  Uncovering the origin of the arrow of time remains a fundamental scientific
challenge. Within the framework of statistical physics, this problem was
inextricably associated with the second law of thermodynamics, which declares
that entropy growth proceeds from the system's entanglement with the
environment. It remains to be seen, however, whether the irreversibility of
time is a fundamental law of nature or whether, on the contrary, it might be
circumvented. Here we show that, while in nature the complex conjugation needed
for time reversal is exponentially improbable, one can design a quantum
algorithm that includes complex conjugation and thus reverses a given quantum
state. Using this algorithm on an IBM quantum computer enables us to
experimentally demonstrate a backward time dynamics for an electron scattered
on a two-level impurity.
