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

Longcheng Li1,2,*, Cheng Guo1,†, Qian Li1,‡, and Xiaoming Sun1,3,§

  • 1Institute of Computing Technology, Chinese Academy of Sciences, 100190 Beijing, China
  • 2School of Computer Science and Technology, University of Chinese Academy of Sciences, 100049 Beijing, China
  • 3CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, 100049 Beijing, China

  • *lilongcheng18@mails.ucas.ac.cn
  • †cheng323232@163.com
  • ‡liqian@ict.ac.cn
  • §sunxiaoming@ict.ac.cn
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Phys. Rev. A 107, 042424 – Published 18 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042424

Abstract

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.

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Phys. Rev. A 107, 042424– Published 18 April, 2023
  • Received 18 January 2023
  • Accepted 16 March 2023
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