The talk will begin with a basic classical problem: Can we efficiently learn and predict an arbitrary classical Boolean circuit? In classical learning theory, a well-known result states that we must obtain exponential-size data to accurately predict a single output bit of the classical circuit over randomly sampled input bitstrings. So the answer is no.

We will then look at a quantum analogue of this problem: Can we efficiently learn and predict an arbitrary quantum circuit/process? Surprisingly, we will find that one could efficiently learn and predict local properties in the output state of an arbitrary quantum circuit/process over a wide range of randomly sampled input quantum states (including random product states).

Our result highlights the potential for learning algorithms to predict the output of complex quantum dynamics much faster than the time needed to run the process. The talk is based on [1].

[1] Huang, Hsin-Yuan, Sitan Chen, and John Preskill. "Learning to predict arbitrary quantum processes." arXiv preprint arXiv:2210.14894 (2022).