Quantum linear algebra is essential for constructing Transformer architectures in quantum computing. This paper investigates how quantum algorithms can be applied to Transformer models, focusing on fault-tolerant quantum computing. The key idea is to use block encodings and quantum singular value transformations to implement the core components of Transformers, such as self-attention, residual connections, and feed-forward networks. The paper shows how to prepare block encodings of the self-attention matrix, implement the softmax function, and construct quantum subroutines for the residual connection and layer normalization. These subroutines are efficient in terms of qubit usage and circuit depth, enabling potential quantum advantages. The paper also discusses the computational complexity of the quantum Transformer and provides insights into the behavior of important parameters that determine the runtime of the quantum algorithm. The results demonstrate that quantum algorithms can be used to construct state-of-the-art machine learning models, with potential for significant speedups in certain regimes. The paper concludes with a discussion of the implications and future directions of quantum computing in the context of large language models.Quantum linear algebra is essential for constructing Transformer architectures in quantum computing. This paper investigates how quantum algorithms can be applied to Transformer models, focusing on fault-tolerant quantum computing. The key idea is to use block encodings and quantum singular value transformations to implement the core components of Transformers, such as self-attention, residual connections, and feed-forward networks. The paper shows how to prepare block encodings of the self-attention matrix, implement the softmax function, and construct quantum subroutines for the residual connection and layer normalization. These subroutines are efficient in terms of qubit usage and circuit depth, enabling potential quantum advantages. The paper also discusses the computational complexity of the quantum Transformer and provides insights into the behavior of important parameters that determine the runtime of the quantum algorithm. The results demonstrate that quantum algorithms can be used to construct state-of-the-art machine learning models, with potential for significant speedups in certain regimes. The paper concludes with a discussion of the implications and future directions of quantum computing in the context of large language models.