I will discuss two recent works that leverage ideas from quantum information dynamics to understand the impact of noise on large-scale quantum systems. First, I will introduce a framework based on information dynamics to describe how noise propagates in ergodic many-body quantum systems. Our framework yields immediate predictions for popular benchmarking protocols involving time-reversal, and provides a potential explanation for recent NMR experiments on ~100s of interacting quantum spins. Second, in a more rigorous context, I will provide a polynomial-time classical algorithm for simulating expectation values in almost any noisy quantum circuit. Our algorithm is provably efficient, and extends recent results on noisy random circuit sampling to a much more general setting. As a corollary, we establish that almost any quantum experiment that provides an exponential speed-up over classical computation must fail in the presence of a noise rate greater than ~1/n, where n is the number of qubits.
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