diff --git a/README.md b/README.md
index 8e9389d..d83d17b 100644
--- a/README.md
+++ b/README.md
@@ -15,7 +15,7 @@ pure Python while browsing short descriptions of famous conjectures.
 ## Features
 
 - **State-vector simulator** implemented in [`quantum_simulator.py`](quantum_simulator.py)
-  with Hadamard, Pauli-X and controlled-NOT gates, custom unitaries and
+  with Hadamard, Pauli-X/Y/Z and controlled-NOT gates, custom unitaries and
   measurement utilities.
 - **Problem compendium** in [`problems.md`](problems.md) covering ten influential
   open problems such as the Riemann Hypothesis, P vs NP and the Navier–Stokes
diff --git a/quantum_simulator.py b/quantum_simulator.py
index 25ef6a0..705eba8 100644
--- a/quantum_simulator.py
+++ b/quantum_simulator.py
@@ -112,6 +112,25 @@ def pauli_x(self, qubit: int) -> None:
 
         self._apply_unitary(_X, (qubit,))
 
+    def pauli_y(self, qubit: int) -> None:
+        """Apply the Pauli-Y gate to ``qubit``.
+
+        The Pauli-Y gate flips the state of a single qubit while also applying a
+        relative phase factor of ``i``.  When acting on ``|0⟩`` the outcome is
+        ``i|1⟩`` and when acting on ``|1⟩`` the outcome is ``-i|0⟩``.
+        """
+
+        self._apply_unitary(_Y, (qubit,))
+
+    def pauli_z(self, qubit: int) -> None:
+        """Apply the Pauli-Z gate to ``qubit``.
+
+        The Pauli-Z gate leaves ``|0⟩`` unchanged and flips the phase of ``|1⟩``
+        by multiplying it with ``-1``.
+        """
+
+        self._apply_unitary(_Z, (qubit,))
+
     def cnot(self, control: int, target: int) -> None:
         """Apply a controlled-NOT operation.
 
@@ -279,6 +298,8 @@ def _distribution_from_probabilities(probabilities: np.ndarray, num_qubits: int)
 
 _H = np.array([[1, 1], [1, -1]], dtype=np.complex128) / np.sqrt(2)
 _X = np.array([[0, 1], [1, 0]], dtype=np.complex128)
+_Y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128)
+_Z = np.array([[1, 0], [0, -1]], dtype=np.complex128)
 _CNOT = np.array(
     [
         [1, 0, 0, 0],
diff --git a/tests/test_quantum_simulator.py b/tests/test_quantum_simulator.py
index c58e759..4ff2818 100644
--- a/tests/test_quantum_simulator.py
+++ b/tests/test_quantum_simulator.py
@@ -20,6 +20,24 @@ def test_pauli_x_flips_ground_state():
     assert probs["0"] == pytest.approx(0.0)
 
 
+def test_pauli_y_flips_state_with_phase():
+    circuit = QuantumCircuit(1)
+    circuit.pauli_y(0)
+    probs = circuit.probabilities()
+    assert probs["1"] == pytest.approx(1.0)
+    assert probs["0"] == pytest.approx(0.0)
+
+
+def test_pauli_z_adds_phase_without_changing_probabilities():
+    circuit = QuantumCircuit(1)
+    circuit.hadamard(0)
+    circuit.pauli_z(0)
+    circuit.hadamard(0)
+    probs = circuit.probabilities()
+    assert probs["1"] == pytest.approx(1.0)
+    assert probs["0"] == pytest.approx(0.0)
+
+
 def test_cnot_creates_bell_state():
     circuit = QuantumCircuit(2)
     circuit.hadamard(0)