[1] Y. Wang, G. Li, and X. Wang, “Variational quantum Gibbs state preparation with a truncated Taylor series,” arXiv:2005.08797, May 2020. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)]
[1] Youle Wang, Guangxi Li, and Xin Wang. 2020. Variational quantum Gibbs state preparation with a truncated Taylor series. arXiv2005.08797. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)]
[2] M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information. Cambridge university press, 2010.
[2] Michael A Nielsen and Isaac L Chuang. 2010. Quantum computation and quantum information. Cambridge university press.
[3] Phillip Kaye, R. Laflamme, and M. Mosca, An Introduction to Quantum Computing. 2007.
[3] Phillip Kaye, Raymond Laflamme, and Michele Mosca. 2007. An Introduction to Quantum Computing.
[4] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,” Nature, vol. 549, no. 7671, pp. 195–202, Sep. 2017. [[pdf](https://arxiv.org/pdf/1611.09347)]
[4] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. 2017. Quantum machine learning. Nature 549, 7671, 195–202. [[pdf](https://arxiv.org/pdf/1611.09347)]
[5] M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum machine learning,” Contemp. Phys., vol. 56, no. 2, pp. 172–185, 2015. [[pdf](https://arxiv.org/pdf/1409.3097)]
[5] Maria Schuld, Ilya Sinayskiy, and Francesco Petruccione. 2015. An introduction to quantum machine learning. Contemp. Phys. 56, 2, 172–185. [[pdf](https://arxiv.org/pdf/1409.3097)]
[6] M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, “Parameterized quantum circuits as machine learning models,” Quantum Sci. Technol., vol. 4, no. 4, p. 043001, Nov. 2019. [[pdf](https://arxiv.org/pdf/1906.07682)]
[6] Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini. 2019. Parameterized quantum circuits as machine learning models. Quantum Sci. Technol. 4, 4, 043001. [[pdf](https://arxiv.org/pdf/1906.07682)]
"Further, each module in the QAOA circuit can be decomposed into a series of operations acting on single qubits and two qubits. In particular, the first has the decomposition of $U_c(\\gamma)=\\prod_{(i, j)}e^{-i \\gamma Z_iZ_j }$ while there is $U_x(\\beta)=\\prod_{i}e^{-i \\beta X_i}$ for the second. This is illustrated in the following figure.\n",
"Further, each module in the QAOA circuit can be decomposed into a series of operations acting on single qubits and two qubits. In particular, the first has the decomposition of $U_c(\\gamma)=\\prod_{(i, j)}e^{-i \\gamma Z_i\\otimes Z_j }$ while there is $U_x(\\beta)=\\prod_{i}e^{-i \\beta X_i}$ for the second. This is illustrated in the following figure.\n",
"我们现在已经完成了量子神经网络的训练,得到的基态能量的估计值大致为-1.136 Ha (注: Ha为[哈特里能量](https://baike.baidu.com/item/%E5%93%88%E7%89%B9%E9%87%8C%E8%83%BD%E9%87%8F/13777793?fr=aladdin),是原子单位制中的能量单位),我们将通过与理论值的对比来测试效果。\n",