Gaussian state superposition ansatz for quantum impurity problems: Numerical methods and applications

Recent work of Bravyi and Gosset [1] demonstrated that superposition of Gaussian states can approximate efficiently the ground state of gapped quantum impurity problems. We introduce an efficient numerical method for finding the ground state approximation in this variational manifold. As a benchmark, we first apply our method, based on imaginary time evolution, to the Anderson impurity model. We then study a generalization of this approach to models of superconducting islands in the Coulomb blockade regime.
[1] Bravyi and Gosset, Commun. Math. Phys. 356, 451 (2017)