Group-invariant estimation of symmetric states generated by noisy quantum computers

The problem of quantum state estimation is crucial in the development of quantum technologies. In particular, the use of symmetric quantum states is useful in many relevant applications. In this work, we analyze the task of reconstructing the density matrices of symmetric quantum states generated by a quantum processor. For this purpose, we take advantage of an estimation technique that results to be equivalent to the quantum Maximum Entropy (MaxEnt) estimation, and which was recently adapted to quantum states with arbitrary symmetries. The smart use of prior knowledge of the quantum state symmetries allows for a reduction in both, the number of measurements that need to be made on the system, and the size of the computational problem to store and process the data, resulting in a better overall performance of the estimator as well. After performing numerical simulations, we implement some examples of symmetric states in IonQ quantum processors, and estimate them using the proposed technique. The results are in a good agreement with numerical simulations, showing that the proposed method is a good estimator that allows to save both, experimental and computational resources.