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

• URL: http://arxiv.org/abs/2312.04105v1
• Date: Thu, 7 Dec 2023 07:39:01 GMT
• Title: Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
• Authors: Rihito Sakurai, Oliver J. Backhouse, George H. Booth, Wataru Mizukami, Hiroshi Shinaoka
• Abstract summary: 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. 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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