  We propose protocols for determining the distances in Hilbert space between
pure and mixed quantum states prepared on a quantum computer. In the case of
pure quantum states the protocol is based on measuring the square of modulus of
scalar product between certain states. Determination of the distance between
mixed quantum states is reduced to measuring the squares of modules of scalar
products between all pure states included in the mixed states. In addition, we
develop a protocol which allows one to determine the speed of evolution of the
spin system simulated by quantum computer. These protocols we apply to measure
distances and speeds of evolution of different quantum systems implemented on
the ibmq-santiago quantum computer.
