  We explore the effect of Shor state construction methods on logical state
encoding and quantum error correction for the [[7,1,3]] Calderbank-Shor-Steane
quantum error correction code in a nonequiprobable error environment. We
determine the optimum number of verification steps to be used in Shor state
construction and whether Shor states without verification are usable for
practical quantum computation. These results are compared to the same processes
of encoding and error correction where Shor states are not used. We demonstrate
that the construction of logical zero states with no first order error terms
may not require the complete edifice of quantum fault tolerance. With respect
to error correction, we show for a particular initial state that error
correction using a single qubit for syndrome measurement yields a similar
output state accuracy to error correction using Shor states as syndrome qubits.
In addition, we demonstrate that error correction with Shor states has an
inherent sensitivity to bit-flip errors. Finally, we suggest that in this type
of error correction scenario one should always repeat a syndrome measurement
until attaining an all zero readout (twice in row).

Quantum Physics