Other authors suggest that the butterfly effect can be observed in quantum systems. Karkuszewski et al. consider the time evolution of quantum systems which have slightly different Hamiltonians . They investigate the level of sensitivity of quantum systems to small changes in their given Hamiltonians.  Poulin et al. presented a quantum algorithm to measure fidelity decay, which "measures the rate at which identical initial states diverge when subjected to slightly different dynamics". They consider fidelity decay to be "the closest quantum analog to the (purely classical) butterfly effect".  Whereas the classical butterfly effect considers the effect of a small change in the position and/or velocity of an object in a given Hamiltonian system , the quantum butterfly effect considers the effect of a small change in the Hamiltonian system with a given initial position and velocity.   This quantum butterfly effect has been demonstrated experimentally.  Quantum and semiclassical treatments of system sensitivity to initial conditions are known as quantum chaos .