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  • Letter
  • Open Access

Toward fault-tolerant quantum memory with universal continuous-variable gates

Sheron Blair1,2,*, Francesco Arzani3, Giulia Ferrini4, and Alessandro Ferraro5

  • *Contact author: sblair13@qub.ac.uk
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Phys. Rev. Research 8, L042006 – Published 19 October, 2026

DOI: https://doi.org/10.1103/45v3-h82q

Abstract

Continuous-variable (CV) systems have shown remarkable potential for quantum computation, particularly excelling in scalability and holding great promise for error correction through bosonic encoding. Within this framework, the foundational notion of computational universality was introduced by Lloyd and Braunstein [Phys. Rev. Lett. 82, 1784 (1999)], and has proven especially successful since it allows for the identification of finite sets of universal CV gates independent of the encoding scheme. However, realizing the full power of this computational model requires achieving fault tolerance, which in turn demands discretization via some form of encoding—and, to date, no proof exists that universal CV gates can give rise to encoded fault tolerance. We present compelling evidence in this direction by utilizing the Gottesman-Kitaev-Preskill (GKP) encoding. Specifically, we numerically optimize the generation of GKP states from vacua using circuits comprised solely of universal CV gates, and demonstrate that the resulting states are of sufficient quality to exhibit error probabilities below the threshold required for fault-tolerant memory via concatenated GKP-stabilizer codes.

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Phys. Rev. Research 8, L042006– Published 19 October, 2026
  • Received 14 August 2025
  • Revised 23 March 2026
  • Accepted 31 August 2026
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