LUCI in the Surface Code with Dropouts

Dripto M. Debroy; Matt McEwen; Craig Gidney; Noah Shutty; Adam Zalcman

doi:10.22331/q-2025-12-11-1936

LUCI in the Surface Code with Dropouts

Dripto M. Debroy¹, Matt McEwen², Craig Gidney², Noah Shutty¹, and Adam Zalcman^1,3

¹Google Quantum AI, Venice, CA 90291, USA
²Google Quantum AI, Santa Barbara, CA 93117, USA
³Google Quantum AI, Tokyo, Japan

Published:	2025-12-11, volume 9, page 1936
Editor:	Nicolai Friis
Eprint:	arXiv:2410.14891v2
Doi:	https://doi.org/10.22331/q-2025-12-11-1936
Citation:	Quantum 9, 1936 (2025).

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Updated version: The authors have uploaded version v3 of this work to the arXiv which may contain updates or corrections not contained in the published version v2.

Abstract

Recently, usage of detecting regions facilitated the discovery of new circuits for fault-tolerantly implementing the surface code. Building on these ideas, we present LUCI, a framework for constructing fault-tolerant circuits flexible enough to construct aperiodic and anisotropic circuits, making it a clear step towards quantum error correction beyond static codes. We show that LUCI can be used to adapt surface code circuits to lattices with imperfect qubit and coupler yield, a key challenge for fault-tolerant quantum computers using solid-state architectures. These circuits preserve spacelike distance for isolated broken couplers or isolated broken measure qubits in exchange for halving timelike distance, substantially reducing the penalty for dropout compared to the state of the art and creating opportunities in device architecture design. For qubit and coupler dropout rates of 1% and a patch diameter of 15, LUCI achieves an average spacelike distance of 13.1, compared to 9.1 for the best method in the literature. For a SI1000(0.001) circuit noise model, this translates to a 36x improvement in median logical error rate per round, a factor which increases with device performance. At these dropout and error rates, LUCI requires roughly 25% fewer physical qubits to reach algorithmically relevant one-in-a-trillion logical codeblock error rates.

Featured image: LUCI Diagrams and their circuit interpretation. (left) LUCI diagram showing the two rounds of a distance-5 three-coupler surface code circuit [10]. Colors indicate the mid-cycle stabilizers of the surface code being measured, with X stabilizers in red and Z stabilizers in blue. The gray shapes inside the squares indicate how that stabilizer will be measured. (right) Circuit compilations for U-shapes on X-type (red) and Z-type (blue) squares. The colored regions depict the detecting region contracting and being measured out, and then a new detecting region expanding from a reset. Shades of gray in the shape denote which circuit layer the operation occurs in. Other shapes, like the L’s on the top and left boundaries, are formed by removing the appropriate CNOT gates from these U-shape compilations.

Popular summary

The surface code is the leading quantum error correcting code for most solid state architectures. Recent progress has expanded the space of possible circuits we use to implement the surface code in experiment. In this work we introduce a near-infinite family of surface code circuits using a framework called LUCI. We show that these LUCI circuits can exists on lattices of qubits that are subsets of the usual square lattice, allowing us to implement surface code circuits on quantum computers with defective qubits or couplers with better performance than the state of the art.

► BibTeX data

@article{Debroy2025luciinsurfacecode,
  doi = {10.22331/q-2025-12-11-1936},
  url = {https://doi.org/10.22331/q-2025-12-11-1936},
  title = {{LUCI} in the {S}urface {C}ode with {D}ropouts},
  author = {Debroy, Dripto M. and McEwen, Matt and Gidney, Craig and Shutty, Noah and Zalcman, Adam},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1936},
  month = dec,
  year = {2025}
}

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