Analysis of Simplified Circuit Level Noise in T Gate Implementation

We study the effect of simplified circuit level noise, consisting of the introduction of depolarizing errors at the input of any quantum gate, in two different implementations of a physical T gate. Both implementations use a magic state and Clifford operations, but one of them utilizes an additional ancilla that allows the reutilization of the magic state in future quantum operations. We assess the degradation experienced by the implemented T gates (due to error propagation) compared with ideal T gates by obtaining, as a function of the depolarizing probability, closed-form expressions for the probability of the error operators that may appear at the output. The resulting expressions match very well with results obtained through simulations and can be approximated by very simple formulas that provide additional insights.