Posted

Xinyu Tan (Oct 01 2025).
Abstract: We present a simple algorithm that implements an arbitrary nn-qubit unitary operator using a Clifford+T circuit with T-count O(24n/3n2/3)O(2^{4n/3} n^{2/3}). This improves upon the previous best known upper bound of O(23n/2n)O(2^{3n/2} n), while the best known lower bound remains Ω(2n)\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 kk-qubit unitaries.

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