Analog–Digital Quantum Simulation of the Dicke Model with Superconducting Circuits

Abstract

We propose a concept of mixed analog–digital quantum simulation of the Dicke model with ensembles of superconducting qubits coupled to the single-mode microwave resonators. Using both single-qubit and twoqubit quantum logic gates, it should be possible to engineer different initial conditions for the ensemble of qubits. Since qubits can interact through the photon field of a common quantum resonator, it is attractive to examine the time evolution of this system depending on various characteristics of the initial state, including entanglement and symmetry. We here study theoretically the dynamics of such systems taking into account energy dissipation, pure decoherence as well as disorder in qubits excitation frequencies, which are unavoidable for macroscopic artificial quantum systems. We reveal unusual effects of these imperfections on the dynamics.