Abstract

Quantum error correction takes a crucial role in building a fault-tolerant quantum computer. With the recent experimental progress toward implementation of a 2D planar surface code, it becomes more important to investigate performance of quantum error correction codes against more general and realistic noise models. The standard approach assuming depolarizing noise models, which is not realistic, can overestimate the performance, and it is not valid to apply the results to experiments. On the other hand, a rigorous approach with the diamond norm is applicable to realistic noise models but greatly underestimates the performance and is not practical. Here we propose a new theoretical framework for evaluating performances of quantum error correction codes, which is practical and applicable to a wider class of noise models. We apply the method to a quantum 1D repetition code, and numerically evaluate the performance. This work is a collaboration with Keisuke Fujii, Haruhisa Nagata, and Fuyuhiko Tanaka.