Gibbs,QAOA,QAOA_en jupyter

tutorial/GIBBS.ipynb

@@ -178,7 +178,7 @@
     "- 具体的我们参考的是[4]中的方法（核心思想是利用吉布斯态达到了最小自由能的性质）。\n",
     "- 通过作用量子神经网络$U(\\theta)$在初始态上，我们可以得到输出态$\\left| {\\psi \\left( {\\bf{\\theta }} \\right)} \\right\\rangle $, 其在第2-4个量子位的态记为$\\rho_B(\\theta)$.\n",
     "- 设置训练模型中的的损失函数，在吉布斯态学习中，我们利用冯诺依曼熵函数的截断来进行自由能的估计，相应的损失函数参考[4]可以设为 \n",
-    "$loss= {L_1} + {L_2} + {L_3}$，其中 ${L_1}= tr(H\\rho_B)$, ${L_2} = 2{\\beta^{-1}}{Tr}(\\rho_B^2)$ , $L_3 = - {\\beta ^{ - 1}}\\frac{{Tr(\\rho_B^3) + 3}}{2}$."
+    "$loss= {L_1} + {L_2} + {L_3}$，其中 ${L_1}= tr(H\\rho_B)$, ${L_2} = 2{\\beta^{-1}}{tr}(\\rho_B^2)$ , $L_3 = - {\\beta ^{ - 1}}\\frac{{tr(\\rho_B^3) + 3}}{2}$."
    ]
   },
   {

tutorial/QAOA.ipynb

@@ -57,7 +57,7 @@
     "量子近似优化算法（QAOA，Quantum Approximate Optimization Algorithm）是可以在近期有噪中等规模（NISQ，Noisy Intermediate-Scale Quantum）量子计算机上运行且具有广泛应用前景的量子算法。例如，QAOA 可以用来处理压缩图信号和二次优化等领域常见的离散组合优化问题。这类优化问题通常可以归结为下面的数学模型：\n",
     "\n",
     "\n",
-    " $$F=\\max_{z_i\\in\\{-1,1\\}} \\sum_{（i,j）} q_{ij}(1-z_iz_j)=-\\min_{z_i\\in\\{-1,1\\}} \\sum_{（i,j）} q_{ij}z_iz_j+ \\sum_{（i,j）}q_{ij}. $$\n",
+    " $$F=\\max_{z_i\\in\\{-1,1\\}} \\sum q_{ij}(1-z_iz_j)=-\\min_{z_i\\in\\{-1,1\\}} \\sum q_{ij}z_iz_j+ \\sum q_{ij}. $$\n",
     "\n",
     "\n",
     "其中, $z_i \\in \\{-1 ,1\\} $ 是待求的二元参数，系数 $q_{ij}$ 是 $z_i z_j$ 的权重 (weight)。一般地，精确求解该问题对于经典计算机是 NP-hard 的，而 QAOA 被认为对近似求解这类困难问题具有潜在速度优势。\n",
@@ -772,7 +772,7 @@
    "source": [
     "# 参考文献\n",
     "\n",
-    "[1] Farhi, E., Goldstone, J., & Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv:1411.4028."
+    "[1] E. Farhi, J. Goldstone, and S. Gutman. 2014. A quantum approximate optimization algorithm. arXiv:1411.4028 "
    ]
   }
  ],

tutorial/QAOA_En.ipynb

@@ -49,7 +49,7 @@
     "\n",
     "QAOA is one of quantum algorithms which can be implemented on near-term quantum processors, also called as noisy intermediate-scale quantum (NISQ) processors, and may have wide applications in solving hard computational problems.  For example, it could be applied to tackle a large family of optimization problems, named as the quadratic unconstrained binary optimization (QUBO) which is ubiquitous in the computer science and operation research. Basically, this class can be modeled with the form of\n",
     "\n",
-    "$$F=\\max_{z_i\\in\\{-1,1\\}} \\sum_{（i,j）} q_{ij}(1-z_iz_j)=-\\min_{z_i\\in\\{-1,1\\}} \\sum_{（i,j）} q_{ij}z_iz_j+ \\sum_{（i,j）}q_{ij} $$\n",
+    "$$F=\\max_{z_i\\in\\{-1,1\\}} \\sum q_{ij}(1-z_iz_j)=-\\min_{z_i\\in\\{-1,1\\}} \\sum q_{ij}z_iz_j+ \\sum q_{ij} $$\n",
     "\n",
     "\n",
     "where $z_i$s are  binary parameters and coefficients $q_{ij}$ refer to the weight associated to $x_i x_j$. Indeed, it is usually extremely difficult for classical computers to give the exact optimal solution, while QAOA provides an alternative approach which may have a speedup advantage over classical ones to solve these hard problems.\n",
@@ -758,7 +758,7 @@
    "source": [
     "# References\n",
     "\n",
-    "[1] Farhi, E., Goldstone, J., & Gutmann, S. (2014). A quantum approximate optimization algorithm. arXiv:1411.4028."
+    "[1] E. Farhi, J. Goldstone, and S. Gutman. 2014. A quantum approximate optimization algorithm. arXiv:1411.4028 "
    ]
   }
  ],

tutorial/VQE.ipynb

@@ -38,7 +38,7 @@
    "metadata": {},
    "source": [
     "## 背景\n",
-    "- 量子计算中在近期非常有前途的一个量子算法是变分量子特征求解器(VQE, variational quantum eigensolver (VQE)) [1-3].\n",
+    "- 量子计算中在近期非常有前途的一个量子算法是变分量子特征求解器(VQE, variational quantum eigensolver) [1-3].\n",
     "- VQE是量子化学在近期有噪量子设备（NISQ device）上的核心应用之一。其核心是去求解一个物理系统的哈密顿量的基态及其对应的能量。数学上，可以理解为求解一个厄米矩阵(Hermitian matrix)的最小特征值及其对应的特征向量。\n",
     "- 接下来我们将通过一个简单的例子学习如何通过训练量子神经网络解决这个问题，我们的目标是通过训练量子神经网络去找到量子态 $\\left| \\phi  \\right\\rangle $ (可以理解为一个归一化的复数向量), 使得 $$\\left\\langle \\phi  \\right|H\\left| \\phi  \\right\\rangle =\\lambda_{\\min}(H)$$, 其中$\\left\\langle \\phi  \\right|$是$\\left| \\phi  \\right\\rangle$的共轭转置，$\\lambda_{\\min}(H)$是矩阵$H$的最小特征值。\n",
     "\n",