quantic Team, INRIA Paris)

  • M. H. Devoret

    (Yale University)

Abstract

The accuracy of logical operations on quantum bits (qubits) must be improved for quantum computers to outperform classical ones in useful tasks. One method to achieve this is quantum error correction (QEC), which prevents noise in the underlying system from causing logical errors. This approach derives from the reasonable assumption that noise is local, that is, it does not act in a coordinated way on different parts of the physical system. Therefore, if a logical qubit is encoded non-locally, we can—for a limited time—detect and correct noise-induced evolution before it corrupts the encoded information1. In 2001, Gottesman, Kitaev and Preskill (GKP) proposed a hardware-efficient instance of such a non-local qubit: a superposition of position eigenstates that forms grid states of a single oscillator2. However, the implementation of measurements that reveal this noise-induced evolution of the oscillator while preserving the encoded information3–7 has proved to be experimentally challenging, and the only realization reported so far relied on post-selection8,9, which is incompatible with QEC. Here we experimentally prepare square and hexagonal GKP code states through a feedback protocol that incorporates non-destructive measurements that are implemented with a superconducting microwave cavity having the role of the oscillator. We demonstrate QEC of an encoded qubit with suppression of all logical errors, in quantitative agreement with a theoretical estimate based on the measured imperfections of the experiment. Our protocol is applicable to other continuous-variable systems and, in contrast to previous implementations of QEC10–14, can mitigate all logical errors generated by a wide variety of noise processes and facilitate fault-tolerant quantum computation.

Suggested Citation

  • P. Campagne-Ibarcq & A. Eickbusch & S. Touzard & E. Zalys-Geller & N. E. Frattini & V. V. Sivak & P. Reinhold & S. Puri & S. Shankar & R. J. Schoelkopf & L. Frunzio & M. Mirrahimi & M. H. Devoret, 2020. "Quantum error correction of a qubit encoded in grid states of an oscillator," Nature, Nature, vol. 584(7821), pages 368-372, August.
  • Handle: RePEc:nat:nature:v:584:y:2020:i:7821:d:10.1038_s41586-020-2603-3
    DOI: 10.1038/s41586-020-2603-3
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    Cited by:

    1. Arjen Vaartjes & Anders Kringhøj & Wyatt Vine & Tom Day & Andrea Morello & Jarryd J. Pla, 2024. "Strong microwave squeezing above 1 Tesla and 1 Kelvin," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    2. Ziqian Li & Tanay Roy & David Rodríguez Pérez & Kan-Heng Lee & Eliot Kapit & David I. Schuster, 2024. "Autonomous error correction of a single logical qubit using two transmons," Nature Communications, Nature, vol. 15(1), pages 1-6, December.
    3. X. L. He & Yong Lu & D. Q. Bao & Hang Xue & W. B. Jiang & Z. Wang & A. F. Roudsari & Per Delsing & J. S. Tsai & Z. R. Lin, 2023. "Fast generation of Schrödinger cat states using a Kerr-tunable superconducting resonator," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    4. Noah Goss & Alexis Morvan & Brian Marinelli & Bradley K. Mitchell & Long B. Nguyen & Ravi K. Naik & Larry Chen & Christian Jünger & John Mark Kreikebaum & David I. Santiago & Joel J. Wallman & Irfan S, 2022. "High-fidelity qutrit entangling gates for superconducting circuits," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    5. Eric Hyyppä & Suman Kundu & Chun Fai Chan & András Gunyhó & Juho Hotari & David Janzso & Kristinn Juliusson & Olavi Kiuru & Janne Kotilahti & Alessandro Landra & Wei Liu & Fabian Marxer & Akseli Mäkin, 2022. "Unimon qubit," Nature Communications, Nature, vol. 13(1), pages 1-14, December.

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