Effect of quantum error correction on detection-induced coherent errors

TL;DR

This paper investigates how detection-induced coherent errors affect quantum error correction, especially surface codes, showing that larger codes mitigate these errors and that the surface code acts as an approximate QECC under such conditions.

Contribution

It demonstrates the impact of detection-induced coherent errors on surface codes and shows that increasing code size reduces their effect, revealing the approximate nature of surface codes in this context.

Findings

Detection-induced coherent errors cause undetected errors that accumulate into logical errors.

Increasing code size alleviates the impact of these errors.

Surface code becomes an approximate QECC under detection-induced coherent errors.

Abstract

We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that such errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detection-induced coherent errors, the exact surface code becomes an approximate QECC.