Two-electron wavefunctions are matrix product states with bond dimension three

Abstract

We prove the statement in the title for a suitable (wavefunction-dependent) choice of the underlying orbitals and show that 3 is optimal. Thus, for two-electron systems, the quantum chemistry density matrix renormalization group (QC-DMRG) method with bond dimension 3 combined with fermionic mode optimization exactly recovers the full configuration-interaction (FCI) energy.