Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

Understand

We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green's functions directly in frequency domain.

• The algorithms are based on the linear combination of unitary (LCU) operations and essentially only use quantum resources.
• To prepare the ground state, we construct the operator ${\exp}(-\tau \hat{H}^2)$ using Hubbard-Stratonovich transformation by LCU and apply it on an easy-to-prepare initial state.
• Our projective state preparation procedure saturates the near-optimal scaling, $\mathcal{O}(\frac{1}{\gamma\Delta} \log \frac{1}{\gamma\eta})$, of other currently known algorithms, in terms of the spectral-gap lower bound $\Delta$, the additive error $\eta$ in the state vector, and the overlap lower bound $\gamma$ between the initial state and the exact ground state.