# Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

 Title: Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance Author: Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei; Lu, Dawei; Whitfield, James D.; Peng, Xinhua; Aspuru-Guzik, Alán; Du, Jiangfeng Note: Order does not necessarily reflect citation order of authors. Citation: Li, Zhaokai, Man-Hong Yung, Hongwei Chen, Dawei Lu, James D. Whitfield, Xinhua Peng, Alán Aspuru-Guzik, and Jiangfeng Du. 2011. Solving quantum ground-state problems with nuclear magnetic resonance. Scientific Reports 1: 88. Full Text & Related Files: Solving_Quantum_Ground_State_Problems.pdf (2.141Mb; PDF) 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 Published Version: doi:10.1038/srep00088 Other Sources: http://arxiv.org/abs/1106.0440 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8404290

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Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University