Unitary synthesis with fewer T gates

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n\mathrm{/}3}{n}^{2\mathrm{/}3})$. This improves upon the previous best known upper bound of $O(2^{3n\mathrm{/}2}n)$, while the best known lower bound remains $\mathrm{\Omega }(2^n)$. 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.