Comparison of ancilla preparation and measurement procedures for the Steane ((7,1,3)) code on a model ion-trap quantum computer

We schedule the Steane [[7,1,3]] error correction on a model ion-trap architecture with ballistic transport. We compare the level-1 error rates for syndrome extraction using the Shor method of ancilla prepared in verified cat states to the DiVincenzo-Aliferis method without verification. The study examines how the quantum error correction circuit latency and error vary with the number of available ancilla and the choice of protocol for ancilla preparation and measurement. We find that, with few exceptions, the DiVincenzo-Aliferis method without cat-state verification outperforms the standard Shor method. We also find that an additional ancilla always reduces the latency but does not significantly change the error due to the high memory fidelity.