Preparation of Strongly Correlated States in Quantum Computer

Solving interacting quantum systems is arguably one of the most important problems in condensed matter physics. Correlated electron states in cuprate materials and interacting electron gas in high magnetic field are prototypical examples where our theoretical understanding is rather limited. The main difficulty can often be captured by the so-called sign problem, which explains the inability of classical computers in describing many-body quantum states. Despite such difficulties, trial wave functions such as the resonating valence bond (RVB) states and the Laughlin state have proved to be successful in understanding the quantum many-body systems. Therefore, it is natural to expect that these wave functions would play important roles when studying correlated systems using quantum computers. In this talk, I will present how one can systematically prepare correlated many-body states in quantum circuits via recently developed amplitude amplification technique. Using the RVB state as our main example, I will explain the relevant parameters needed for building quantum circuits can all be efficiently computed in classical computers. This includes the estimation of the amplitude of our target RVB state in a Bardeen-Cooper-Schrieffer state, unlike in the general cases where the estimation of the target state in an initial state is challenging. I will conclude by discussing the generality of our approach in tackling strongly interacting systems using quantum computers.