Efficient criteria of quantumness for a large system of qubits

In order to model and evaluate large-scale quantum systems, e.g. quantum computer and quantum annealer, it is necessary to quantify the "quantumness" of such systems. In this paper, we discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems, which could be used to characterize their degree of quantumness. Based on model analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution. Applying it to the case of D-Wave One superconducting quantum annealing device, we find that its operation as described falls well within the quantum domain.