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arXiv · 2604.20033

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

Vadym Kliuchnikov·Jendrik Brachter·Marcus P. da Silva
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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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Vadym Kliuchnikov, Jendrik Brachter, Marcus P. da Silva. 2026-04-21. Direct U(2) approximation via repeat-until-success circuits. https://arxiv.org/abs/2604.20033

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