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Solving linear systems of equations is a fundamental problem that serves as a crucial foundation in numerous fields. Initiated by the pioneering Harrow-Hassidim-Lloyd algorithm, the asymptotic performance of quantum linear system solvers has steadily improved over time. However, there remains a lack of quantitative evaluation of quantum resources based on explicit gate implementations. In this study, we particularly focus on the matrix inversion method via quantum singular value transformation and explicitly construct a quantum circuit to invert specific matrices using the standard universal gate set, Clifford+T gates. We examine the detailed methods for block-encoding, QSP angle finding, and gate decompositions, and numerically evaluate the overall resources required for the quantum circuit.

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Resource Estimation for Matrix Inversion via QSVT with the Clifford+T Gate Set

  • 会议论文

  • 发表日期：

    2026年

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  • Hiroaki Murakami,
  • Kenzo Makino,
  • Yasunori Lee,
  • Keita Kanno,
  • Tomonori Fukuta

摘要

Solving linear systems of equations is a fundamental problem that serves as a crucial foundation in numerous fields. Initiated by the pioneering Harrow-Hassidim-Lloyd algorithm, the asymptotic performance of quantum linear system solvers has steadily improved over time. However, there remains a lack of quantitative evaluation of quantum resources based on explicit gate implementations. In this study, we particularly focus on the matrix inversion method via quantum singular value transformation and explicitly construct a quantum circuit to invert specific matrices using the standard universal gate set, Clifford+T gates. We examine the detailed methods for block-encoding, QSP angle finding, and gate decompositions, and numerically evaluate the overall resources required for the quantum circuit.