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  • Open Access

Modeling Logical Gates and Readout of Superconducting Gottesman-Kitaev-Preskill Qubits

Mackenzie H. Shaw1,2,3,*, Andrew C. Doherty1, and Arne L. Grimsmo1,4,5

  • *Contact author: M.H.Shaw@tudelft.nl
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PRX Quantum 7, 043020 – Published 29 October, 2026

DOI: https://doi.org/10.1103/k1tk-wh93

Abstract

The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve universal quantum computing. However, there is a disconnect between the noise model that GKP qubits are in theory designed to correct—uniform random displacement errors—and the conditions that affect GKP qubits in superconducting devices in practice: realistic noise channels, logical gates, and inefficient measurements. In this work we bridge this gap in three ways. First, we approximate the effect loss and dephasing on approximate GKP codestates using a random displacement channel, and show that this approximation matches well with numerics. Second, we analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Finally, we consider the effect of homodyne measurement inefficiencies on logical state readout and analyze a scheme to improve the measurement efficiency using the theory of quantum trajectories.

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Popular Summary

In order to achieve the low error rates required for useful quantum computation, we must use quantum error correction to protect the quantum information from noise. The Gottesman-Kitaev-Preskill (GKP) code is one promising approach to quantum error correction because it encodes a qubit into a single quantum harmonic oscillator, which can be implemented using either optical photons or superconducting resonators. However, important practical effects—including energy loss, dephasing, imperfect gates, and inefficient measurements—can substantially affect its performance. In this work, we develop theoretical tools and methods to analyze and counteract these practical effects in GKP quantum computing. We show that loss and dephasing can be accurately approximated by a simpler model of random shifts of the quantum state, making these errors easier to analyze and correct. We also find that GKP quantum gates can spread errors in ways that are not captured by standard decoding methods. By adapting the decoder after each gate, we can reduce the resulting logical errors that occur. Finally, we study how imperfect measurements affect the ability to read out GKP-encoded information and analyze two possible ways to improve the measurement quality. Together, these results connect the theoretical error-correction properties of GKP codes with the practical challenges of implementing them in quantum hardware.

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Outline

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PRX Quantum 7, 043020– Published 29 October, 2026
  • Received 9 April 2024
  • Revised 29 July 2026
  • Accepted 24 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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