import json
import pennylane as qml
import pennylane.numpy as np
def hydrogen_hamiltonian(coordinates):
"""Calculates the qubit Hamiltonian of the hydrogen molecule.
Args:
coordinates (list(float)): Cartesian coordinates of each hydrogen molecule.
Returns:
(qml.Hamiltonian): A PennyLane Hamiltonian.
"""
molecule = qml.qchem.Molecule(["H", "H"], coordinates)
return qml.qchem.molecular_hamiltonian(
molecule
)[0]
def hf(num_qubits):
"""Calculates the Hartree-Fock state of the hydrogen molecule.
Args:
num_qubits (int): The number of qubits needed to represent the hydrogen molecule Hamiltonian.
Returns:
(numpy.tensor): The HF state.
"""
# Put your solution here #
return
def run_VQE(coordinates):
"""Performs a VQE routine for the given hydrogen molecule.
Args:
coordinates (list(float)): Cartesian coordinates of each hydrogen molecule.
Returns:
(float): The expectation value of the hydrogen Hamiltonian.
"""
hamiltonian = hydrogen_hamiltonian(np.array(coordinates))
num_qubits = len(hamiltonian.wires)
hf_state = hf(num_qubits)
# singles and doubles are used to make the AllSinglesDoubles template
singles, doubles = qml.qchem.excitations(2, num_qubits)
dev = qml.device("default.qubit", wires=num_qubits)
@qml.qnode(dev)
def cost(weights):
"""A circuit with tunable parameters/weights that measures the expectation value of the hydrogen Hamiltonian.
Args:
weights (numpy.array): An array of tunable parameters.
Returns:
(float): The expectation value of the hydrogen Hamiltonian.
"""
# Put your solution here #
return
np.random.seed(1234)
weights = np.random.normal(
0, np.pi, len(singles) + len(doubles), requires_grad=True
)
opt = qml.AdamOptimizer(0.5)
for _ in range(200):
weights = opt.step(cost, weights)
return cost(weights)
# These functions are responsible for testing the solution.
def run(test_case_input: str) -> str:
coordinates = json.loads(test_case_input)
energy = run_VQE(coordinates)
return str(energy)
def check(solution_output: str, expected_output: str) -> None:
solution_output = json.loads(solution_output)
expected_output = json.loads(expected_output)
assert np.allclose(solution_output, expected_output, rtol=1e-3)
# These are the public test cases
test_cases = [
('[0.0, 0.0, -0.8, 0.0, 0.0, 0.8]', '-1.1288156435018968'),
('[0.0, 0.0, -0.45, 0.0, 0.0, 0.45]', '-1.0310430254415315')
]
# 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!")