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Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector

Shruti Puri 1, 2 Alexander Grimm 2, 1 Philippe Campagne-Ibarcq 2, 1 Alec Eickbusch 2, 1 Kyungjoo Noh 1, 2 Gabrielle Roberts 1, 2 Liang Jiang 2, 1 Mazyar Mirrahimi 3 Michel H. Devoret 2, 1 Steven M. Girvin 1, 2
3 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
Abstract : In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat- and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.
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Submitted on : Tuesday, November 27, 2018 - 3:27:10 PM
Last modification on : Friday, October 15, 2021 - 1:41:31 PM

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Shruti Puri, Alexander Grimm, Philippe Campagne-Ibarcq, Alec Eickbusch, Kyungjoo Noh, et al.. Stabilized Cat in Driven Nonlinear Cavity: A Fault-Tolerant Error Syndrome Detector. Physical Review X, American Physical Society, 2019, ⟨10.1103/PhysRevX.9.041009⟩. ⟨hal-01936700⟩



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