Sharp Transitions for Subsystem Complexity
The circuit complexity of time-evolved pure quantum states
grows linearly in time for an exponentially long time. This behavior has
been proven in certain models, is conjectured to hold for generic
quantum many-body systems, and is believed to be dual to the long-time
growth of black hole interiors in AdS/CFT. Achieving a similar
understanding for mixed states remains an important problem. We
demonstrate that holography predicts several sharp transitions in the
time evolution of subsystem complexity and show that at least some of
these transitions are also realized in random quantum circuits.