diff --git a/qiskit/circuit/__init__.py b/qiskit/circuit/__init__.py
index 6003ffbd20dd..f23a7dfed9b3 100644
--- a/qiskit/circuit/__init__.py
+++ b/qiskit/circuit/__init__.py
@@ -59,6 +59,7 @@
 from .classicalregister import ClassicalRegister, Clbit
 from .quantumregister import QuantumRegister, Qubit
 from .gate import Gate
+# pylint: disable=cyclic-import
 from .controlledgate import ControlledGate
 from .instruction import Instruction
 from .instructionset import InstructionSet
diff --git a/qiskit/circuit/add_control.py b/qiskit/circuit/add_control.py
index ae85a063b62e..df74771de7da 100644
--- a/qiskit/circuit/add_control.py
+++ b/qiskit/circuit/add_control.py
@@ -14,22 +14,39 @@
 """
 Add control to operation if supported.
 """
-from qiskit import QiskitError
+from typing import Union, Optional
+
+from qiskit.circuit.exceptions import CircuitError
 from qiskit.extensions import UnitaryGate
+from . import ControlledGate, Gate, QuantumRegister, QuantumCircuit
+
+
+def add_control(operation: Union[Gate, ControlledGate],
+                num_ctrl_qubits: int,
+                label: Union[str, None],
+                ctrl_state: Union[int, str, None]) -> ControlledGate:
+    """For standard gates, if the controlled version already exists in the
+    library, it will be returned (e.g. XGate.control() = CnotGate().
 
+    For more generic gates, this method implements the controlled
+    version by first decomposing into the ['u1', 'u3', 'cx'] basis, then
+    controlling each gate in the decomposition.
 
-def add_control(operation, num_ctrl_qubits, label):
-    """Add num_ctrl_qubits controls to operation
+    Open controls are implemented by conjugating the control line with
+    X gates. Adds num_ctrl_qubits controls to operation.
 
     Args:
-        operation (Gate or ControlledGate): operation to add control to.
-        num_ctrl_qubits (int): number of controls to add to gate (default=1)
-        label (str): optional gate label
+        operation: Operation for which control will be added.
+        num_ctrl_qubits: The number of controls to add to gate (default=1).
+        label: Optional gate label.
+        ctrl_state (int or str or None): The control state in decimal or as
+            a bitstring (e.g. '111'). If specified as a bitstring the length
+            must equal num_ctrl_qubits, MSB on left. If None, use
+            2**num_ctrl_qubits-1.
 
     Returns:
-        ControlledGate: controlled version of gate. This default algorithm
-            uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size
-            num_qubits + 2*num_ctrl_qubits - 1.
+        Controlled version of gate.
+
     """
     import qiskit.extensions.standard as standard
     if isinstance(operation, standard.RZGate) or operation.name == 'rz':
@@ -42,29 +59,34 @@ def add_control(operation, num_ctrl_qubits, label):
     if isinstance(operation, UnitaryGate):
         # attempt decomposition
         operation._define()
-    return control(operation, num_ctrl_qubits=num_ctrl_qubits, label=label)
+    return control(operation, num_ctrl_qubits=num_ctrl_qubits, label=label,
+                   ctrl_state=ctrl_state)
 
 
-def control(operation, num_ctrl_qubits=1, label=None):
+def control(operation: Union[Gate, ControlledGate],
+            num_ctrl_qubits: Optional[int] = 1,
+            label: Optional[Union[None, str]] = None,
+            ctrl_state: Optional[Union[None, int, str]] = None) -> ControlledGate:
     """Return controlled version of gate using controlled rotations
 
     Args:
-        operation (Gate or Controlledgate): gate to create ControlledGate from
-        num_ctrl_qubits (int): number of controls to add to gate (default=1)
-        label (str): optional gate label
+        operation: gate to create ControlledGate from
+        num_ctrl_qubits: number of controls to add to gate (default=1)
+        label: optional gate label
+        ctrl_state: The control state in decimal or as
+            a bitstring (e.g. '111'). If specified as a bitstring the length
+            must equal num_ctrl_qubits, MSB on left. If None, use
+            2**num_ctrl_qubits-1.
+
     Returns:
-        ControlledGate: controlled version of gate. This default algorithm
-            uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size
-            num_qubits + 2*num_ctrl_qubits - 1.
+        Controlled version of gate.
 
