AlphaTensor-Quantum is a deep reinforcement learning method that optimizes T-count in quantum circuits by leveraging tensor decomposition. It addresses the problem of minimizing the number of T gates required to implement a given quantum circuit. Unlike existing methods, AlphaTensor-Quantum incorporates domain-specific knowledge and uses gadgets to reduce T-count. It outperforms existing methods on arithmetic benchmarks and discovers efficient algorithms similar to Karatsuba's method for multiplication in finite fields. It also finds optimal solutions for relevant quantum computations, such as those used in Shor's algorithm and quantum chemistry simulations. AlphaTensor-Quantum is able to automatically optimize circuits, saving hundreds of hours of research. It uses a tensor decomposition approach, with a key component being the symmetric signature tensor. The method is based on a game-like framework where the goal is to decompose the tensor into low-rank factors. It incorporates gadgets, such as the Toffoli and CS gates, to further reduce T-count. The method is able to scale to large tensors and is flexible, allowing for different complexity metrics and domain knowledge. It has been applied to various quantum computing applications, including arithmetic operations, quantum chemistry, and fault-tolerant quantum circuits. The results show that AlphaTensor-Quantum can effectively exploit domain knowledge and state-of-the-art magic state factories to find optimal constructions. It is expected to significantly accelerate discoveries in quantum computation by automatically optimizing circuits.AlphaTensor-Quantum is a deep reinforcement learning method that optimizes T-count in quantum circuits by leveraging tensor decomposition. It addresses the problem of minimizing the number of T gates required to implement a given quantum circuit. Unlike existing methods, AlphaTensor-Quantum incorporates domain-specific knowledge and uses gadgets to reduce T-count. It outperforms existing methods on arithmetic benchmarks and discovers efficient algorithms similar to Karatsuba's method for multiplication in finite fields. It also finds optimal solutions for relevant quantum computations, such as those used in Shor's algorithm and quantum chemistry simulations. AlphaTensor-Quantum is able to automatically optimize circuits, saving hundreds of hours of research. It uses a tensor decomposition approach, with a key component being the symmetric signature tensor. The method is based on a game-like framework where the goal is to decompose the tensor into low-rank factors. It incorporates gadgets, such as the Toffoli and CS gates, to further reduce T-count. The method is able to scale to large tensors and is flexible, allowing for different complexity metrics and domain knowledge. It has been applied to various quantum computing applications, including arithmetic operations, quantum chemistry, and fault-tolerant quantum circuits. The results show that AlphaTensor-Quantum can effectively exploit domain knowledge and state-of-the-art magic state factories to find optimal constructions. It is expected to significantly accelerate discoveries in quantum computation by automatically optimizing circuits.