Hybrid quantum-classical algorithms for quantum impurity problems

Jia Li, Yang Yu, Emanuel Gull +1 more

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. The problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

Sergey Bravyi, David Gosset

Rihito Sakurai, Oliver J. Backhouse, George H. Booth +2 more

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 , k -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

Sean M. Harding

Arne Ludwig

Rihito Sakurai, Wataru Mizukami, Hiroshi Shinaoka

Quantitative descriptions of strongly correlated materials pose a considerable challenge in condensed matter physics and chemistry. A promising approach to address this problem is quantum embedding methods. In particular, the dynamical mean-field theory (DMFT) maps the original system to an effective quantum impurity model comprising correlated orbitals embedded in an electron bath. The biggest bottleneck in DMFT calculations is numerically solving the quantum impurity model, i.e., computing the Green's function. Past studies have proposed theoretical methods to compute the Green's function of a quantum impurity model in polynomial time using a quantum computer. So far, however, efficient methods for computing the imaginary-time Green's functions have not been established despite the advantages of the imaginary-time formulation. We propose a quantum-classical hybrid algorithm for computing imaginary-time Green's functions on quantum devices with limited hardware resources by applying the variational quantum simulation. Using a quantum circuit simulator, we verified this algorithm by computing Green's functions for a dimer model as well as a four-site impurity model obtained by DMFT calculations of the single-band Hubbard model, although our method can be applied to general imaginary-time correlation functions.