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 #

# Return the required density matrix.

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

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

# 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!")

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