     Raises:
-        QiskitError: gate contains non-gate in definitionl
+        CircuitError: gate contains non-gate in definition
     """
     from math import pi
     # pylint: disable=cyclic-import
     import qiskit.circuit.controlledgate as controlledgate
-    from qiskit.circuit.quantumregister import QuantumRegister
-    from qiskit.circuit.quantumcircuit import QuantumCircuit
     # pylint: disable=unused-import
     import qiskit.extensions.standard.multi_control_rotation_gates
     import qiskit.extensions.standard.multi_control_toffoli_gate
@@ -73,7 +95,6 @@ def control(operation, num_ctrl_qubits=1, label=None):
     q_control = QuantumRegister(num_ctrl_qubits, name='control')
     q_target = QuantumRegister(operation.num_qubits, name='target')
     q_ancillae = None  # TODO: add
-
     qc = QuantumCircuit(q_control, q_target)
 
     if operation.name == 'x' or (
@@ -122,7 +143,7 @@ def control(operation, num_ctrl_qubits=1, label=None):
                        None,
                        mode='noancilla')
             else:
-                raise QiskitError('gate contains non-controllable instructions')
+                raise CircuitError('gate contains non-controllable instructions')
     instr = qc.to_instruction()
     if isinstance(operation, controlledgate.ControlledGate):
         new_num_ctrl_qubits = num_ctrl_qubits + operation.num_ctrl_qubits
@@ -146,20 +167,19 @@ def control(operation, num_ctrl_qubits=1, label=None):
                                           operation.params,
                                           label=label,
                                           num_ctrl_qubits=new_num_ctrl_qubits,
-                                          definition=instr.definition)
+                                          definition=instr.definition,
+                                          ctrl_state=ctrl_state)
     cgate.base_gate = base_gate
     return cgate
 
 
 def _gate_to_circuit(operation):
-    from qiskit.circuit.quantumcircuit import QuantumCircuit
-    from qiskit.circuit.quantumregister import QuantumRegister
     qr = QuantumRegister(operation.num_qubits)
     qc = QuantumCircuit(qr, name=operation.name)
     if hasattr(operation, 'definition') and operation.definition:
         for rule in operation.definition:
             if rule[0].name in {'id', 'barrier', 'measure', 'snapshot'}:
-                raise QiskitError('Cannot make controlled gate with {} instruction'.format(
+                raise CircuitError('Cannot make controlled gate with {} instruction'.format(
                     rule[0].name))
             qc.append(rule[0], qargs=[qr[bit.index] for bit in rule[1]], cargs=[])
     else:
diff --git a/qiskit/circuit/controlledgate.py b/qiskit/circuit/controlledgate.py
index 5d67261d1b6d..6f97eef1870b 100644
--- a/qiskit/circuit/controlledgate.py
+++ b/qiskit/circuit/controlledgate.py
@@ -15,17 +15,21 @@
 """
 Controlled unitary gate.
 """
-
 from qiskit.circuit.exceptions import CircuitError
 from .gate import Gate
+from . import QuantumRegister
 
 
 class ControlledGate(Gate):
     """Controlled unitary gate."""
 
     def __init__(self, name, num_qubits, params, label=None, num_ctrl_qubits=1,
-                 definition=None):
-        """Create a new gate.
+                 definition=None, ctrl_state=None):
+        """Create a controlled gate.
+
+        Attributes:
+            num_ctrl_qubits (int): The number of control qubits.
+            ctrl_state (int): The control state in decimal notation.
 
