Quantum error correction for long chains of trapped ions

We propose a model for quantum computing with long chains of trapped ions and we design quantum error correction schemes for this model. The main components of a quantum error correction scheme are the quantum code and a quantum circuit called the syndrome extraction circuit, which is executed to perform error correction with this code. In this work, we design syndrome extraction circuits tailored to our ion chain model, a syndrome extraction tuning protocol to optimize these circuits, and we construct new quantum codes that outperform the state-of-the-art for chains of about 50 qubits. To establish a baseline under the ion chain model, we simulate the performance of surface codes and bivariate bicycle (BB) codes equipped with our optimized syndrome extraction circuits. Then, we propose a new variant of BB codes defined by weight-five measurements, that we refer to as BB5 codes and we identify BB5 codes that achieve a better minimum distance than any BB codes with the same number of logical qubits and data qubits, such as a [ [ 48, 4, 7 ] ] BB5 code. For a physical error rate of 10 − 3, the [ [ 48, 4, 7 ] ] BB5 code achieves a logical error rate per logical qubit of 5 ⋅ 10 − 5, which is four times smaller than the best BB code in our baseline family. It also achieves the same logical error rate per logical qubit as the distance-7 surface code but using four times fewer physical qubits per logical qubit.

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Authors

Min Ye; Nicolas Delfosse

Published

Nov 27, 2025

Journal or venue

Quantum

DOI

10.22331/q-2025-11-27-1920

Paper type

journal article

Source

Crossref