Multivariate trace estimation using quantum state space linear algebra

arXiv:2405.01098v1 Announce Type: cross
Abstract: In this paper, we present a quantum algorithm for approximating multivariate traces, i.e. the traces of matrix products. Our research is motivated by the extensive utility of multivariate traces in elucidating spectral characteristics of matrices, as well as by recent advancements in leveraging quantum computing for faster numerical linear algebra. Central to our approach is a direct translation of a multivariate trace formula into a quantum circuit, achieved through a sequence of low-level circuit construction …

abstract algebra algorithm arxiv computing cs.lg cs.na linear linear algebra math.na matrix multivariate paper products quant-ph quantum quantum computing research space state trace traces type utility