arXiv (OAI Expanded)
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One Gate at a Time: Complexity Growth in Random Quantum Circuits
A random unitary quantum circuit is expected to be incompressible for exponentially long times. We show that the constant-error circuit complexity of a random unitary circuit grows almost linearly with time as $Ω(T/\log T)$. The bound holds for all $2\leq T\leq 4^n$ where $n$ is the system size, and
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