We present an efficient machine learning (ML) algorithm for predicting any
unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of
distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML
algorithm can learn to predict any local property of the output from the
unknown process~$\mathcal{E}$, with a small average error over input states
drawn from $\mathcal{D}$. The ML algorithm is computationally efficient even
when the unknown process is a quantum circuit with exponentially many gates.
Our algorithm combines efficient procedures for learning properties of an
unknown state and for learning a low-degree approximation to an unknown
observable. The analysis hinges on proving new norm inequalities, including a
quantum analogue of the classical Bohnenblust-Hille inequality, which we derive
by giving an improved algorithm for optimizing local Hamiltonians. Numerical
experiments on predicting quantum dynamics with evolution time up to $10^6$ and
system size up to $50$ qubits corroborate our proof. Overall, our results
highlight the potential for ML models to predict the output of complex quantum
dynamics much faster than the time needed to run the process itself.

研究了预测 n 个量子比特上任何未知量子过程的机器学习算法，该算法可在广泛分布的任意 n 比特状态下学习预测来自未知过程 E 的任何本地属性，具有小的平均误差率。本文的算法组合了学习未知状态属性和学习低阶近似未知的可观测量的有效过程，并证明了新的范数不等式，包括一个量子模拟 Bohnenblust-Hille 不等式。通过数值实验证明，机器学习模型能够比运行过程本身快得多地预测复杂量子动态的输出。