Add symmetric depol (#3361)

For issue #3220

cirq/ops/common_channels.py

@@ -14,6 +14,7 @@
 
 """Quantum channels that are commonly used in the literature."""
 
+import itertools
 from typing import (Any, Dict, Iterable, Optional, Sequence, Tuple, Union,
                     TYPE_CHECKING)
 
@@ -77,8 +78,13 @@ def __init__(self,
                     raise ValueError(f"{k} must have {num_qubits} Pauli gates.")
             for k, v in error_probabilities.items():
                 value.validate_probability(v, f"p({k})")
-            value.validate_probability(sum(error_probabilities.values()),
-                                       'sum(error_probabilities)')
+            sum_probs = sum(error_probabilities.values())
+            # TODO(tonybruguier): Instead of forcing the probabilities to add up
+            # to 1, check whether the identity is missing, and if that is the
+            # case, automatically add it with the missing probability mass.
+            if abs(sum_probs - 1.0) > 1e-6:
+                raise ValueError(
+                    f"Probabilities do not add up to 1 but to {sum_probs}")
             self._num_qubits = num_qubits
             self._error_probabilities = error_probabilities
         else:
@@ -227,33 +233,53 @@ def asymmetric_depolarize(p_x: Optional[float] = None,
 class DepolarizingChannel(gate_features.SingleQubitGate):
     """A channel that depolarizes a qubit."""
 
-    def __init__(self, p: float) -> None:
+    def __init__(self, p: float, n_qubits: int = 1) -> None:
         r"""The symmetric depolarizing channel.
 
-        This channel applies one of four disjoint possibilities: nothing (the
-        identity channel) or one of the three pauli gates. The disjoint
-        probabilities of the three gates are all the same, p / 3, and the
-        identity is done with probability 1 - p. The supplied probability
-        must be a valid probability or else this constructor will raise a
-        ValueError.
+        This channel applies one of 4**n disjoint possibilities: nothing (the
+        identity channel) or one of the 4**n - 1 pauli gates. The disjoint
+        probabilities of the non-identity Pauli gates are all the same,
+        p / (4**n - 1), and the identity is done with probability 1 - p. The
+        supplied probability must be a valid probability or else this
+        constructor will raise a ValueError.
+
 
         This channel evolves a density matrix via
 
             $$
             \rho \rightarrow (1 - p) \rho
-                    + (p / 3) X \rho X + (p / 3) Y \rho Y + (p / 3) Z \rho Z
+                + 1 / (4**n - 1) \sum _i P_i X P_i
             $$
 
+            where P_i are the 4**n - 1 Pauli gates (excluding the identity).
+
         Args:
             p: The probability that one of the Pauli gates is applied. Each of
-                the Pauli gates is applied independently with probability p / 3.
+                the Pauli gates is applied independently with probability
+                p / (4**n - 1).
+            n_qubits: the number of qubits.
 
         Raises:
             ValueError: if p is not a valid probability.
         """
 
+        error_probabilities = {}
+
+        p_depol = p / (4**n_qubits - 1)
+        p_identity = 1.0 - p
+        for pauli_tuple in itertools.product(['I', 'X', 'Y', 'Z'],
+                                             repeat=n_qubits):
+            pauli_string = ''.join(pauli_tuple)
+            if pauli_string == 'I' * n_qubits:
+                error_probabilities[pauli_string] = p_identity
+            else:
+                error_probabilities[pauli_string] = p_depol
+
         self._p = p
-        self._delegate = AsymmetricDepolarizingChannel(p / 3, p / 3, p / 3)
+        self._n_qubits = n_qubits
+
+        self._delegate = AsymmetricDepolarizingChannel(
+            error_probabilities=error_probabilities)
 
     def _mixture_(self) -> Sequence[Tuple[float, np.ndarray]]:
         return self._delegate._mixture_()
@@ -265,55 +291,70 @@ def _value_equality_values_(self):
         return self._p
 
     def __repr__(self) -> str:
-        return 'cirq.depolarize(p={!r})'.format(self._p)
+        if self._n_qubits == 1:
+            return f"cirq.depolarize(p={self._p})"
+        return f"cirq.depolarize(p={self._p},n_qubits={self._n_qubits})"
 
     def __str__(self) -> str:
-        return 'depolarize(p={!r})'.format(self._p)
+        if self._n_qubits == 1:
+            return f"depolarize(p={self._p})"
+        return f"depolarize(p={self._p},n_qubits={self._n_qubits})"
 
     def _circuit_diagram_info_(self,
                                args: 'protocols.CircuitDiagramInfoArgs') -> str:
         if args.precision is not None:
-            f = '{:.' + str(args.precision) + 'g}'
-            return 'D({})'.format(f).format(self._p)
-        return 'D({!r})'.format(self._p)
+            return f"D({self._p:.{args.precision}g})"
+        return f"D({self._p})"
 
     @property
     def p(self) -> float:
         """The probability that one of the Pauli gates is applied.
 
