June 11, 2024, 4:48 a.m. | Alessandro Luongo, Changpeng Shao

cs.LG updates on arXiv.org arxiv.org

arXiv:2011.06475v2 Announce Type: replace-cross
Abstract: We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$ are the eigenvalues of $A$. Typical examples of spectral sums are the von Neumann entropy, the trace of $A^{-1}$, the log-determinant, and the Schatten $p$-norm, where the latter does not require the matrix to be PSD. The current best …

abstract algorithms arxiv cs.ai cs.ds cs.lg examples function matrix positive quant-ph quantum replace semi sum text type

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