title: Solving quantum ground-state problems with nuclear magnetic resonance.
abstract: Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10⁻⁵ decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers.
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, People's Republic of China.
authors.forename: Zhaokai
authors.initials: Z
authors.lastname: Li
authors.forename: Man-Hong
authors.initials: MH
authors.lastname: Yung
authors.forename: Hongwei
authors.initials: H
authors.lastname: Chen
authors.forename: Dawei
authors.initials: D
authors.lastname: Lu
authors.forename: James D
authors.initials: JD
authors.lastname: Whitfield
authors.forename: Xinhua
authors.initials: X
authors.lastname: Peng
authors.forename: Alán
authors.initials: A
authors.lastname: Aspuru-Guzik
authors.forename: Jiangfeng
authors.initials: J
authors.lastname: Du