Hi Pennlane Team,

I’m trying to solve this challenge, but facing a problem related to time variable. I’m using qml.ApproxTimeEvaluation for generating the time evolve sate and qml.math.purity to check the purity of the state. But in the main function, I’m not sure how to increase the time and get the incoherence time. Can some one help me with it? Below is my code and please provide any suggestions for improvement.

```
import json
import pennylane as qml
import pennylane.numpy as np
dev = qml.device("default.qubit", wires=5)
@qml.qnode(dev)
def evolve_state(coeffs, time):
"""
Args:
coeffs (list(float)): A list of the coupling constants g_1, g_2, g_3, and g_4
time (float): The evolution time of th system under the given Hamiltonian
Returns:
(numpy.tensor): The density matrix for the evolved state of the central spin.
"""
# We build the Hamiltonian for you
operators = [
qml.PauliZ(0) @ qml.PauliZ(1),
qml.PauliZ(0) @ qml.PauliZ(2),
qml.PauliZ(0) @ qml.PauliZ(3),
qml.PauliZ(0) @ qml.PauliZ(4),
]
hamiltonian = qml.dot(coeffs, operators)
# Put your code here #
qml.ApproxTimeEvolution(hamiltonian, time, 1)
# Return the required density matrix.
return qml.density_matrix([0])
def purity(rho):
"""
Args:
rho (array(array(complex))): An array-like object representing a density matrix
Returns:
(float): The purity of the density matrix rho
"""
# Put your code here
# Return the purity
return qml.math.purity(rho, [0])
def recoherence_time(coeffs):
"""
Args:
coeffs (list(float)): A list of the coupling constants g_1, g_2, g_3, and g_4.
Returns:
(float): The recoherence time of the central spin.
"""
# Return the recoherence time
time=0.1
while purity(evolve_state(coeffs, time))!=1:
time=time+0.15
return time
# These functions are responsible for testing the solution.
def run(test_case_input: str) -> str:
params = json.loads(test_case_input)
output = recoherence_time(params)
return str(output)
def check(solution_output: str, expected_output: str) -> None:
solution_output = json.loads(solution_output)
expected_output = json.loads(expected_output)
assert np.isclose(solution_output, expected_output, rtol=5e-2)
# These are the public test cases
test_cases = [
('[5,5,5,5]', '0.314'),
('[1.1,1.3,1,2.3]', '15.71')
]
# This will run the public test cases locally
for i, (input_, expected_output) in enumerate(test_cases):
print(f"Running test case {i} with input '{input_}'...")
try:
output = run(input_)
except Exception as exc:
print(f"Runtime Error. {exc}")
else:
if message := check(output, expected_output):
print(f"Wrong Answer. Have: '{output}'. Want: '{expected_output}'.")
else:
print("Correct!")
```