Quantum computers hold the promise of executing tasks beyond the capability
of classical computers. Noise competes with coherent evolution and destroys
long-range correlations, making it an outstanding challenge to fully leverage
the computation power of near-term quantum processors. We report Random Circuit
Sampling (RCS) experiments where we identify distinct phases driven by the
interplay between quantum dynamics and noise. Using cross-entropy benchmarking,
we observe phase boundaries which can define the computational complexity of
noisy quantum evolution. We conclude by presenting an RCS experiment with 70
qubits at 24 cycles. We estimate the computational cost against improved
classical methods and demonstrate that our experiment is beyond the
capabilities of existing classical supercomputers