Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models

Predicting the properties of strongly correlated materials is a significant challenge in condensed matter theory. The widely used dynamical mean-field theory faces difficulty in solving quantum impurity models numerically. Hybrid quantum-classical algorithms such as variational quantum eigensolvers emerge as a potential solution for quantum impurity models. A common challenge in these algorithms is the rapid growth of the number of variational parameters with the number of spin-orbitals in the impurity. In our approach to this problem, we develop compact using a combination of two different strategies. First, we employ a compact physics-inspired , <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>k</a:mi></a:math>-unitary cluster Jastrow , developed in the field of quantum chemistry. Second, we eliminate largely redundant variational parameters of physics-inspired associated with bath sites based on physical intuition. This is based on the fact that a quantum impurity model with a star-like geometry has no direct hopping between bath sites. We benchmark the accuracy of these for both ground-state energy and dynamic quantities by solving typical quantum impurity models with and without shot noise. The results suggest that we can maintain the accuracy of ground-state energy while we drop the number of variational parameters associated with bath sites. Furthermore, we demonstrate that a moment expansion, when combined with the proposed , can calculate the imaginary-time Green's functions under the influence of shot noise. This study demonstrates the potential for addressing complex impurity models in large-scale quantum simulations with fewer variational parameters without sacrificing accuracy. Published by the American Physical Society 2024