Construction of Anti-Symmetrized Variational Quantum States with Real Space Representation on Quantum Circuits

For quantum chemistry simulations on quantum computers, the variational quantum eigensolver (VQE) is widely adopted. The usual VQE is based on the second quantization, which is suitable for qubit representation. Another way to describe electronic states on a quantum computer is the first quantization, which offers the possibility of achieving smaller scaling with respect to the number of basis sets than the second quantization. A major difficulty with the first quantization is how to construct anti-symmetrized many-body wave functions on quantum circuits. In this work, we propose a method to construct an anti-symmetrized variational quantum state based on a real space basis. The proposed circuit can generate the superposition of exponentially many Slater determinants, i.e., multireference states, by repeatedly applying the one-body circuit and the two-body circuit alternately to the seed state. We performed the VQE with the proposed circuit to obtain the potential energy curve of a one-dimensional hydrogen molecule and obtained the energy values which agree with the result of the exact diagonalization. Although the challenges of measurement and calculation costs in evaluating energy expectations exist, our work may pave the way to future quantum simulations on quantum computers.