         Args:
             name (str): The Qobj name of the gate.
@@ -34,8 +38,13 @@ def __init__(self, name, num_qubits, params, label=None, num_ctrl_qubits=1,
             label (str or None): An optional label for the gate [Default: None]
             num_ctrl_qubits (int): Number of control qubits.
             definition (list): list of gate rules for implementing this gate.
+            ctrl_state (int or str or None): The control state in decimal or as
+                a bitstring (e.g. '111'). If specified as a bitstring the length
+                must equal num_ctrl_qubits, MSB on left. If None, use
+                2**num_ctrl_qubits-1.
         Raises:
             CircuitError: num_ctrl_qubits >= num_qubits
+            CircuitError: ctrl_state < 0 or ctrl_state > 2**num_ctrl_qubits.
         """
         super().__init__(name, num_qubits, params, label=label)
         if num_ctrl_qubits < num_qubits:
@@ -50,14 +59,76 @@ def __init__(self, name, num_qubits, params, label=None, num_ctrl_qubits=1,
                     self.base_gate = base_gate.base_gate
                 else:
                     self.base_gate = base_gate
+        self._ctrl_state = None
+        self.ctrl_state = ctrl_state
+
+    @property
+    def definition(self):
+        """Return definition in terms of other basic gates. If the gate has
+        open controls, as determined from `self.ctrl_state`, the returned
+        definition is conjugated with X."""
+        if not self._definition:
+            self._define()
+        # pylint: disable=cyclic-import
+        from qiskit.extensions.standard import XGate, CnotGate
+        bit_ctrl_state = bin(self.ctrl_state)[2:].zfill(self.num_ctrl_qubits)
+        # hacky way to get register assuming single register
+        if self._definition:
+            qreg = self._definition[0][1][0].register
+        elif isinstance(self, CnotGate):
+            qreg = QuantumRegister(self.num_qubits, 'q')
+            self._definition = [(self, [qreg[0], qreg[1]], [])]
+        open_rules = []
+        for qind, val in enumerate(bit_ctrl_state[::-1]):
+            if val == '0':
+                open_rules.append([XGate(), [qreg[qind]], []])
+        return open_rules + self._definition + open_rules
+
+    @definition.setter
+    def definition(self, excited_def):
+        """Set controlled gate definition with closed controls."""
+        super(Gate, self.__class__).definition.fset(self, excited_def)
+
+    @property
+    def ctrl_state(self):
+        """Return the control state of the gate as a decimal integer."""
+        return self._ctrl_state
+
+    @ctrl_state.setter
+    def ctrl_state(self, ctrl_state):
+        """Set the control state of this gate.
+
+        Args:
+            ctrl_state (int or str or None): The control state of the gate.
+
+        Raises:
+            CircuitError: ctrl_state is invalid.
+        """
+        if isinstance(ctrl_state, str):
+            try:
+                assert len(ctrl_state) == self.num_ctrl_qubits
+                ctrl_state = int(ctrl_state, 2)
+            except ValueError:
+                raise CircuitError('invalid control bit string: ' + ctrl_state)
+            except AssertionError:
+                raise CircuitError('invalid control bit string: length != '
+                                   'num_ctrl_qubits')
+        if isinstance(ctrl_state, int):
+            if 0 <= ctrl_state < 2**self.num_ctrl_qubits:
+                self._ctrl_state = ctrl_state
+            else:
+                raise CircuitError('invalid control state specification')
+        elif ctrl_state is None:
+            self._ctrl_state = 2**self.num_ctrl_qubits - 1
+        else:
+            raise CircuitError('invalid control state specification')
 
     def __eq__(self, other):
         if not isinstance(other, ControlledGate):
             return False
         else:
             return (other.num_ctrl_qubits == self.num_ctrl_qubits and
-                    self.base_gate == other.base_gate and
-                    super().__eq__(other))
+                    self.base_gate == other.base_gate)
 
     def inverse(self):
         """Invert this gate by calling inverse on the base gate."""
diff --git a/qiskit/circuit/gate.py b/qiskit/circuit/gate.py
index a8095fded48c..618435474f23 100644
--- a/qiskit/circuit/gate.py
+++ b/qiskit/circuit/gate.py
@@ -106,24 +106,24 @@ def label(self, name):
         else:
             raise TypeError('label expects a string or None')
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Return controlled version of gate
 
         Args:
             num_ctrl_qubits (int): number of controls to add to gate (default=1)
-            label (str): optional gate label
+            label (str or None): optional gate label
+            ctrl_state (int or str or None): The control state in decimal or as
+                a bitstring (e.g. '111'). If None, use 2**num_ctrl_qubits-1.
 
