Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors

Abstract

I describe a procedure for calculating thresholds for quantum computation as a function of error model given the availability of ancillae prepared in logical states with independent, identically distributed errors. The thresholds are determined via a simple counting argument performed on a single qubit of an infinitely large CSS code. I give concrete examples of thresholds thus achievable for both Steane and Knill style fault-tolerant implementations and investigate their relation to threshold estimates in the literature.