Digital Simulations of Fermion-Boson Models on a Quantum Computer*

Performing simulations of many-body correlated systems formed both by fermions and bosons on quantum computers is a demanding challenge. Current techniques are often based on digital approaches encoding all degrees of freedom into the qubits and simulating, for instance, the time evolution. These encoding methods, though, have been found to be very inefficient. We propose an alternative architecture to solve this problem, which is based on a superconducting platform with transmons coupled to additional resonators traditionally used for quantum-information storage. This architecture expands the native set of gates of the quantum processor by adding an entangling gate between the transmons, which encode the fermions, and the resonators, which store the bosons without any need for approximations related to the truncation of the bosonic Fock space. We illustrate the potential of our approach by presenting a number of examples for the Trotterized time evolution of models from solid-state physics and quantum optics.