Variational post-selection for ground states and thermal states simulation

Variational quantum algorithms, as one of the most promising routes in the noisy intermediate-scale quantum era, offer various potential applications while also confronting severe challenges due to near-term quantum hardware restrictions. In this work, we propose a framework to enhance the expressiveness of a variational quantum ansatz by incorporating variational post-selection techniques. These techniques apply variational modules and neural network post-processing on ancilla qubits, which are compatible with the current generation of quantum devices. Equipped with variational post-selection, we demonstrate that the accuracy of the variational ground state and thermal state preparation for both quantum spin and molecule systems is substantially improved. Notably, in the case of estimating the local properties of a thermalized quantum system, we present a scalable approach that outperforms previous methods through the combination of neural post-selection and a new optimization objective.