Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term computers. It based McLachlan's principle applied to wave functions. The parameters evolve deterministically according equations motions minimize the difference exact evolution, which quantified by McLachlan distance. Rather than working with a fixed ansatz, where distance constrained quality AVQITE method iteratively expands ansatz along dynamical path keep below chosen threshold. This ensures state able follow in system Hilbert space rather restricted manifold set predefined ansatz. used prepare H4, H2O, and BeH2 molecules, it compact ansätze energies within chemical accuracy. Polynomial scaling circuit depth size shown through calculations spin models. Finally, Lanczos are demonstrated alongside without additional resource costs.