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Quantum Algorithms for Ground-State Preparation and Green's Function Calculation by Keen, Trevor; Dumitrescu, Eugene; Wang, Yan is a scholarly article available to read on EtoBox.

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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. It is straightforward to combine our algorithm with spectral-gap amplification technique to achieve quadratically improved scaling $\mathcal{O}(1/\sqrt{\Delta})$ for ground-state preparation of frustration-free Hamiltonians, which we demonstrate with numerical results of the $q$-deformed XXZ chain. To compute the Green's functions, including the single-particle and other r

Author

Keen, Trevor; Dumitrescu, Eugene; Wang, Yan

Published

2021

Language

EN