         Returns:
-            ControlledGate: controlled version of gate. This default algorithm
-                uses num_ctrl_qubits-1 ancillae qubits so returns a gate of size
-                num_qubits + 2*num_ctrl_qubits - 1.
+            ControlledGate: controlled version of gate.
 
         Raises:
-            QiskitError: unrecognized mode
+            QiskitError: unrecognized mode or invalid ctrl_state
         """
         # pylint: disable=cyclic-import
         from .add_control import add_control
-        return add_control(self, num_ctrl_qubits, label)
+        return add_control(self, num_ctrl_qubits, label, ctrl_state)
 
     @staticmethod
     def _broadcast_single_argument(qarg):
diff --git a/qiskit/extensions/standard/h.py b/qiskit/extensions/standard/h.py
index 002bca37b813..5e3d1629235f 100644
--- a/qiskit/extensions/standard/h.py
+++ b/qiskit/extensions/standard/h.py
@@ -46,19 +46,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CHGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CHGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/standard/rx.py b/qiskit/extensions/standard/rx.py
index c14335e654a8..49003f14c85f 100644
--- a/qiskit/extensions/standard/rx.py
+++ b/qiskit/extensions/standard/rx.py
@@ -46,19 +46,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CrxGate(self.params[0])
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CrxGate(self.params[0])
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate.
diff --git a/qiskit/extensions/standard/ry.py b/qiskit/extensions/standard/ry.py
index f9d86892e47c..071ff385a0ea 100644
--- a/qiskit/extensions/standard/ry.py
+++ b/qiskit/extensions/standard/ry.py
@@ -46,19 +46,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CryGate(self.params[0])
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CryGate(self.params[0])
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate.
diff --git a/qiskit/extensions/standard/rz.py b/qiskit/extensions/standard/rz.py
index f215c276a9a5..83571433811b 100644
--- a/qiskit/extensions/standard/rz.py
+++ b/qiskit/extensions/standard/rz.py
@@ -43,19 +43,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CrzGate(self.params[0])
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CrzGate(self.params[0])
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate.
diff --git a/qiskit/extensions/standard/swap.py b/qiskit/extensions/standard/swap.py
index 1cfce87a4840..43aee0c1c4ec 100644
--- a/qiskit/extensions/standard/swap.py
+++ b/qiskit/extensions/standard/swap.py
@@ -46,19 +46,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return FredkinGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return FredkinGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/standard/u1.py b/qiskit/extensions/standard/u1.py
index 014d24d90718..c8a506110299 100644
--- a/qiskit/extensions/standard/u1.py
+++ b/qiskit/extensions/standard/u1.py
@@ -42,19 +42,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return Cu1Gate(*self.params)
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return Cu1Gate(*self.params)
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/standard/u3.py b/qiskit/extensions/standard/u3.py
index 3a4449a69b28..832b8c04d680 100644
--- a/qiskit/extensions/standard/u3.py
+++ b/qiskit/extensions/standard/u3.py
@@ -39,19 +39,23 @@ def inverse(self):
         """
         return U3Gate(-self.params[0], -self.params[2], -self.params[1])
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return Cu3Gate(*self.params)
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return Cu3Gate(*self.params)
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def to_matrix(self):
         """Return a Numpy.array for the U3 gate."""
diff --git a/qiskit/extensions/standard/x.py b/qiskit/extensions/standard/x.py
index 93457b083fb3..83f7de4642d0 100644
--- a/qiskit/extensions/standard/x.py
+++ b/qiskit/extensions/standard/x.py
@@ -47,21 +47,25 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CnotGate()
-        elif num_ctrl_qubits == 2:
-            return ToffoliGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CnotGate()
+            elif num_ctrl_qubits == 2:
+                return ToffoliGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
@@ -114,19 +118,23 @@ def __init__(self):
         super().__init__("cx", 2, [], num_ctrl_qubits=1)
         self.base_gate = XGate()
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return ToffoliGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return ToffoliGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/standard/y.py b/qiskit/extensions/standard/y.py
index 25f85bd34586..8a66c1957808 100644
--- a/qiskit/extensions/standard/y.py
+++ b/qiskit/extensions/standard/y.py
@@ -42,19 +42,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CyGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CyGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/standard/z.py b/qiskit/extensions/standard/z.py
index 2c970b8781f5..ff1dbb3d0cde 100644
--- a/qiskit/extensions/standard/z.py
+++ b/qiskit/extensions/standard/z.py
@@ -42,19 +42,23 @@ def _define(self):
             definition.append(inst)
         self.definition = definition
 
