Sequence-Model-Guided Measurement Selection for Quantum State Learning

Machine learning provides a powerful tool for characterizing quantum systems based on measurement data [1-40]. In particular, deep neural networks have played an important role across a range of tasks, including quantum state reconstruction [7-16], quantum similarity testing [17, 20, 37], prediction of quantum entanglement [21, 24, 40], and state classification [25-33]. Recent progress has enabled sequence models to predict diverse quantum properties of scalable quantum systems, by modeling the measurement outcome distributions [18, 19, 22, 23, 39, 41]. An important question in quantum state learning is how to choose the appropriate measurements to gather information about an unknown quantum state. While an optimized adaptive choice can be found for small quantum systems [42-44], a full optimization quickly becomes intractable as the size of the system grows large. For scalable quantum systems, a widespread approach is to employ randomized measurements [45-51]. This approach enables the estimation of a wide range of observables without performing a full tomography of the quantum state, which is not feasible for large quantum systems. When prior knowledge is available, the randomized measurement choices can be further optimized [52-54]. In general, however, determining the optimal distributions is computationally challenging for large-scale quantum systems, especially when an approximated classical description is lacking.