Concept learning of parameterized quantum models from limited measurements
This work addresses the challenge of efficiently learning quantum models with limited measurements, which is incremental as it builds on existing learning-theoretic frameworks to provide new analytical tools.
The authors tackled the problem of quantifying the interplay between sample complexity and measurement shots in learning expectation values of observables for quantum states, showing that increasing measurements beyond a constant factor yields asymptotically trivial improvements while sample size enhances performance. They applied this framework to analyze measurement noise in classical surrogation of parameterized quantum circuits.
Classical learning of the expectation values of observables for quantum states is a natural variant of learning quantum states or channels. While learning-theoretic frameworks establish the sample complexity and the number of measurement shots per sample required for learning such statistical quantities, the interplay between these two variables has not been adequately quantified before. In this work, we take the probabilistic nature of quantum measurements into account in classical modelling and discuss these quantities under a single unified learning framework. We provide provable guarantees for learning parameterized quantum models that also quantify the asymmetrical effects and interplay of the two variables on the performance of learning algorithms. These results show that while increasing the sample size enhances the learning performance of classical machines, even with single-shot estimates, the improvements from increasing measurements become asymptotically trivial beyond a constant factor. We further apply our framework and theoretical guarantees to study the impact of measurement noise on the classical surrogation of parameterized quantum circuit models. Our work provides new tools to analyse the operational influence of finite measurement noise in the classical learning of quantum systems.