Modular fault-tolerant quantum computing on a non-CSS code

@misc{freund2026modular,
  title = {{Modular fault-tolerant quantum computing on a non-CSS code}},
  author = {Robert Freund and Friederike Butt and César Benito and Ivan Pogorelov and Marcel Meyer and Alex Steiner and Alejandro Bermudez and Markus Müller and Thomas Monz},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22572},
  eprint = {2609.22572},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22572},
}

TY  - UNPB
TI  - Modular fault-tolerant quantum computing on a non-CSS code
AU  - Robert Freund
AU  - Friederike Butt
AU  - César Benito
AU  - Ivan Pogorelov
AU  - Marcel Meyer
AU  - Alex Steiner
AU  - Alejandro Bermudez
AU  - Markus Müller
AU  - Thomas Monz
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22572
UR  - https://arxiv.org/abs/2609.22572
AB  - Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect $[[5, 1, 3]]$ code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.
ER  -