Near-optimal ground state preparation

Lin Lin; Yu Tong

doi:10.22331/q-2020-12-14-372

Near-optimal ground state preparation

Lin Lin^1,2 and Yu Tong¹

¹Department of Mathematics, University of California, Berkeley, CA 94720, USA
²Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Published:	2020-12-14, volume 4, page 372
Eprint:	arXiv:2002.12508v3
Doi:	https://doi.org/10.22331/q-2020-12-14-372
Citation:	Quantum 4, 372 (2020).

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Abstract

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below. With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error. When such an upper bound is not known, we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to the current state-of-the-art algorithm proposed in [Ge et al. 2019]. These two algorithms can then be combined to prepare a ground state without knowing an upper bound of the ground energy. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem.

► BibTeX data

@article{Lin2020nearoptimalground,
  doi = {10.22331/q-2020-12-14-372},
  url = {https://doi.org/10.22331/q-2020-12-14-372},
  title = {Near-optimal ground state preparation},
  author = {Lin, Lin and Tong, Yu},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {372},
  month = dec,
  year = {2020}
}

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