  In this work we explore the accuracy of quantum error correction depending of
the order of the implemented syndrome measurements. CSS codes require bit-flip
and phase flip-syndromes be measured separately. To comply with fault tolerant
demands and to maximize accuracy this set of syndrome measurements should be
repeated allowing for flexibility in the order of their implementation. We
examine different possible orders of Shor state and Steane state syndrome
measurements for the [[7,1,3]] quantum error correction code. We find that the
best choice of syndrome order, determined by the fidelity of the state after
noisy error correction, will depend on the error environment. We also compare
the fidelity when syndrome measurements are done with Shor states versus Steane
states and find that Steane states generally, but not always, lead to final
states with higher fidelity. Together, these results allow a quantum computer
programmer to choose the optimal syndrome measurement scheme based on the
system's error environment.
