Direct U(2) approximation via repeat-until-success circuits

• URL: http://arxiv.org/abs/2604.20033v1
• Date: Tue, 21 Apr 2026 22:35:49 GMT
• Title: Direct U(2) approximation via repeat-until-success circuits
• Abstract summary: We show how to approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem.<n>Our technique also applies to approximating unitaries with multi-qubit gate sets such as Clifford and CS, or Clifford and CCZ, as well as to approximating matrices using multi-qubit gate sets such as Real Clifford and CCZ.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We show how to directly and efficiently approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem, at the cost of one ancillary qubit. Our technique also applies to approximating unitaries with multi-qubit gate sets such as Clifford and CS, or Clifford and CCZ, as well as to approximating orthogonal matrices using multi-qubit gate sets such as Real Clifford and CCZ. The key tools are repeat-until-success circuits, lattice-based exact synthesis algorithms, integer point enumeration in convex sets, and relative norm equations.

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