  The integration of deep neural networks with the Variational Monte Carlo
(VMC) method has marked a significant advancement in solving the Schr\"odinger
equation. In this work, we enforce spin symmetry in the neural network-based
VMC calculation with modified optimization target. Our method is designed to
solve for the ground state and multiple excited states with target spin
symmetry at a low computational cost. It predicts accurate energies while
maintaining the correct symmetry in strongly correlated systems, even in cases
where different spin states are nearly degenerate. Our approach also excels at
spin-gap calculations, including the singlet-triplet gap in biradical systems,
which is of high interest in photochemistry. Overall, this work establishes a
robust framework for efficiently calculating various quantum states with
specific spin symmetry in correlated systems, paving the way for novel
discoveries in quantum science.