-    def control(self, num_ctrl_qubits=1, label=None):
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
         """Controlled version of this gate.
 
         Args:
             num_ctrl_qubits (int): number of control qubits.
             label (str or None): An optional label for the gate [Default: None]
+            ctrl_state (int or str or None): control state expressed as integer,
+                string (e.g. '110'), or None. If None, use all 1s.
 
         Returns:
             ControlledGate: controlled version of this gate.
         """
-        if num_ctrl_qubits == 1:
-            return CzGate()
-        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label)
+        if ctrl_state is None:
+            if num_ctrl_qubits == 1:
+                return CzGate()
+        return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label,
+                               ctrl_state=ctrl_state)
 
     def inverse(self):
         """Invert this gate."""
diff --git a/qiskit/extensions/unitary.py b/qiskit/extensions/unitary.py
index a5247c57a6ed..c2b0c6f88586 100644
--- a/qiskit/extensions/unitary.py
+++ b/qiskit/extensions/unitary.py
@@ -22,6 +22,7 @@
 from qiskit.circuit import Gate
 from qiskit.circuit import QuantumCircuit
 from qiskit.circuit import QuantumRegister
+from qiskit.exceptions import QiskitError
 from qiskit.extensions.standard import U3Gate
 from qiskit.quantum_info.operators.predicates import matrix_equal
 from qiskit.quantum_info.operators.predicates import is_unitary_matrix
@@ -111,44 +112,24 @@ def _define(self):
             raise NotImplementedError("Not able to generate a subcircuit for "
                                       "a {}-qubit unitary".format(self.num_qubits))
 
-    def control(self, num_ctrl_qubits=1, label=None):
-        """Return controlled version of gate
+    def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
+        r"""Return controlled version of gate
 
         Args:
             num_ctrl_qubits (int): number of controls to add to gate (default=1)
             label (str): optional gate label
+            ctrl_state (int or str or None): The control state in decimal or as a
+                bit string (e.g. '1011'). If None, use 2**num_ctrl_qubits-1.
 
         Returns:
             UnitaryGate: controlled version of gate.
 
         Raises:
-            QiskitError: unrecognized mode
+            QiskitError: invalid ctrl_state
         """
-        cmat = self._compute_control_matrix(self.to_matrix(), num_ctrl_qubits)
+        cmat = _compute_control_matrix(self.to_matrix(), num_ctrl_qubits)
         return UnitaryGate(cmat, label=label)
 
