Unitary synthesis with fewer T gates

Abstract

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

13 pages