Qubit-oscillator-based gate implementations for approximate Gottesman-Kitaev-Preskill codes

2025/09/19 by Brenner, Lukas, Dias, Beatriz, Koenig, Robert
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2509.15707

Abstract

We consider hybrid qubit-oscillator systems together with Gaussian, multi-qubit 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 certain Cliffords, our constructions overcome a shortcoming of well-known Gaussian implementations which have a constant logical gate error even in the absence of noise.

Citations

• Composable logical gate error in approximate quantum error correction: reexamining gate implementations in Gottesman-Kitaev-Preskill codes
• Factoring an integer with three oscillators and a qubit
• The complexity of Gottesman-Kitaev-Preskill states
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Gaussian quantum information
• Encoding a qubit in an oscillator

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