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  • Open Access

Characterizing Physical and Logical Errors in a Transversal CNOT Gate via Cycle Error Reconstruction

Nicholas Fazio1,*, Robert Freund2,*, Debankan Sannamoth3,4, Alex Steiner2, Christian D. Marciniak2, Manuel Rispler5,6, Robin Harper1, Thomas Monz2,†, Joseph Emerson3,4 et al.

Stephen D. Bartlett1

  • *These authors contributed equally to this work.
  • †Also at: Alpine Quantum Technologies GmbH, Innsbruck, Austria.
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Phys. Rev. X 16, 011030 – Published 20 February, 2026

DOI: https://doi.org/10.1103/qfwc-584t

Abstract

The development of prototype quantum information processors has progressed to a stage where small instances of logical qubit systems perform better than the best of their physical constituents. Advancing toward fault-tolerant quantum computing will require an understanding of the underlying error mechanisms in logical primitives as they relate to the performance of quantum error correction. In this work we demonstrate the novel capability to characterize the physical error properties relevant to fault-tolerant operations via cycle error reconstruction. We illustrate this diagnostic capability for a transversal controlled-not (cnot) gate, a prototypical component of quantum logical operations, in a 16-qubit register of a trapped-ion quantum computer. Our error characterization technique offers three key capabilities: (i) identifying context-dependent physical layer errors, enabling their mitigation, (ii) contextualizing component gates in the environment of logical operators, validating the performance differences in terms of characterized component-level physics, and (iii) providing a scalable method for predicting quantum error correction performance using pertinent error terms, differentiating correctable versus uncorrectable physical layer errors. The methods with which our results are obtained have scalable resource requirements that can be extended with moderate overhead to capture overall logical performance in increasingly large and complex systems.

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Advancing toward fault-tolerant quantum computing requires a deep understanding of how underlying physical error mechanisms impact the performance of error-corrected logic gates. We demonstrated the novel capability to characterize these error properties using cycle error reconstruction, a scalable method for extracting representative error descriptions across many qubits. By applying this technique to a transversal cnot gate within a 16-qubit trapped-ion register, we identified context-dependent physical layer errors, such as localized dephasing and gate miscalibrations, and validated detailed noise models for multiqubit systems. Our framework further leverages Gibbs random fields to provide a scalable method for predicting quantum error correction performance, effectively differentiating between correctable and uncorrectable physical layer errors. This approach establishes a resource-efficient foundation for diagnosing critical error pathways and accelerating the realization of practical, error-corrected quantum information processors.

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Outline

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Phys. Rev. X 16, 011030– Published 20 February, 2026
  • Received 22 April 2025
  • Revised 29 August 2025
  • Accepted 18 December 2025
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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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