  Quantum computers promise to perform computations beyond the reach of modern
computers with profound implications for scientific research. Due to remarkable
technological advances, small scale devices are now becoming available for use.
One of the most apparent applications for such a device is the study of complex
many-body quantum systems, where classical computers are unable to deal with
the generic exponential complexity of quantum states. Even zero-temperature
equilibrium phases of matter and the transitions between them have yet to be
fully classified, with topologically protected phases presenting major
difficulties. We construct and measure a continuously parametrized family of
states crossing a symmetry protected topological phase transition on the IBM Q
quantum computers. We present two complementary methods for measuring string
order parameters that reveal the transition, and additionally analyse the
effects of noise in the device using simple error models. The simulation that
we perform is easily scalable and is a practical demonstration of the utility
of near-term quantum computers for the study of quantum phases of matter and
their transitions.
