Quantum-classical hybrid algorithms for computing imaginary-time response functions on noisy intermediate-scale quantum devices*

Quantum embedding methods are theoretical approaches to study strongly correlated systems, formulated in terms of correlated electrons coupled to an effective environment. The dynamic mean-field theory (DMFT) is a representative example [1,2], where the effective environment is represented by a quantum impurity problem. The biggest bottleneck in DMFT calculations is solving the quantum impurity model numerically, i.e., computing the Green's function.

Past studies have proposed the theoretical methods to compute Green's function of a quantum impurity model in polynomial time using a quantum computer [3,4,5]. However, none of the methods has utilized imaginary-time Green's functions despite the advantage of the imaginary-time formulation.

Here, we propose a quantum-classical hybrid algorithm for computing imaginary-time Green's functions on noisy intermediate-scale quantum devices by extending the variational quantum simulation [6].  Using a quantum circuit simulator, we verify this algorithm by computing Green's functions for typical impurity problems such as dimer model and single-band impurity problem obtained by DMFT. Based on the results, we discuss the computational resources and numerical stability of our algorithm and compare them with those of other proposals [4, 5].

References:

[1] G. Kotliar et al., Rev. Mod. Phys. 78, 865 (2006). 

[2] A. Georges et al., Rev. Mod. Phys. 68, 13 (1996). 

[3] B. Bauer et al., Phys. Rev. X 6, 3 031045 (2016).

[4] I. Rungger et al., arXiv:1910.04735v2. 

[5] H. Chen et al., arXiv:2105.01703v2. 

[6] S. McArdle et al., npj Quantum Inf 5, 75 (2019).