Abstract:
We present an information-theoretic approach to quantum state classification based on sequential Bayesian inference. In each measurement step, the algorithm updates a probability distribution over candidate states by applying Bayes’ rule to the observed outcome. For each measurement shot on an unknown quantum state, the algorithm selects the observable with the highest expected information gain, continuing until convergence. We demonstrate using the simulations that this algorithm effectively identifies quantum states sampled from the Haar-random distribution. However, despite not relying on circuit-based quantum neural networks, the algorithm still encounters challenges akin to the barren plateau problem. In the leading order, we show that the information gain is proportional to the variance of the observable’s expectation values over candidate states. As the system size increases, the variance and consequently the information gain are exponentially suppressed, which poses significant challenges for classifying general Haar-random quantum states. Finally, we apply the Bayesian search algorithm to classify the ground states of various Hamiltonians using physically motivated observables. On both simulators and quantum computers, the Bayesian search algorithm yields better performances when compared to methods that are not information-optimized. This indicates that the measurement of physically motivated observables can significantly improve the classification performance, guiding toward the future direction of this approach.