Quantum simulation of the spin-boson model with noisy gate-based quantum computer

We consider noisy gate-based quantum computers for the purpose of simulating the spin-boson model. We establish a bosonic bath by an ensemble of qubits with finite coherence times. The energy-level broadening of qubits is mapped to broadening of the simulated bath spectral density. We study how desired forms of the spectral density can be constructed by optimizing simulated spin-bath couplings and bath energies. We study the effect of different gate decompositions and system connectivity on the quality of the mapping to the desired form. In the ideal situation, the spin-bath couplings can be decomposed using only variable angle two-qubit gates, such as a variable Mølmer-Sørensen gate. In other cases, qubit noise can get mapped to two-body noise in the simulated spin-bath system, which does not have exact correspondence in the original spin-boson formulation. We show a numeric comparison of the quality of the mapping for various decompositions. Furthermore we compare the full inclusion of the two-body noise terms with an approximate mapping of the effects on the spectral density of the simulated spin-boson problem.