Scaling Law in Large Quantum Devices with Dissipation*

Recently, the Google reported quantum supremacy using 53-qubits with Sycamore chip, the D-wave systems released "Advantage" 5000-qubits quantum annealing machine, and the IBM announced a roadmap of chips: Eagle with 127-qubits in 2021, Osprey with 433-qubits in 2022, and Condor with 1121-qubits in 2023. While large enough quantum systems have been developed and will be developed, the full description of quantum mechanics for such a large system cannot be simulated with classical computers, and the question naturally arises: how we test if it is capable of performing quantum computing? The answer may be given by a reduced description of qualitatively different regimes of behavior of such systems. In this talk, we present a statistical approach to such a description of large quantum systems.