  A legend tells that once Loschmidt asked Boltzmann on what happens to his
statistical theory if one inverts the velocities of all particles, so that, due
to the reversibility of Newton's equations, they return from the equilibrium to
a nonequilibrium initial state. Boltzmann only replied ``then go and invert
them''. This problem of the relationship between the microscopic and
macroscopic descriptions of the physical world and time-reversibility has been
hotly debated from the XIXth century up to nowadays. At present, no modern
computer is able to perform Boltzmann's demand for a macroscopic number of
particles. In addition, dynamical chaos implies exponential growth of any
imprecision in the inversion that leads to practical irreversibility. Here we
show that a quantum computer composed of a few tens of qubits, and operating
even with moderate precision, can perform Boltzmann's demand for a macroscopic
number of classical particles. Thus, even in the regime of dynamical chaos, a
realistic quantum computer allows to rebuild a specific initial distribution
from a macroscopic state given by thermodynamic laws.
