Optimizing T gates in Clifford+T circuit as $\pi/4$ rotations around Paulis

In this work, we introduce a new circuit optimization technique to reduce the number of T gates in Clifford+T circuits by treating T gates conjugated by Clifford gates as $\frac{\pi}{4}$-rotations around Pauli operators. The tested benchmarks shows up to $71.43\%$ and an average $42.67\%$ reduction in T-count, both surpass the best performance reported. The worst case complexity of our algorithm is $O(nk^2)$ where $n$ is the number of qubits and $k$ is the number of T gates in the original Clifford+T circuit.