Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914786486255616 |
|---|---|
| author | Sakurai, Rihito Backhouse, Oliver J. Booth, George H. Mizukami, Wataru Shinaoka, Hiroshi |
| author_facet | Sakurai, Rihito Backhouse, Oliver J. Booth, George H. Mizukami, Wataru Shinaoka, Hiroshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04105 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models Sakurai, Rihito Backhouse, Oliver J. Booth, George H. Mizukami, Wataru Shinaoka, Hiroshi Quantum Physics Strongly Correlated Electrons 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. |
| title | Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2312.04105 |