Learning to predict arbitrary quantum processes

TL;DR

This paper introduces a machine learning algorithm capable of efficiently predicting local properties of unknown quantum processes across many qubits, even when the processes are complex and involve exponentially many gates.

Contribution

The paper presents a novel ML method that efficiently predicts quantum process outputs, leveraging new norm inequalities and low-degree observable approximations.

Findings

Successfully predicts quantum dynamics up to 50 qubits

Handles processes with exponentially many gates efficiently

Numerical results confirm theoretical predictions

Abstract

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.