Efficient Quantum Circuit Preparation of Resonating Valence Bond States

Byungmin Kang, Vito W Scarola, Kwon Park

When studying strongly correlated systems using quantum circuits, it is important to prepare good initial states from which the target many-body states can easily be accessed. Here, we discuss an efficient quantum circuit preparation of the resonating valence bond (RVB) state, which plays an essential role in understanding the high-Tc superconductivity and the spin liquid physics. It is known that the RVB state is given by the Gutzwiller projection of a Bardeen-Cooper-Schrieffer (BCS) state for which an efficient quantum circuit construction is known. However, since the overlap between the RVB state and the BCS state decays exponentially in the system size, naive implementation of the Gutzwiller projection as projective measurements in quantum circuit would require exponentially many repetitions in order to obtain the RVB state. In this talk, we discuss how to systematically amplify the amplitude associated with the RVB state in the BCS state using a recently developed amplitude amplification technique. Following our construction, one can construct a quantum circuit for the RVB state with an arbitrarily high success probability.