Quantum Simulation of the Spin-Boson Model

The spin-boson model, which characterizes the interaction between a collection of spins and a collection of bosons, describes a wide variety of physical phenomena. However, exploration of the model on superconducting quantum hardware has been limited. We detail the study of the spin-boson system in the regime of a boson with a finite number of occupation modes coupled to a collection of spins. To accurately map this model onto current hardware, we compare different encoding schemes for the bosonic modes, and perform a resource estimation of these encoding schemes. To isolate the ground state and map the parameter space for the mean occupation number and magnetization observables, we utilize a hybrid quantum-classical workflow based on a sample-based quantum diagonalization (SQD) algorithm. The first step involves sampling bit strings from a quantum circuit ansatz for the ground state wavefunction executed on RPI's IBM System One quantum computer, ibm_rensselaer. The output bit strings are then classically post-processed using symmetries of the multi-qubit states to select only the physical ones. Finally, the Hamiltonian is diagonalized in the subspace spanned by the selected physical states to estimate the true ground state of the system. We analyze the convergence rate of the SQD algorithm and the accuracy of the estimated ground state in different spin-boson coupling regimes.