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Qubit-oscillator-based gate implementations for approximate Gottesman-Kitaev-Preskill codes
Phys. Rev. A 113, 042447 – Published 20 April, 2026
DOI: https://doi.org/10.1103/x758-5lc2
Abstract
We consider hybrid qubit-oscillator systems together with Gaussian, multiqubit, as well as qubit-controlled Gaussian unitaries. We propose implementations of logical gates for approximate Gottesman-Kitaev-Preskill codes in this model using two oscillators and three qubits. We show that these gate implementations become exact in the limit of large squeezing: The logical gate error is upper-bounded by a linear function of the squeezing parameter and depends polynomially on the number of encoded qubits. For a subset of Clifford gates, our constructions overcome a fundamental drawback of well-known Gaussian implementations, which—when executed without subsequent error correction—suffer from a constant logical gate error. In contrast, our fully unitary circuit construction achieves an asymptotically vanishing logical gate error rate even without applying a recovery map, i.e., performing syndrome measurements and adaptive corrections.
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