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

TL;DR

This paper compares ancilla preparation and measurement procedures for the Steane [[7,1,3]] quantum error correction code on a model ion trap computer, focusing on error rates and circuit latency.

Contribution

It evaluates and compares the performance of Shor and DiVincenzo-Aliferis ancilla methods, highlighting the advantages of the latter without verification.

Findings

DiVincenzo-Aliferis method generally outperforms Shor method

Adding more ancilla reduces circuit latency

Error rates are minimally affected by additional ancilla due to high memory fidelity

Abstract

We schedule the Steane [[7,1,3]] error correction on a model ion trap architecture with ballistic transport. We compare the level one 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 additional ancilla always reduces the latency but does not significantly change the error due to the high memory fidelity.