-    def _compute_control_matrix(self, base_mat, num_ctrl_qubits):
-        """
-        Compute the controlled version of the input matrix with qiskit ordering.
-
-        Args:
-            base_mat (ndarray): unitary to be controlled
-            num_ctrl_qubits (int): number of controls for new unitary
-
-        Returns:
-            ndarray: controlled version of base matrix.
-        """
-        num_target = int(numpy.log2(base_mat.shape[0]))
-        ctrl_dim = 2**num_ctrl_qubits
-        ctrl_grnd = numpy.repeat([[1], [0]], [1, ctrl_dim-1])
-        full_mat_dim = ctrl_dim * base_mat.shape[0]
-        full_mat = numpy.zeros((full_mat_dim, full_mat_dim), dtype=base_mat.dtype)
-        ctrl_proj = numpy.diag(numpy.roll(ctrl_grnd, ctrl_dim - 1))
-        full_mat = (numpy.kron(numpy.eye(2**num_target),
-                               numpy.eye(ctrl_dim) - ctrl_proj)
-                    + numpy.kron(base_mat, ctrl_proj))
-        return full_mat
-
     def qasm(self):
         """ The qasm for a custom unitary gate
         This is achieved by adding a custom gate that corresponds to the definition
@@ -199,6 +180,52 @@ def qasm(self):
         return self._qasm_definition + self._qasmif(self._qasm_name)
 
 
+def _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=None):
+    r"""
+    Compute the controlled version of the input matrix with qiskit ordering.
+    This function computes the controlled unitary with :math:`n` control qubits
+    and :math:`m` target qubits,
+
+    .. math::
+
+        V_n^j(U_{2^m}) = (U_{2^m} \otimes |j\rangle\!\langle j|) +
+                         (I_{2^m} \otimes (I_{2^n} - |j\rangle\!\langle j|)).
+
+    where :math:`|j\rangle \in \mathcal{H}^{2^n}` is the control state.
+
+    Args:
+        base_mat (ndarray): unitary to be controlled
+        num_ctrl_qubits (int): number of controls for new unitary
+        ctrl_state (int or str or None): The control state in decimal or as
+            a bitstring (e.g. '111'). If None, use 2**num_ctrl_qubits-1.
+
+    Returns:
+        ndarray: controlled version of base matrix.
+
+    Raises:
+        QiskitError: unrecognized mode or invalid ctrl_state
+    """
+    num_target = int(numpy.log2(base_mat.shape[0]))
+    ctrl_dim = 2**num_ctrl_qubits
+    ctrl_grnd = numpy.repeat([[1], [0]], [1, ctrl_dim-1])
+    if ctrl_state is None:
+        ctrl_state = ctrl_dim - 1
+    elif isinstance(ctrl_state, str):
+        ctrl_state = int(ctrl_state, 2)
+    if isinstance(ctrl_state, int):
+        if not 0 <= ctrl_state < ctrl_dim:
+            raise QiskitError('Invalid control state value specified.')
+    else:
+        raise QiskitError('Invalid control state type specified.')
+    full_mat_dim = ctrl_dim * base_mat.shape[0]
+    full_mat = numpy.zeros((full_mat_dim, full_mat_dim), dtype=base_mat.dtype)
+    ctrl_proj = numpy.diag(numpy.roll(ctrl_grnd, ctrl_state))
+    full_mat = (numpy.kron(numpy.eye(2**num_target),
+                           numpy.eye(ctrl_dim) - ctrl_proj)
+                + numpy.kron(base_mat, ctrl_proj))
+    return full_mat
+
+
 def unitary(self, obj, qubits, label=None):
     """Apply u2 to q."""
     if isinstance(qubits, QuantumRegister):
diff --git a/releasenotes/notes/add-open-controls-bb21111b866ada43.yaml b/releasenotes/notes/add-open-controls-bb21111b866ada43.yaml
new file mode 100644
index 000000000000..8efb4bde8f38
--- /dev/null
+++ b/releasenotes/notes/add-open-controls-bb21111b866ada43.yaml
@@ -0,0 +1,19 @@
+---
+features:
+  - |
+    Add ability to specify control conditioned on a qubit being in the
+    ground state. The state of the control qubits is represented by a
+    decimal integer. For example:
+
+      from qiskit import QuantumCircuit
+      from qiskit.extensions.standard import XGate
+
+      qc = QuantumCircuit(4)
+      cgate = XGate().control(3, ctrl_state=6)
+      qc.append(cgate, [0, 1, 2, 3])
+
+    Creates a four qubit gate where the fourth qubit gets flipped if
+    the first qubit is in the ground state and the second and third
+    qubits are in the excited state. If ctrl_state is None, the
+    default, control is conditioned on all control qubits being
+    excited.
diff --git a/test/python/circuit/test_controlled_gate.py b/test/python/circuit/test_controlled_gate.py
index d0ad34219a07..c1bfb7d63e83 100644
--- a/test/python/circuit/test_controlled_gate.py
+++ b/test/python/circuit/test_controlled_gate.py
@@ -19,13 +19,15 @@
 from inspect import signature
 import numpy as np
 from numpy import pi
-import scipy
 from ddt import ddt, data
 
