Fault tolerance on near-term trapped-ion logical qubits with a neural-network decoder

A crucial step towards the construction of a fault-tolerant quantum computer is the implementation of a logical qubit with a higher fidelity than its constituent physical qubits. In this context, we perform simulations of three promising distance-3 quantum error-correcting codes: the color, surface, and Bacon-Shor codes implemented on a state-of-the-art ion trap with realistic noise sources. Our goal is to find the break-even point where the logical memory outperforms the physical one. In previous works [1], after each error correction step, a correction was performed based exclusively on the syndromes of that step. We now use the syndromes of all previous error correction steps and employ a neural-network-based decoder, which has the advantage of not discarding the syndrome history and also being flexible to different noise models. For each code, we compare the two correction approaches and find a clear improvement in the logical fidelity when the neural-network-based decoder is used. These results will serve as a useful guide to future experiments.
[1] arXiv:1810.09199