Two-level approximation of transmons in quantum quench experiments

Quantum quench is a typical protocol in the study of nonequilibrium dynamics of quantum many-body systems. Recently a number of experiments with superconducting transmon qubits are reported, in which the celebrated spin and hard-core Bose-Hubbard models with two energy levels on individual sites are used. The transmons have nonequidistant energy levels, among which the two lowest levels form the computational subspace. In this work, we numerically simulate realistic experiments of quantum quench dynamics and discuss the applicability of the two-level approximation for the multilevel transmons. We calculate the fidelity decay (i.e., the time-dependent overlap of evolving wave functions) due to the state leakage to transmon high energy levels for two kinds of quantum quench experiments with time reversal and time evolution in one direction, respectively. We present the results of the fidelity decay for different system Hamiltonians with various initial state, qubit coupling strength, and external driving. The extent to which the spin and hard-core Bose-Hubbard models can be applied under various circumstances is discussed and compared with experimental observations. Our work provides a precise way to assess the two-level approximation of transmons in quantum quench experiments and shows that good approximation is reachable using the present-day superconducting circuit architecture.