Spin-boson model on a quantum computer

The spin-boson model is a paradigmatic model in quantum many-body physics used to describe a collection of coupled spins and harmonic bosons, for example, impurities or quantum nanoparticles interacting with a bosonic environment. It has proven instrumental in studying phenomena including dissipation, superadiance, and quantum chaos. Although certain spin-boson models are analytically solvable in specific limits, the general model is non-integrable, necessitating a scalable computational approach.

In this work, we focus on setting up the simulation of the spin-boson model on real quantum hardware. We discuss how to map the spin-boson Hamiltonian onto IBM’s quantum processor with considerations on hardware connectivity constraints and limited qubit coherence times. We demonstrate the workflow of using the Sample-based Krylov Diagonalization (SKQD) algorithm to compute the low-lying eigenspectrum of the spin-boson Hamiltonian for different coupling regimes. We examine the convergence of the SKQD method with respect to computational resources and analyze the algorithm runtime scaling as a function of the Hilbert space dimensionality. Based on the estimated eigenspectrum, we compute the interacting Green’s function and self-energy and discuss the results compared to the literature.