 from qiskit import QuantumRegister, QuantumCircuit, execute, BasicAer, QiskitError
 from qiskit.test import QiskitTestCase
 from qiskit.circuit import ControlledGate
+from qiskit.circuit.exceptions import CircuitError
 from qiskit.quantum_info.operators.predicates import matrix_equal, is_unitary_matrix
+from qiskit.quantum_info.random import random_unitary
+from qiskit.quantum_info.states import Statevector
 import qiskit.circuit.add_control as ac
 from qiskit.transpiler.passes import Unroller
 from qiskit.converters.circuit_to_dag import circuit_to_dag
@@ -37,7 +39,7 @@
                                         RYGate, CryGate, CrxGate, FredkinGate,
                                         U3Gate, CHGate, CrzGate, Cu3Gate,
                                         MSGate, Barrier, RCCXGate, RCCCXGate)
-from qiskit.extensions.unitary import UnitaryGate
+from qiskit.extensions.unitary import _compute_control_matrix
 import qiskit.extensions.standard as allGates
 
 
@@ -156,8 +158,8 @@ def test_single_controlled_composite_gate(self):
         num_target = cgate.width()
         gate = cgate.to_gate()
         cont_gate = gate.control(num_ctrl_qubits=num_ctrl)
-        control = QuantumRegister(num_ctrl)
-        target = QuantumRegister(num_target)
+        control = QuantumRegister(num_ctrl, 'control')
+        target = QuantumRegister(num_target, 'target')
         qc = QuantumCircuit(control, target)
         qc.append(cont_gate, control[:]+target[:])
         simulator = BasicAer.get_backend('unitary_simulator')
@@ -400,13 +402,52 @@ def test_controlled_unitary(self, num_ctrl_qubits):
     def test_controlled_random_unitary(self, num_ctrl_qubits):
         """test controlled unitary"""
         num_target = 2
-        base_gate = UnitaryGate(scipy.stats.unitary_group.rvs(num_target))
+        base_gate = random_unitary(2**num_target).to_instruction()
         base_mat = base_gate.to_matrix()
         cgate = base_gate.control(num_ctrl_qubits)
         test_op = Operator(cgate)
         cop_mat = _compute_control_matrix(base_mat, num_ctrl_qubits)
         self.assertTrue(matrix_equal(cop_mat, test_op.data, ignore_phase=True))
 
