Neural network decoders on near term trapped-ion logical qubits

The implementation of a logical qubit with a higher fidelity than its constituent physical qubits is an essential process towards the construction of a fault tolerant quantum computer. Under this framework, we perform simulations of two promising distance-3 quantum error-correcting codes: the surface-17 and the Bacon-Shor codes, implemented on ion-traps with realistic noise sources. We use the syndromes of multiple error-correcting cycles and employ neural networks (NN) as decoders, with the goal of preserving the syndrome history and increasing the flexibility to different noise models. Under certain noise conditions, we find an improvement in the logical fidelity with the NN-based decoder compared to the most commonly used minimum-weight perfect matching and look-up table decoders