-        Each of the Pauli gates is applied independently with probability p / 3.
+        Each of the Pauli gates is applied independently with probability
+        p / (4**n_qubits - 1).
         """
         return self._p
 
+    @property
+    def n_qubits(self) -> int:
+        """The number of qubits"""
+        return self._n_qubits
+
     def _json_dict_(self) -> Dict[str, Any]:
-        return protocols.obj_to_dict_helper(self, ['p'])
+        if self._n_qubits == 1:
+            return protocols.obj_to_dict_helper(self, ['p'])
+        return protocols.obj_to_dict_helper(self, ['p', 'n_qubits'])
 
 
-def depolarize(p: float) -> DepolarizingChannel:
+def depolarize(p: float, n_qubits: int = 1) -> DepolarizingChannel:
     r"""Returns a DepolarizingChannel with given probability of error.
 
-    This channel applies one of four disjoint possibilities: nothing (the
-    identity channel) or one of the three pauli gates. The disjoint
-    probabilities of the three gates are all the same, p / 3, and the
-    identity is done with probability 1 - p. The supplied probability
-    must be a valid probability or else this constructor will raise a
-    ValueError.
+    This channel applies one of 4**n disjoint possibilities: nothing (the
+    identity channel) or one of the 4**n - 1 pauli gates. The disjoint
+    probabilities of the non-identity Pauli gates are all the same,
+    p / (4**n - 1), and the identity is done with probability 1 - p. The
+    supplied probability must be a valid probability or else this constructor
+    will raise a ValueError.
 
     This channel evolves a density matrix via
 
         $$
         \rho \rightarrow (1 - p) \rho
-                + (p / 3) X \rho X + (p / 3) Y \rho Y + (p / 3) Z \rho Z
+            + 1 / (4**n - 1) \sum _i P_i X P_i
         $$
 
+        where P_i are the 4**n - 1 Pauli gates (excluding the identity).
+
     Args:
         p: The probability that one of the Pauli gates is applied. Each of
-            the Pauli gates is applied independently with probability p / 3.
+            the Pauli gates is applied independently with probability
+            p / (4**n - 1).
+        n_qubits: The number of qubits.
 
     Raises:
         ValueError: if p is not a valid probability.
     """
-    return DepolarizingChannel(p)
+    return DepolarizingChannel(p, n_qubits)
 
 
 @value.value_equality

cirq/ops/common_channels_test.py

@@ -131,31 +131,77 @@ def test_asymmetric_depolarizing_channel_text_diagram():
 
 def test_depolarizing_channel():
     d = cirq.depolarize(0.3)
-    np.testing.assert_almost_equal(cirq.channel(d),
-                                   (np.sqrt(0.7) * np.eye(2),
-                                    np.sqrt(0.1) * X,
-                                    np.sqrt(0.1) * Y,
-                                    np.sqrt(0.1) * Z))
+    np.testing.assert_almost_equal(cirq.channel(d), (
+        np.sqrt(0.7) * np.eye(2),
+        np.sqrt(0.1) * X,
+        np.sqrt(0.1) * Y,
+        np.sqrt(0.1) * Z,
+    ))
+    assert cirq.has_channel(d)
+
+
+def test_depolarizing_channel_two_qubits():
+    d = cirq.depolarize(0.15, n_qubits=2)
+    np.testing.assert_almost_equal(cirq.channel(d), (
+        np.sqrt(0.85) * np.eye(4),
+        np.sqrt(0.01) * np.kron(np.eye(2), X),
+        np.sqrt(0.01) * np.kron(np.eye(2), Y),
+        np.sqrt(0.01) * np.kron(np.eye(2), Z),
+        np.sqrt(0.01) * np.kron(X, np.eye(2)),
+        np.sqrt(0.01) * np.kron(X, X),
+        np.sqrt(0.01) * np.kron(X, Y),
+        np.sqrt(0.01) * np.kron(X, Z),
+        np.sqrt(0.01) * np.kron(Y, np.eye(2)),
+        np.sqrt(0.01) * np.kron(Y, X),
+        np.sqrt(0.01) * np.kron(Y, Y),
+        np.sqrt(0.01) * np.kron(Y, Z),
+        np.sqrt(0.01) * np.kron(Z, np.eye(2)),
+        np.sqrt(0.01) * np.kron(Z, X),
+        np.sqrt(0.01) * np.kron(Z, Y),
+        np.sqrt(0.01) * np.kron(Z, Z),
+    ))
     assert cirq.has_channel(d)
 
