diff --git a/examples/examples_test.py b/examples/examples_test.py
index 641c383ee51..d5918e3f021 100644
--- a/examples/examples_test.py
+++ b/examples/examples_test.py
@@ -1,6 +1,7 @@
 # pylint: disable=wrong-or-nonexistent-copyright-notice
 import itertools
 
+import networkx
 import numpy as np
 import pytest
 import matplotlib.pyplot as plt
@@ -93,7 +94,28 @@ def test_example_heatmaps():
 
 
 def test_example_runs_qaoa():
-    examples.qaoa.main(repetitions=10, maxiter=5)
+    examples.qaoa.main(repetitions=10, maxiter=5, use_boolean_hamiltonian_gate=False)
+    examples.qaoa.main(repetitions=10, maxiter=5, use_boolean_hamiltonian_gate=True)
+
+
+def test_example_qaoa_same_unitary():
+    n = 6
+    p = 2
+
+    qubits = cirq.LineQubit.range(n)
+
+    graph = networkx.random_regular_graph(3, n)
+
+    betas = np.random.uniform(-np.pi, np.pi, size=p)
+    gammas = np.random.uniform(-np.pi, np.pi, size=p)
+    circuits = [
+        examples.qaoa.qaoa_max_cut_circuit(
+            qubits, betas, gammas, graph, use_boolean_hamiltonian_gate
+        )
+        for use_boolean_hamiltonian_gate in [True, False]
+    ]
+
+    assert cirq.allclose_up_to_global_phase(cirq.unitary(circuits[0]), cirq.unitary(circuits[1]))
 
 
 def test_example_runs_quantum_teleportation():
diff --git a/examples/qaoa.py b/examples/qaoa.py
index 8bf5b1ee38d..47a4df06aa3 100644
--- a/examples/qaoa.py
+++ b/examples/qaoa.py
@@ -58,7 +58,7 @@
 import cirq
 
 
-def main(repetitions=1000, maxiter=50):
+def main(repetitions=10, maxiter=50, use_boolean_hamiltonian_gate=False):
     # Set problem parameters
     n = 6
     p = 2
@@ -72,7 +72,7 @@ def main(repetitions=1000, maxiter=50):
     # Print an example circuit
     betas = np.random.uniform(-np.pi, np.pi, size=p)
     gammas = np.random.uniform(-np.pi, np.pi, size=p)
-    circuit = qaoa_max_cut_circuit(qubits, betas, gammas, graph)
+    circuit = qaoa_max_cut_circuit(qubits, betas, gammas, graph, use_boolean_hamiltonian_gate)
     print('Example QAOA circuit:')
     print(circuit.to_text_diagram(transpose=True))
 
@@ -89,7 +89,7 @@ def f(x):
         # Create circuit
         betas = x[:p]
         gammas = x[p:]
-        circuit = qaoa_max_cut_circuit(qubits, betas, gammas, graph)
+        circuit = qaoa_max_cut_circuit(qubits, betas, gammas, graph, use_boolean_hamiltonian_gate)
         # Sample bitstrings from circuit
         result = simulator.run(circuit, repetitions=repetitions)
         bitstrings = result.measurements['m']
@@ -128,18 +128,29 @@ def rzz(rads):
     return cirq.ZZPowGate(exponent=2 * rads / np.pi, global_shift=-0.5)
 
 
-def qaoa_max_cut_unitary(qubits, betas, gammas, graph):  # Nodes should be integers
-    for beta, gamma in zip(betas, gammas):
-        yield (rzz(-0.5 * gamma).on(qubits[i], qubits[j]) for i, j in graph.edges)
-        yield cirq.rx(2 * beta).on_each(*qubits)
-
-
-def qaoa_max_cut_circuit(qubits, betas, gammas, graph):  # Nodes should be integers
+def qaoa_max_cut_unitary(
+    qubits, betas, gammas, graph, use_boolean_hamiltonian_gate
+):  # Nodes should be integers
+    if use_boolean_hamiltonian_gate:
+        booleans = [f"x{i} ^ x{j}" for i, j in sorted(graph.edges)]
+        param_names = [f"x{i}" for i in range(len(qubits))]
+        for beta, gamma in zip(betas, gammas):
+            yield cirq.BooleanHamiltonianGate(param_names, booleans, 2.0 * gamma).on(*qubits)
+            yield cirq.rx(2 * beta).on_each(*qubits)
+    else:
+        for beta, gamma in zip(betas, gammas):
+            yield (rzz(-0.5 * gamma).on(qubits[i], qubits[j]) for i, j in graph.edges)
+            yield cirq.rx(2 * beta).on_each(*qubits)
+
+
+def qaoa_max_cut_circuit(
+    qubits, betas, gammas, graph, use_boolean_hamiltonian_gate
+):  # Nodes should be integers
     return cirq.Circuit(
         # Prepare uniform superposition
         cirq.H.on_each(*qubits),
         # Apply QAOA unitary
-        qaoa_max_cut_unitary(qubits, betas, gammas, graph),
+        qaoa_max_cut_unitary(qubits, betas, gammas, graph, use_boolean_hamiltonian_gate),
         # Measure
         cirq.measure(*qubits, key='m'),
     )