Fix #1076: Update orbital_energies to diagonalizing_bogoliubov_transform (#1085)

For issues
[1076](#1076),
specifically:
- update call sites from `intro_workshop_exercises.ipynb` and
`intro_to_openfermion.ipynb`
- also changed `initial_state` as a [key
variable](https://github.com/quantumlib/Cirq/blob/609d93dbc51a6608a0d0c3f5d50d51325052e027/cirq-core/cirq/circuits/circuit.py#L1114)

Author: SamKChang

docs/tutorials/intro_to_openfermion.ipynb

@@ -840,7 +840,7 @@
    },
    "outputs": [],
    "source": [
-    "orbital_energies, constant = quadratic_hamiltonian.orbital_energies()\n",
+    "orbital_energies, _, constant = quadratic_hamiltonian.diagonalizing_bogoliubov_transform()\n",
     "print(orbital_energies)\n",
     "print()\n",
     "print(constant)"

docs/tutorials/intro_workshop_exercises.ipynb

@@ -902,7 +902,7 @@
     ")\n",
     "\n",
     "# Apply the circuit to the initial state\n",
-    "result = circuit.final_state_vector(initial_state)\n",
+    "result = circuit.final_state_vector(initial_state=initial_state)\n",
     "\n",
     "# Compute the fidelity with the final state from exact evolution\n",
     "fidelity = abs(np.dot(exact_state, result.conj())) ** 2\n",
@@ -2050,7 +2050,7 @@
     }
    ],
    "source": [
-    "orbital_energies, constant = quad_ham.orbital_energies()\n",
+    "orbital_energies, _, constant = quad_ham.diagonalizing_bogoliubov_transform()\n",
     "\n",
     "print(orbital_energies)\n",
     "print(constant)"
@@ -2168,7 +2168,7 @@
     "# ---------------------------------------------\n",
     "\n",
     "# Apply the circuit to the initial state\n",
-    "result = circuit.final_state_vector(initial_state)\n",
+    "result = circuit.final_state_vector(initial_state=initial_state)\n",
     "\n",
     "# Compute the fidelity with the correct final state\n",
     "fidelity = abs(np.dot(final_state, result.conj())) ** 2\n",
@@ -2209,8 +2209,7 @@
     "# You should define the `circuit` variable here\n",
     "# ---------------------------------------------\n",
     "def exponentiate_quad_ham(qubits, quad_ham):\n",
-    "    _, basis_change_matrix, _ = quad_ham.diagonalizing_bogoliubov_transform()\n",
-    "    orbital_energies, _ = quad_ham.orbital_energies()\n",
+    "    orbital_energies, basis_change_matrix, _ = quad_ham.diagonalizing_bogoliubov_transform()\n",
     "\n",
     "    yield cirq.inverse(of.bogoliubov_transform(qubits, basis_change_matrix))\n",
     "    for i in range(len(qubits)):\n",
@@ -2222,7 +2221,7 @@
     "# ---------------------------------------------\n",
     "\n",
     "# Apply the circuit to the initial state\n",
-    "result = circuit.final_state_vector(initial_state)\n",
+    "result = circuit.final_state_vector(initial_state=initial_state)\n",
     "\n",
     "# Compute the fidelity with the correct final state\n",
     "fidelity = abs(np.dot(final_state, result.conj())) ** 2\n",