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. 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.

翻译：我们提出了一个高效的机器学习算法,用于预测任何未知的量子进程$\mathcal{E}$nbits $\mathcal{D}$@qubits。对于任意的美元平方元状态上范围广泛的分布程序$\mathcal{D}$,我们显示,这个ML算法可以学习预测未知过程$\mathcal{E}$(ML)输出的任何本地属性,输入状态从$\mathcal{D}$(美元)中得出一个小的平均错误。即使未知过程是一个数量回路,有指数式的多个大门,ML算法也具有计算效率。我们的算法将学习未知状态特性和学习低度近似度到未知的观察状态的有效程序结合起来。分析取决于证明新的规范不平等性,包括经典的Bohnenblust-Hille不平等的量子类比,我们通过给优化本地汉密尔顿人的算法来得出。总体而言,我们的结果突出了ML模型预测复杂量子动态输出的可能性,比运行过程所需的时间要快得多。