{"ID":2872391,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.08196","arxiv_id":"2509.08196","title":"Quantum Fisher information matrix via its classical counterpart from random measurements","abstract":"Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart: the classical Fisher information matrix (CFIM). It is known that averaging the classical Fisher information matrix over Haar-random measurement bases yields $\\mathbb{E}_{U\\simμ_H}[F^U(\\boldsymbolθ)] = \\frac{1}{2}Q(\\boldsymbolθ)$ for pure states in $\\mathbb{C}^N$. In this paper, we review this identity by revealing its connection to covariant measurement in quantum metrology. Furthermore, we go beyond this and obtain the exact variance of CFIM ($O(N^{-1})$), estimate its moment, and establish non-asymptotic concentration bounds ($\\exp(-Θ(N)t^2)$), demonstrating that using few random measurement bases is sufficient to approximate the QFIM accurately in high-dimensional settings. This work establishes a solid theoretical foundation for efficient quantum natural gradient methods via randomized measurements.","short_abstract":"Preconditioning with the quantum Fisher information matrix (QFIM) is a popular approach in quantum variational algorithms. Yet the QFIM is costly to obtain directly, usually requiring more state preparation than its classical counterpart: the classical Fisher information matrix (CFIM). It is known that averaging the cl...","url_abs":"https://arxiv.org/abs/2509.08196","url_pdf":"https://arxiv.org/pdf/2509.08196v4","authors":"[\"Jianfeng Lu\",\"Kecen Sha\"]","published":"2025-09-10T00:00:02Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"math-ph\",\"math.OC\"]","methods":"[]","has_code":false}