Benchmarking the Spin-Boson Model on Quantum Computers

The spin-boson model describes N spin particles interacting with a bath of M bosons approximated as harmonic oscillators. It is a useful framework for understanding physical dynamics especially for describing impurities or coupled quantum nanoparticles. We have performed perturbative calculation of the six lowest energy eigenvalues at second order for general boson frequencies and of the spectral density of the model, alongside an examination of the matching between spin and boson modes. These perturbative calculations serve as a standard mathematical cross-check to the Sample-Based Quantum Diagonalization (SQD), a hybrid classical-quantum algorithm, both for simulations and on quantum hardware. The motivation of the project is to demonstrate the advantage of quantum computers for diagonalizing Hamiltonians in large Hilbert spaces as they posit significant improvements over powerful classical hardware. These efforts are crucial for benchmarking the capabilities of current quantum computing platforms and advancing our understanding of open quantum systems in a practical setting.