Superconducting simulators for quantum impurity models

We introduce a mapping between a variety of superconducting circuits and a family of Hamiltonians describing localized magnetic impurities interacting with conduction bands. This includes the Anderson model, the single impurity one- and two-channel Kondo problem, as well as the one-dimensional Kondo lattice. We compare the requirements for performing quantum simulations using the proposed circuits to those of universal quantum computation with superconducting qubits, singling out the specific challenges that will have to be addressed.We introduce a mapping between a variety of superconducting circuits and a family of Hamiltonians describing localized magnetic impurities interacting with conduction bands. This includes the Anderson model, the single impurity one- and two-channel Kondo problem, as well as the one-dimensional Kondo lattice. We compare the requirements for performing quantum simulations using the proposed circuits to those of universal quantum computation with superconducting qubits, singling out the specific challenges that will have to be addressed.

arXiv:0709.1573Physical Review BJan 24, 200841 citations

QUANTUM SIMULATION OF SUPERCONDUCTIVITY

Masatoshi IMADA

Elsevier eBooksJan 1, 19900 citations

QUANTUM SIMULATION OF SUPERCONDUCTIVITY

Masatoshi Imada

Elsevier eBooksJan 1, 19904 citations

Surrogate model solver for impurity-induced superconducting subgap states

V. Baran, Emil J. P. Frost, Jens Paaske

A simple impurity solver is shown to capture impurity-induced superconducting subgap states in quantitative agreement with the numerical renormalization group and quantum Monte Carlo simulations. The solver is based on the exact diagonalization of a single-impurity Anderson model with discretized superconducting reservoirs including only a small number of effective levels. Their energies and couplings to the impurity $d$ level are chosen so as to best reproduce the Matsubara frequency dependence of the hybridization function. We provide a number of critical benchmarks and demonstrate the solver's efficiency in combination with the reduced basis method [V. V. Baran and D. R. Nichita, Phys. Rev. B 107, 144503 (2023)] by calculating the phase diagram for an interacting three-terminal junction.A simple impurity solver is shown to capture impurity-induced superconducting subgap states in quantitative agreement with the numerical renormalization group and quantum Monte Carlo simulations. The solver is based on the exact diagonalization of a single-impurity Anderson model with discretized superconducting reservoirs including only a small number of effective levels. Their energies and couplings to the impurity $d$ level are chosen so as to best reproduce the Matsubara frequency dependence of the hybridization function. We provide a number of critical benchmarks and demonstrate the solver's efficiency in combination with the reduced basis method [V. V. Baran and D. R. Nichita, Phys. Rev. B 107, 144503 (2023)] by calculating the phase diagram for an interacting three-terminal junction.

arXiv:2307.11646Physical review. B./Physical review. BDec 20, 202322 citations

d

level are chosen so as to best reproduce the Matsubara frequency dependence of the hybridization function. We provide a number of critical benchmarks and demonstrate the solver's efficiency in combination with the reduced basis method [V. V. Baran and D. R. Nichita, Phys. Rev. B 107, 144503 (2023)] by calculating the phase diagram for an interacting three-terminal junction.