Digital quantum simulations of t-J model in one and two dimensions on NISQ devices

High temperature superconductors are prototypical strongly correlated electron systems. Among the strongly correlated models, t-J model is believed to be a candidate model to explain salient physical properties of high-T_c cuperate superconductors. Due to the strong correlations, the classical approaches to solve the t-J model are limited. One of the promising avenues for digital quantum simulations is to solve strongly interacting quantum systems. In this talk, we will present quantum simulations of t-J model in one and two dimensions. By using quantum algorithms, we will present two-particle correlation functions that characterize quantum fluctuations and the relationship between superconducting and magnetic instabilities. We will present our results on NISQ devices like superconducting qubits and trapped Ion systems and discuss their performance.