# QRL_graph
Reinforcement Learning for the quantum speedup in the graph
Given a graph, we try to compute the classical and quantum critical time. The definition of the criticial time is defined as the hitting time of the endpoints with the probility bigger than $p_0$.
### Install
```markdown
pip install qrl_graph==0.0.13
```
### Usage
```python
import numpy as np
from scipy.sparse.csgraph import laplacian
import networkx as nx
import matplotlib.pyplot as plt
import matplotlib
from qrl_graph.graph_env.graph import Graph
g = np.array([[0, 1, 1, 0],
[1, 0, 0, 1],
[1, 0, 0, 1],
[0, 1, 1, 0]])
g_env = Graph(g=g)
print('Laplacian matrix:\n', g_env.laplacian)
t_cl = g_env.get_classical_time(p0=0.1)
t_q = g_env.get_quantum_time(p0=0.1)
print('Classical time:', t_cl)
print('Quantum time:', t_q)
print('Speed up:', t_cl / t_q)
# uncomment to show the graph
# g_env.show_graph()
```
The results are
```markdown
Laplacian matrix:
[[ 2 -1 -1 0]
[-1 2 0 -1]
[-1 0 2 -1]
[ 0 -1 -1 2]]
Classical time: 0.25000000000000006
Quantum time: 0.6000000000000003
Speed up: 0.4166666666666665
```
##### Linear chain
```python
from qrl_graph.graph_env.graph import Graph
from qrl_graph.utils import construct_linear_graph
N = 40
g = construct_linear_graph(N)
g_env = Graph(g=g)
# print('Laplacian matrix:\n', g_env.laplacian)
p0 = 1.0/(2*N)
t_cl = g_env.get_classical_time(p0=p0)
t_q = g_env.get_quantum_time(p0=p0)
print('Linear chain, N =', N)
print('Classical time:', t_cl)
print('Quantum time:', t_q)
print('Speed up:', t_cl / t_q)
```
#### glued tree
```python
from qrl_graph.graph_env.graph import Graph
from qrl_graph.utils import construct_glued_tree_graph
# this is the height of binary tree, and total height of the glued tree is 2*height
h = 3
g = construct_glued_tree_graph(h)
N = g.shape[0]
g_env = Graph(g=g)
# print('Laplacian matrix:\n', g_env.laplacian)
p0 = 1.0/(2*N)
t_cl = g_env.get_classical_time(p0=p0)
t_q = g_env.get_quantum_time(p0=p0)
print('Glued tree, N =', N)
print('Classical time:', t_cl)
print('Quantum time:', t_q)
print('Speed up:', t_cl / t_q)
```
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"description": "# QRL_graph\nReinforcement Learning for the quantum speedup in the graph\n\nGiven a graph, we try to compute the classical and quantum critical time. The definition of the criticial time is defined as the hitting time of the endpoints with the probility bigger than $p_0$. \n\n### Install\n\n```markdown\npip install qrl_graph==0.0.13\n```\n\n\n### Usage\n\n```python\nimport numpy as np\nfrom scipy.sparse.csgraph import laplacian\nimport networkx as nx\nimport matplotlib.pyplot as plt\nimport matplotlib \nfrom qrl_graph.graph_env.graph import Graph\n\ng = np.array([[0, 1, 1, 0],\n [1, 0, 0, 1],\n [1, 0, 0, 1],\n [0, 1, 1, 0]])\n\ng_env = Graph(g=g)\nprint('Laplacian matrix:\\n', g_env.laplacian)\n\nt_cl = g_env.get_classical_time(p0=0.1)\nt_q = g_env.get_quantum_time(p0=0.1)\n\nprint('Classical time:', t_cl)\nprint('Quantum time:', t_q)\nprint('Speed up:', t_cl / t_q)\n\n\n# uncomment to show the graph\n# g_env.show_graph()\n```\n\n\nThe results are \n```markdown\nLaplacian matrix:\n [[ 2 -1 -1 0]\n [-1 2 0 -1]\n [-1 0 2 -1]\n [ 0 -1 -1 2]]\nClassical time: 0.25000000000000006\nQuantum time: 0.6000000000000003\nSpeed up: 0.4166666666666665\n```\n\n\n##### Linear chain \n\n```python\nfrom qrl_graph.graph_env.graph import Graph\nfrom qrl_graph.utils import construct_linear_graph\n\nN = 40\ng = construct_linear_graph(N)\n\ng_env = Graph(g=g)\n# print('Laplacian matrix:\\n', g_env.laplacian)\n\np0 = 1.0/(2*N)\nt_cl = g_env.get_classical_time(p0=p0)\nt_q = g_env.get_quantum_time(p0=p0)\n\nprint('Linear chain, N =', N)\nprint('Classical time:', t_cl)\nprint('Quantum time:', t_q)\nprint('Speed up:', t_cl / t_q)\n```\n\n\n#### glued tree\n\n```python\nfrom qrl_graph.graph_env.graph import Graph\nfrom qrl_graph.utils import construct_glued_tree_graph\n\n# this is the height of binary tree, and total height of the glued tree is 2*height\nh = 3\ng = construct_glued_tree_graph(h)\nN = g.shape[0]\n\ng_env = Graph(g=g)\n# print('Laplacian matrix:\\n', g_env.laplacian)\n\np0 = 1.0/(2*N)\nt_cl = g_env.get_classical_time(p0=p0)\nt_q = g_env.get_quantum_time(p0=p0)\n\nprint('Glued tree, N =', N)\nprint('Classical time:', t_cl)\nprint('Quantum time:', t_q)\nprint('Speed up:', t_cl / t_q)\n```\n",
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