Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications quantum systems. It highly desired to design algorithms that can speedup diagonalization, especially those be implemented on near-term devices. In this work, we propose a variational algorithm for Hamiltonians (VQHD) systems, which explores important properties, such as temperature, local...

The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343-356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals produce new kinds of 2D spectra. The resolution obtained by FDM can be far superior to that obtained...

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at data representations suited to NMF. In this work, we relate TL-NMF the classical joint-diagonalization (JD) problem. We show that, when number of realizations sufficiently large, can be replaced by two-step approach -- termed as JD+NMF estimates through JD, prior NMF computation. contrast, found lim...