Fast exact synthesis of two-qubit unitaries using a near-minimum number of T gates

This is the authors' abstract. We don't add key points for this paper.

This paper focuses on exact synthesis of two-qubit unitaries using Clifford and T gates. We propose an ancilla-free synthesis algorithm (i) which uses T gates no more than ten times the minimum possible number of T gates, also known as the T count, and (ii) whose time complexity is linear with the T count and thus instance optimal. Our synthesis algorithm relies on a characterization of the T count of two-qubit unitaries based on Lie group homomorphism, which may be interest of its own. Precisely, we show that for any two-qubit unitary generated by Clifford and T gates, its T count is equivalent to the least denominator exponent of its SO(6) representation up to a factor of at most 10.