"最后，我们读出测量结果的概率分布：$p(z)=\\left|\\left\\langle z \\mid \\vec{\\theta}^*\\right\\rangle\\right|^2$，即由量子编码还原出原先比特串的信息。某个比特串出现的概率越大，意味着其是投资组合优化问题最优解的可能性越大。"
]
...
...
@@ -225,7 +225,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.8.13 ('pq')",
"display_name": "pq-dev",
"language": "python",
"name": "python3"
},
...
...
@@ -239,12 +239,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.13"
"version": "3.8.15 (default, Nov 10 2022, 13:17:42) \n[Clang 14.0.6 ]"
"where $Z_i=I \\otimes I \\otimes \\ldots \\otimes Z \\otimes \\ldots \\otimes I$, i.e., $Z_{i}$ is the Pauli operator acting solely on the $i$-th qubit. Thus using the above mapping, we can transform the cost function $C_x$ into a Hamiltonian $H_C$ for the system of $n$ qubits, the ground state of which represents the solution of the portfolio optimization problem. In order to find the ground state, we use the idea of variational quantum algorithms. We implement a parametric quantum circuit, and use it to generate a trial state $|\\theta^* \\rangle$. We use the quantum circuit to measure the expectation value of the Hamiltonian on this state. Then, classical gradient descent algorithm is implemented to adjust the parameters of the parametric circuit, where the expectation value evolves towards the ground state energy. After some iterations, we arrive at the optimal value\n",
"Finally, we read out the probability distribution from the measurement result (i.e. decoding the quantum problem to give information about the original bit string)\n",
...
...
@@ -238,7 +238,7 @@
],
"metadata": {
"kernelspec": {
"display_name": "Python 3.8.13 ('pq')",
"display_name": "pq-dev",
"language": "python",
"name": "python3"
},
...
...
@@ -252,12 +252,12 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.13"
"version": "3.8.15 (default, Nov 10 2022, 13:17:42) \n[Clang 14.0.6 ]"
