Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
arxiv(2023)
摘要
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 eigensolver 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 ansatzes using a combination of two different strategies.
First, we employ compact physics-inspired ansatz, k-unitary cluster Jastrow
ansatz, developed in the field of quantum chemistry. Second, we eliminate
largely redundant variational parameters of physics-inspired ansatzes
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 ansatzes for
both ground-state energy and dynamic quantities by solving typical quantum
impurity models with/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 ansatzes, 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.
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