Xinyu Tan (Oct 01 2025).
Abstract: We present a simple algorithm that implements an arbitrary
n-qubit unitary operator using a Clifford+T circuit with T-count
O(24n/3n2/3). This improves upon the previous best known upper bound of
O(23n/2n), while the best known lower bound remains
Ω(2n). Our construction is based on a recursive application of the cosine-sine decomposition, together with a generalization of the optimal diagonal unitary synthesis method by Gosset, Kothari, and Wu to multi-controlled
k-qubit unitaries.