Sugisaki Kenji, Nakazawa Shigeaki, Toyota Kazuo, Sato Kazunobu, Shiomi Daisuke, Takui Takeji
Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan.
Phys Chem Chem Phys. 2019 Jul 17;21(28):15356-15361. doi: 10.1039/c9cp02546d.
Quantum computers have an enormous impact on quantum chemical calculations. Approaches to calculate the energies of atoms and molecules on quantum computers by utilizing quantum phase estimation (QPE) and the variational quantum eigensolver (VQE) have been well documented, and dozens of methodological improvements to decrease computational costs and to mitigate errors have been reported until recently. However, the possible methodological implementation of observables on quantum computers such as calculating the spin quantum numbers of arbitrary wave functions, which is a crucial issue in quantum chemistry, has been discussed less. Here, we propose a quantum circuit to simulate the time evolution of wave functions under an S2 operator, exp(-iS2t)|Ψ, and integrate it into the QPE circuit enabling us to determine the spin quantum number of the arbitrary wave functions. We demonstrate that the spin quantum numbers of up to three spins can be determined by only one qubit measurement in QPE.
量子计算机对量子化学计算有着巨大的影响。利用量子相位估计（QPE）和变分量子本征求解器（VQE）在量子计算机上计算原子和分子能量的方法已有详细记载，并且直到最近还报道了许多降低计算成本和减轻误差的方法改进。然而，对于量子计算机上可观测量的可能方法实现，例如计算任意波函数的自旋量子数，这在量子化学中是一个关键问题，却较少被讨论。在这里，我们提出一个量子电路来模拟在S2算符exp(-iS2t)|Ψ下波函数的时间演化，并将其集成到QPE电路中，使我们能够确定任意波函数的自旋量子数。我们证明，在QPE中仅通过一次量子比特测量就可以确定多达三个自旋的自旋量子数。
