Thesis: Global Synthesis for 3-Qubit Restricted Clifford+T Circuits
Abstract: We describe a global synthesis method for the group O8(Z[1/2]) of 8-dimensional orthogonal matrices with entries in Z[1/2]. This group arises in the study of quantum circuits, and it corresponds to the group of 3-qubit restricted Clifford+T circuits composed of NOT, CNOT, Toffoli, and an analogue of the Hadamard gate. Our method achieves a bound of O(k) gates using decomposition into 1-, 2-, and 4-level operators which was first proposed by Amy, Glaudell, and Ross in 2020.