Algorithmic simulation of far-from-equilibrium dynamics using quantum
  computer
We point out that superconducting quantum computers are prospective for the
simulation of the dynamics of spin models far from equilibrium, including
nonadiabatic phenomena and quenches. The important advantage of these machines
is that they are programmable, so that different spin models can be simulated
in the same chip, as well as various initial states can be encoded into it in a
controllable way. This opens an opportunity to use superconducting quantum
computers in studies of fundamental problems of statistical physics such as the
absence or presence of thermalization in the free evolution of a closed quantum
system depending on the choice of the initial state as well as on the
integrability of the model. In the present paper, we performed
proof-of-principle digital simulations of two spin models, which are the
central spin model and the transverse-field Ising model, using 5- and 16-qubit
superconducting quantum computers of the IBM Quantum Experience. We found that
these devices are able to reproduce some important consequences of the symmetry
of the initial state for the system's subsequent dynamics, such as the
excitation blockade. However, lengths of algorithms are currently limited due
to quantum gate errors. We also discuss some heuristic methods which can be
used to extract valuable information from the imperfect experimental data.
A. A. Zhukov S. V. Remizov W. V. Pogosov Yu. E. Lozovik