量子計算的發展大幅受限於硬體技術，因此量子錯誤更正碼對於量子計算的
普及與實現是非常重要的因素之一。因著與古典錯誤更正碼有強烈的連結關
係，量子穩定碼是最為重要的量子錯誤更正碼之一。而量子表面碼是一種量子
拓樸穩定碼，其穩定元與資料位元有著特殊的幾何結構，使其能被更為容易的
分析與解碼。也因這樣的特性，使得許多人認為量子表面碼具有很大的潛力能
協助推進大規模的量子計算。通常為了簡化問題，在對量子表面碼做解碼時，
位元反轉錯誤與相位反轉錯誤常會被假設為彼此獨立。然而在真實系統中，此
二種錯誤形式是會具有相關性。本篇論文即是探討量子表面碼在去極化通道
下，位元反轉錯誤與相位反轉錯誤具有相關性時的解碼問題。

The development of quantum computing is highly restricted by the limit of hardware implementation. Therefore, the development of quantum error-correcting codes is a very important issue to quantum computing. The class of stabilizer codes is one of the most important quantum error-correcting codes since it has a strong relation with classical error-correcting codes. Surface codes are a kind of quantum topological stabilizer codes whose stabilizers and qubits have a geometrical structure that makes them easier to be analyzed and decoded. People believe that surface codes have a very large potential to lead us to large-scale quantum computation. In the decoding of surface codes, the bit-flip errors and phase-flip errors are often assumed to be independent for simplicity. However, these two kinds of errors are likely to be correlated in the real world. In this thesis, we will discuss the decoding of surface codes over the depolarizing channels where bit-flip errors and phase-flip errors are correlated.

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