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  • Open Access

Interplay of resources for universal continuous-variable quantum computing

Varun Upreti* and Ulysse Chabaud†

  • *Contact author: varun.upreti@inria.fr
  • †Contact author: ulysse.chabaud@inria.fr
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Phys. Rev. Research 8, 033379 – Published 29 September, 2026

DOI: https://doi.org/10.1103/2str-dhrg

Abstract

Quantum resource theories identify the features of quantum computers that provide their computational advantage over classical systems. We investigate the resources driving the complexity of classical simulation in the standard model of continuous-variable quantum computing, and their interplay enabling computational universality. Specifically, we uncover a new property in continuous-variable circuits, analogous to coherence in discrete-variable systems, termed symplectic coherence, defined as the ability of Gaussian gates to mix position and momentum operators. Using quadrature propagation across multiple computational paths, we develop an efficient classical simulation algorithm for continuous-variable computations with symplectic coherence constant in the size of the circuit. This establishes symplectic coherence as a necessary resource for universality in continuous-variable quantum computing, alongside non-Gaussianity and entanglement. Via the Gottesman-Kitaev-Preskill encoding, we show that the interplay of these three continuous-variable quantum resources mirrors the discrete-variable relationship between coherence, magic, and entanglement.

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Phys. Rev. Research 8, 033379– Published 29 September, 2026
  • Received 21 February 2025
  • Revised 18 November 2025
  • Accepted 26 June 2026
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