 def test_depolarizing_mixture():
     d = cirq.depolarize(0.3)
     assert_mixtures_equal(cirq.mixture(d),
-                          ((0.7, np.eye(2)),
-                           (0.1, X),
-                           (0.1, Y),
-                           (0.1, Z)))
+                          ((0.7, np.eye(2)), (0.1, X), (0.1, Y), (0.1, Z)))
+    assert cirq.has_mixture(d)
+
+
+def test_depolarizing_mixture_two_qubits():
+    d = cirq.depolarize(0.15, n_qubits=2)
+    assert_mixtures_equal(cirq.mixture(d),
+                          ((0.85, np.eye(4)), (0.01, np.kron(np.eye(2), X)),
+                           (0.01, np.kron(np.eye(2), Y)),
+                           (0.01, np.kron(np.eye(2), Z)),
+                           (0.01, np.kron(X, np.eye(2))), (0.01, np.kron(X, X)),
+                           (0.01, np.kron(X, Y)), (0.01, np.kron(X, Z)),
+                           (0.01, np.kron(Y, np.eye(2))), (0.01, np.kron(Y, X)),
+                           (0.01, np.kron(Y, Y)), (0.01, np.kron(Y, Z)),
+                           (0.01, np.kron(Z, np.eye(2))), (0.01, np.kron(Z, X)),
+                           (0.01, np.kron(Z, Y)), (0.01, np.kron(Z, Z))))
     assert cirq.has_mixture(d)
 
 
 def test_depolarizing_channel_repr():
     cirq.testing.assert_equivalent_repr(cirq.DepolarizingChannel(0.3))
 
 
+def test_depolarizing_channel_repr_two_qubits():
+    cirq.testing.assert_equivalent_repr(
+        cirq.DepolarizingChannel(0.3, n_qubits=2))
+
+
 def test_depolarizing_channel_str():
     assert str(cirq.depolarize(0.3)) == 'depolarize(p=0.3)'
 
 
+def test_depolarizing_channel_str_two_qubits():
+    assert str(cirq.depolarize(0.3,
+                               n_qubits=2)) == 'depolarize(p=0.3,n_qubits=2)'
+
+
 def test_depolarizing_channel_eq():
     et = cirq.testing.EqualsTester()
     c = cirq.depolarize(0.0)
@@ -166,9 +212,9 @@ def test_depolarizing_channel_eq():
 
 
 def test_depolarizing_channel_invalid_probability():
-    with pytest.raises(ValueError, match='was less than 0'):
+    with pytest.raises(ValueError, match=re.escape('p(I) was greater than 1.')):
         cirq.depolarize(-0.1)
-    with pytest.raises(ValueError, match='was greater than 1'):
+    with pytest.raises(ValueError, match=re.escape('p(I) was less than 0.')):
         cirq.depolarize(1.1)
 
 
@@ -180,6 +226,22 @@ def test_depolarizing_channel_text_diagram():
     assert (cirq.circuit_diagram_info(
         d, args=round_to_2_prec) == cirq.CircuitDiagramInfo(
             wire_symbols=('D(0.12)',)))
+    assert (cirq.circuit_diagram_info(
+        d, args=no_precision) == cirq.CircuitDiagramInfo(
+            wire_symbols=('D(0.1234567)',)))
+
+
+def test_depolarizing_channel_text_diagram_two_qubits():
+    d = cirq.depolarize(0.1234567, n_qubits=2)
+    assert (cirq.circuit_diagram_info(
+        d, args=round_to_6_prec) == cirq.CircuitDiagramInfo(
+            wire_symbols=('D(0.123457)',)))
+    assert (cirq.circuit_diagram_info(
+        d, args=round_to_2_prec) == cirq.CircuitDiagramInfo(
+            wire_symbols=('D(0.12)',)))
+    assert (cirq.circuit_diagram_info(
+        d, args=no_precision) == cirq.CircuitDiagramInfo(
+            wire_symbols=('D(0.1234567)',)))
 
 
 def test_generalized_amplitude_damping_channel():
@@ -539,9 +601,8 @@ def test_bad_error_probabilities_gate():
 def test_bad_probs():
     with pytest.raises(ValueError, match=re.escape('p(X) was greater than 1.')):
         cirq.asymmetric_depolarize(error_probabilities={'X': 1.1, 'Y': -0.1})
-    with pytest.raises(
-            ValueError,
-            match=re.escape('sum(error_probabilities) was greater than 1.')):
+    with pytest.raises(ValueError,
+                       match=re.escape('Probabilities do not add up to 1')):
         cirq.asymmetric_depolarize(error_probabilities={'X': 0.7, 'Y': 0.6})
 
 

cirq/protocols/json_test_data/MultiDepolarizingChannel.json

@@ -0,0 +1,5 @@
+{
+  "cirq_type": "DepolarizingChannel",
+  "p": 0.5,
+  "n_qubits": 2
+}

cirq/protocols/json_test_data/MultiDepolarizingChannel.repr

@@ -0,0 +1 @@
+cirq.depolarize(p=0.5,n_qubits=2)