Schrieffer-Wolff Transformation on IBM Quantum Computer

TL;DR

This paper develops and demonstrates a quantum algorithm for performing the Schrieffer-Wolff transformation on IBM Quantum computers, enabling the derivation of effective Hamiltonians like the Kondo model from the Anderson impurity model.

Contribution

It introduces the first quantum algorithm for Schrieffer-Wolff transformation and implements it on IBM Quantum hardware for the single impurity Anderson model.

Findings

Successful implementation of SWT on IBM Quantum computers.

Derivation of Kondo model from Anderson impurity model using quantum algorithms.

First demonstration of SWT on quantum hardware.

Abstract

Schrieffer-Wolff transformation (SWT) has been extensively used in quantum many-body physics to calculate the low energy effective Hamiltonian. It provides a perturbative method to comprehend the renormalization effects of strong correlations in the quantum many-body models. The generator for Schrieffer-Wolff transformation is calculated usually by heuristic methods. Recently, a systematic and elegant method for the calculation of this extremely significant transformation has been reported [1]. Given the huge significance of SWT for many areas including quantum condensed matter physics, quantum optics and quantum cavity electrodynamics, it is imperative to develop quantum algorithm for carrying out SWT on quantum computer. In this paper, we put forward this quantum algorithm and demonstrate it for single impurity Anderson model (SIAM), thereby arriving at Kondo model as effective Hamiltonian. We implement our quantum algorithm in QisKit and carry out SWT for SIAM on IBM Quantum computers. To the best of our knowledge, this work is the first of its kind to obtain Kondo model from Anderson impurity model using a quantum algorithm.