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

Robert Freund; Friederike Butt; César Benito; Ivan Pogorelov; Marcel Meyer; Alex Steiner; Alejandro Bermudez; Markus Müller; Thomas Monz

arXiv · 2609.22572

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

Robert Freund·Friederike Butt·César Benito·Ivan Pogorelov·Marcel Meyer·Alex Steiner·Alejandro Bermudez·Markus Müller·Thomas Monz

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Abstract

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.

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BibTeX RIS

Robert Freund, Friederike Butt, César Benito, Ivan Pogorelov, Marcel Meyer, Alex Steiner, Alejandro Bermudez, Markus Müller, Thomas Monz. 2026-09-18. Modular fault-tolerant quantum computing on a non-CSS code. https://arxiv.org/abs/2609.22572

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