Symmetry-adapted sample-based quantum diagonalization: Application to lattice model

Abstract: We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that rigorously embeds space-group symmetry into the many-body subspace sampled by quantum hardware. The method is benchmarked on the two-leg ladder Hubbard model using both molecular orbital and momentum bases. Energy convergence is shown to be improved in the momentum basis compared to the molecular orbital basis for both the spin-quintet ground state and the spin-singlet excited state. We clarify the relationship between the compactness of the many-body wave function and the sparsity of the representation matrices of symmetry operations. Furthermore, the enhancement of the superconducting correlation function due to the Coulomb interaction is demonstrated. Our method highlights the importance of symmetry structure in random-sampling quantum simulation of correlated systems