Learning to predict arbitrary quantum processes

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 10⁶ 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.