Logical Noise Bias in Magic State Injection

Nicholas Fazio; Robin Harper; Stephen D. Bartlett

doi:10.22331/q-2025-06-24-1779

Logical Noise Bias in Magic State Injection

Nicholas Fazio, Robin Harper, and Stephen D. Bartlett

Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia.

Published:	2025-06-24, volume 9, page 1779
Editor:	Mohan Sarovar
Eprint:	arXiv:2401.10982v3
Doi:	https://doi.org/10.22331/q-2025-06-24-1779
Citation:	Quantum 9, 1779 (2025).

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Abstract

Fault-tolerant architectures aim to reduce the noise of a quantum computation. Despite such architectures being well studied a detailed understanding of how noise is transformed in a fault-tolerant primitive such as magic state injection is currently lacking. We use numerical simulations of logical process tomography on a fault-tolerant gadget that implements a logical $T = Z(\pi/4)$ gate using magic state injection, to understand how noise characteristics at the physical level are transformed into noise characteristics at the logical level. We show how, in this gadget, a significant phase ($Z$) bias can arise in the logical noise, even with unbiased noise at the physical level. While the magic state injection gadget intrinsically induces biased noise, with extant phase bias being further amplified at the logical level, we identify noisy error correction circuits as a key limiting factor in the circuits studied on the magnitude of this logical noise bias. Our approach provides a framework for assessing the detailed noise characteristics, as well as the overall performance, of fault-tolerant logical primitives.

► BibTeX data

@article{Fazio2025logicalnoisebiasin,
  doi = {10.22331/q-2025-06-24-1779},
  url = {https://doi.org/10.22331/q-2025-06-24-1779},
  title = {Logical {N}oise {B}ias in {M}agic {S}tate {I}njection},
  author = {Fazio, Nicholas and Harper, Robin and Bartlett, Stephen D.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1779},
  month = jun,
  year = {2025}
}

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Cited by

[1] Hansol Kim, Wonjae Choi, and Younghun Kwon, "Implementation of magic state injection within heavy-hexagon architectures", Quantum Information Processing 24 12, 384 (2025).

[2] Seok-Hyung Lee, Felix Thomsen, Nicholas Fazio, Benjamin J. Brown, and Stephen D. Bartlett, "Low-Overhead Magic State Distillation with Color Codes", PRX Quantum 6 3, 030317 (2025).

[3] Yunzhe Zheng, Yuanchen Zhao, and Dong E. Liu, "Fragility of Magic State Distillation under Imperfect Measurements", arXiv:2503.01165, (2025).

[4] Jacob S. Nelson and Andrew D. Baczewski, "Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers", Physical Review A 110 4, 042420 (2024).

[5] Nicholas Fazio, Mark Webster, and Zhenyu Cai, "Low-overhead Magic State Circuits with Transversal CNOTs", arXiv:2501.10291, (2025).

[6] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

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