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.
Sci Rep. 2011;1:88. doi: 10.1038/srep00088. Epub 2011 Sep 9.
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.
量子基态问题是一般多体哈密顿量的计算难题；目前还没有已知的经典或量子算法能够有效地解决它们。然而，如果有一个近似基态的试探波函数，就像物理和化学中的许多问题经常发生的那样，量子计算机可以利用这个试探波函数通过相位估计算法（PEA）来投影基态。我们通过使用 NMR 量子模拟器来实现这个想法，实现了一种变分波函数方法来解决海森堡自旋模型的基态问题。我们的迭代相位估计过程对本征能（到小数点后 10⁻⁵ 位）具有很高的精度。基态保真度被提炼到超过 80%，并且在临界场附近可靠地捕获了单态到三重态的转换。这一结果表明，量子模拟器可以比经典计算机更好地利用经典试探波函数。
