Error range for encoding in imperfect quantum error correction

Abstract Quantum error correction (QEC) codes are vital for scalable and robust computations of quantum operations. The main challenge lies in introducing ancilla qubits with minimal side effect in the resultant computation, particularly considering state-of-the-art near-term devices. With the aim of identifying error value ranges that make encoding advantageous, the Shor code stands out as a viable first approach for a physical implementation of quantum error correction, due to its simpler structure. The noise models utilized, through their Operator Sum Representation (OSR), can be extrapolated, as these are typical of the majority of current technologies. In this article, error widths are analytically determined such that it becomes worthwhile to transmit information through encoding.