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Bibliographic Details
Main Authors: Rodríguez, John A. Mora, Dutra, Arthur C. R., Earp, Henrique N. Sá, Cunha, Marcelo Terra
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.05468
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Table of Contents:
  • We present a novel algorithm for performing the Cartan-Khaneja-Glaser decomposition of unitary matrices in $SU(2^n)$, a critical task for efficient quantum circuit design. Building upon the approach introduced by Sá Earp and Pachos (2005), we overcome key limitations of their method, such as reliance on ill-defined matrix logarithms and the convergence issues of truncated Baker-Campbell-Hausdorff(BCH) series. Our reformulation leverages the algebraic structure of involutive automorphisms and symmetric Lie algebra decompositions to yield a stable and recursive factorization process. We provide a full Python implementation of the algorithm, available in an open-source repository, and validate its performance on matrices in $SU(8)$ and $SU(16)$ using random unitary benchmarks. The algorithm produces decompositions that are directly suited to practical quantum hardware, with factors that can be implemented near-optimally using standard gate sets.