Improving ancilla states for quantum computation

We analyze the improvement in output state fidelity upon improving the construction accuracy of ancilla states. Specifically, we simulate gates and syndrome measurements on a single qubit of information encoded into the [[7,1,3]] quantum error correction code and determine the output state fidelity as a function of the accuracy with which Shor states (for syndrome measurements) and magic states (to implement T -gates) are constructed. When no syndrome measurements are applied during the gate sequence, we observe that the fidelity increases after performance of a T -gate and improving magic states construction slows the fidelity decay rate. In contrast, when syndrome measurements are applied, loss of fidelity occurs primarily after the syndrome measurements taken after a T -gate. Improving magic state construction slows the fidelity decay rate, and improving Shor state construction raises the initial fidelity but does not slow the fidelity decay rate. Along the way, we show that applying syndrome measurements after every gate does not maximize the output state fidelity. Rather, syndrome measurements should be applied sparingly.