Quantum Filter Diagonalization with Compressed Double-Factorized Hamiltonians

We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum-classical solution of the time-independent electronic Schrdinger equation with a low-rank double factorization (DF) approach for the representation of the electronic Hamiltonian. In particular, we explore the use of a novel sparse "compressed" double factorization (C-DF) truncation of the Hamiltonian within the time-propagation elements of QFD, while retaining a similarly compressed but numerically converged double-factorized representation of the Hamiltonian for the operator expectation values needed in the QFD quantum matrix elements. The new C-DF method is found to provide substantial additional compression at any given accuracy metric over the traditional "explicit" double factorization approach. Together with significant circuit reduction optimizations and number-preserving postselection and echosequencing error mitigation strategies, the method is found to provide accurate predictions for low-lying eigenspectra in a number of representative molecular systems, while requiring reasonably short circuit depths and modest measurement costs. The method is demonstrated by experiments on noise-free simulators, simulations including models of decoherence and shot-noise, and real quantum hardware.