Hybrid Lattice Surgery between Smooth Boundaries

Abstract

We develop smooth hybrid lattice surgery for group surface codes, enabling joint logical measurements through merge and split operations along smooth boundaries. The code patches may correspond to identical or different finite groups, including non-Abelian groups. Our central result is that smooth merge and split realize a logical K-coset measurement, where K is the subgroup defining the interface. This generalizes the joint logical parity measurement of ordinary surface codes. Using a tensor-network representation, we derive explicit measurement circuits and develop procedures for correcting nonidentity measurement outcomes. We illustrate the framework through a generalized controlled multiplication gate between group surface codes and protocols for preparing the T, CZ, CCX, and CS magic states, producing resources encoded in one or more ℤ₂ surface code patches. Our results show how smooth hybrid lattice surgery broadens the range of logical operations available for group surface codes.

Two temperature scales in the Ising model on the {5,4} hyperbolic lattice with free boundaries: susceptibility peak and boundary-induced order
Sebastian Jaroszewicz, Nahuel Mendez, Maria P. Beccar-Varela +1
arXiv24 Sep 2026PreprintarXiv licenceFull textStatistical & nonlinear physicsarXiv
A non-uniform local reference frame method for the simulation of rotating geometries with non-conformal grids on the hybrid recursive regularized lattice Boltzmann method
R. Vazquez Casique, J F Boussuge, P. Sagaut
Physics of Fluids1 Sep 2026Peer-reviewedPublisher termsFull textFluid dynamicsHAL
Long-distance hybrid spin-dependent and hybrid-quarkonium mixing potentials from lattice gauge theory
Vilija de Jonge, Paul Pütz, Antonio Vairo +1
arXiv1 Sep 2026PreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
Demand-Driven Routing Space for Lattice-Surgery Compilation
Hanyu Wang, Wan-Hsuan Lin, Zihan Chen +2
arXiv22 Oct 2026PreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv
Patchwork: automated lattice surgery and space-time partitioning for real-time decoding
Christopher Chamberland, Muyuan Li, Scott Thornton +3
arXiv15 Oct 2026PreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv

Cite

BibTeX RIS

BibTeX

@misc{ding2026hybrid,
  title = {{Hybrid Lattice Surgery between Smooth Boundaries}},
  author = {Grace Ding and Yanzhu Chen and Sheng-Jie Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27556},
  eprint = {2610.27556},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27556},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Hybrid Lattice Surgery between Smooth Boundaries
AU  - Grace Ding
AU  - Yanzhu Chen
AU  - Sheng-Jie Huang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27556
UR  - https://arxiv.org/abs/2610.27556
AB  - We develop smooth hybrid lattice surgery for group surface codes, enabling joint logical measurements through merge and split operations along smooth boundaries. The code patches may correspond to identical or different finite groups, including non-Abelian groups. Our central result is that smooth merge and split realize a logical K-coset measurement, where K is the subgroup defining the interface. This generalizes the joint logical parity measurement of ordinary surface codes. Using a tensor-network representation, we derive explicit measurement circuits and develop procedures for correcting nonidentity measurement outcomes. We illustrate the framework through a generalized controlled multiplication gate between group surface codes and protocols for preparing the T, CZ, CCX, and CS magic states, producing resources encoded in one or more ℤ_2 surface code patches. Our results show how smooth hybrid lattice surgery broadens the range of logical operations available for group surface codes.
ER  -

Abstract

Related

Cite