Reinforced Learning Explicit Circuit Representations for Quantum State Characterization from Local Measurements

Characterizing quantum states is essential for advancing many quantum technologies. Recently, deep neural networks have been applied to learn quantum states by generating compressed implicit representations. Despite their success in predicting properties of the states, these representations remain a black box, lacking insights into strategies for experimental reconstruction. In this work, we aim to open this black box by developing explicit representations through generating surrogate state preparation circuits for property estimation. We design a reinforcement learning agent equipped with a Transformer-based architecture and a local fidelity reward function. Relying solely on measurement data from a few neighboring qubits, our agent accurately recovers properties of target states. We also theoretically analyze the global fidelity the agent can achieve when it learns a good local approximation. Extensive experiments demonstrate the effectiveness of our framework in learning various states of up to 100 qubits, including those generated by shallow Instantaneous Quantum Polynomial circuits, evolved by Ising Hamiltonians, and many-body ground states. Furthermore, the learned circuit representations can be applied to Hamiltonian learning as a downstream task utilizing a simple linear model.

Characterizing and understanding quantum states is crucial for the development of quantum technologies, but doing so becomes increasingly difficult as quantum systems grow in size. Recent machine learning approaches can predict properties of quantum states, but they work like black boxes and do not provide a clear way to reconstruct the state in actual quantum experiments.We propose a new framework that makes the representation of quantum states more transparent and usable. Our framework learns an explicit circuit representation, a step-by-step recipe that can be used to physically recreate the state on a quantum computer. We achieve this by training a reinforcement learning agent that uses only experimentally available measurement settings. Our framework is validated through extensive experiments on quantum systems with up to 100 qubits.Our framework makes quantum state representations both interpretable and experimentally implementable. It enables large-scale quantum state characterization and provides a way for downstream applications such as learning the underlying physical model of a system. Our framework bridges the gap between machine-learned representations and real-world quantum hardware implementation.