量子電腦 (Quantum computing) 比起傳統電腦有更為強大的計算能力，他也被認為可以有希望解決傳統電腦上所遇到的計算瓶頸。所以即便在如今主流的量子電腦上仍有許多的問題要解決或是改進，仍有許多在量子點腦上的相關研究在進行，像是量子加密 (Quantum cryptography)、量子機器學習 (Quantum machine learning)，或是二次約束優化問題 (quadratic unconstrained binary optimization, QUBO)。
量子電腦能夠擁有比傳統電腦更為強大的計算能力，主要要歸功於量子位元(quantum bit, qubit) 上兩個特殊的特性，疊加態 (superposition) 和糾纏態 (entanglement)。如今的研究中大量使用這兩種特殊的特性來設計量子電路，但是在設計的同時，如何為量子程式進行偵錯儼然已經成為了一個潛在的問題。為量子電腦進行偵錯是一個困難的問題，主要是因為兩項原因，第一項是量子不可複製原理 (quantum non-cloning theorem)，我們無法隨意地複製一個量子位元的狀態，第二是隨意地進行測量可能會導致一個或多個處於量子疊加態的量子位元坍縮成某一個狀態，基於上述兩個原因，除了設計量子電路外，如何為量子電路做偵錯也是重要的。
在量子計算領域中，所有的運算都可以使用矩陣來進行表達。在過去的相關文獻中，有作者試圖使用矩陣的方式來為量子狀態做偵錯。但是在如今的量子電腦上，還不能進行矩陣運算，使用者必須將矩陣轉換成量子邏輯閘 (quantum gate)，才可以運行在現今的量子電腦上，而從矩陣變成量子邏輯閘的過程是非常困難的，甚至有書籍指出這個問題如今仍然沒有辦法定義他是屬於哪一種難度的問題，甚至在如今的解決方法上仍可能只是一個大約近似的解決方法，所以在本篇論文中，我們分別為 Quantum Fourier transform(QFT), Quantum phase estimation(QPE), 特定的最大糾纏態(Specific maximally entanglment state) 設計它們各自的偵錯電路，除了希望能有驗證資源上的減少外，在最大糾纏狀態的偵測中，透過我們的偵錯電路可以知道是屬於狀態 (state) 還是相位 (phase) 的錯誤。
本論文中的所有偵錯電路都是基於量子穩定器 (quantum stabilizer) 所組成的，並且本論文中的所提出的量子偵錯電路是可以直接由量子基本邏輯閘組成，不需要經過矩陣的分解，如此可以減少從矩陣轉換成量子邏輯閘上的不精確。

Debugging quantum circuit has become a potential barrier because traditional runtime debugging techniques are feasible due to the quantum non-cloning theorem and measurement collapsing. Based on the concept of quantum dynamic runtime assertion, we propose the dynamic assertion circuit (DAC) based on stabilizer to detect the quantum Fourier transform (QFT), quantum phase estimation (QPE), and two specific maximally entanglement with arbitrary relative phase. Due to the related works’ DAC is based on the unitary matrix, the unitary matrix needs to be decomposed to the basic quantum gates in the Noisy Intermediate Scale Quantum (NISQ) real device and some books discuss that that most unitary matrix decomposition are very inefficiently. Thus, the DACs proposed in this paper is based on stabilizers, which can be composed by the basic quantum gates orininally. For all the SBDACs we proposed, we provide formal proofs to show
that if the under-test quantum state is the correct state, the asserion bit should all be |0⟩ and our DAC should not affect the under-test quantum state.

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