+    @data(1, 2, 3)
+    def test_open_controlled_unitary_matrix(self, num_ctrl_qubits):
+        """test open controlled unitary matrix"""
+        # verify truth table
+        num_target_qubits = 2
+        num_qubits = num_ctrl_qubits + num_target_qubits
+        target_op = Operator(XGate())
+        for i in range(num_target_qubits - 1):
+            target_op = target_op.tensor(XGate())
+        print('')
+        for i in range(2**num_qubits):
+            input_bitstring = bin(i)[2:].zfill(num_qubits)
+            input_target = input_bitstring[0:num_target_qubits]
+            input_ctrl = input_bitstring[-num_ctrl_qubits:]
+            phi = Statevector.from_label(input_bitstring)
+            cop = Operator(_compute_control_matrix(target_op.data,
+                                                   num_ctrl_qubits,
+                                                   ctrl_state=input_ctrl))
+            for j in range(2**num_qubits):
+                output_bitstring = bin(j)[2:].zfill(num_qubits)
+                output_target = output_bitstring[0:num_target_qubits]
+                output_ctrl = output_bitstring[-num_ctrl_qubits:]
+                psi = Statevector.from_label(output_bitstring)
+                cxout = np.dot(phi.data, psi.evolve(cop).data)
+                if input_ctrl == output_ctrl:
+                    # flip the target bits
+                    cond_output = ''.join([str(int(not int(a))) for a in input_target])
+                else:
+                    cond_output = input_target
+                if cxout == 1:
+                    self.assertTrue(
+                        (output_ctrl == input_ctrl) and
+                        (output_target == cond_output))
+                else:
+                    self.assertTrue((
+                        (output_ctrl == input_ctrl) and
+                        (output_target != cond_output)) or
+                                    output_ctrl != input_ctrl)
+
     def test_base_gate_setting(self):
         """
         Test all gates in standard extensions which are of type ControlledGate
@@ -516,28 +557,51 @@ def test_relative_phase_toffoli_gates(self, num_ctrl_qubits):
         # compare simulated matrix with the matrix representation provided by the class
         self.assertTrue(matrix_equal(simulated_mat, repr_mat))
 
-
-def _compute_control_matrix(base_mat, num_ctrl_qubits):
-    """
-    Compute the controlled version of the input matrix with qiskit ordering.
-
-    Args:
-        base_mat (ndarray): unitary to be controlled
-        num_ctrl_qubits (int): number of controls for new unitary
-
-    Returns:
-        ndarray: controlled version of base matrix.
-    """
-    num_target = int(np.log2(base_mat.shape[0]))
-    ctrl_dim = 2**num_ctrl_qubits
-    ctrl_grnd = np.repeat([[1], [0]], [1, ctrl_dim-1])
-    full_mat_dim = ctrl_dim * base_mat.shape[0]
-    full_mat = np.zeros((full_mat_dim, full_mat_dim), dtype=base_mat.dtype)
-    ctrl_proj = np.diag(np.roll(ctrl_grnd, ctrl_dim - 1))
-    full_mat = (np.kron(np.eye(2**num_target),
-                        np.eye(ctrl_dim) - ctrl_proj)
-                + np.kron(base_mat, ctrl_proj))
-    return full_mat
+    def test_open_controlled_gate(self):
+        """
+        Test controlled gates with control on '0'
+        """
+        base_gate = XGate()
+        base_mat = base_gate.to_matrix()
+        num_ctrl_qubits = 3
+
+        ctrl_state = 5
+        cgate = base_gate.control(num_ctrl_qubits, ctrl_state=ctrl_state)
+        target_mat = _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=ctrl_state)
+        self.assertEqual(Operator(cgate), Operator(target_mat))
+
+        ctrl_state = None
+        cgate = base_gate.control(num_ctrl_qubits, ctrl_state=ctrl_state)
+        target_mat = _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=ctrl_state)
+        self.assertEqual(Operator(cgate), Operator(target_mat))
+
+        ctrl_state = 0
+        cgate = base_gate.control(num_ctrl_qubits, ctrl_state=ctrl_state)
+        target_mat = _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=ctrl_state)
+        self.assertEqual(Operator(cgate), Operator(target_mat))
+
+        ctrl_state = 7
+        cgate = base_gate.control(num_ctrl_qubits, ctrl_state=ctrl_state)
+        target_mat = _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=ctrl_state)
+        self.assertEqual(Operator(cgate), Operator(target_mat))
+
+        ctrl_state = '110'
+        cgate = base_gate.control(num_ctrl_qubits, ctrl_state=ctrl_state)
+        target_mat = _compute_control_matrix(base_mat, num_ctrl_qubits, ctrl_state=ctrl_state)
+        self.assertEqual(Operator(cgate), Operator(target_mat))
+
+    def test_open_controlled_gate_raises(self):
+        """
+        Test controlled gates with open controls raises if ctrl_state isn't allowed.
+        """
+        base_gate = XGate()
+        num_ctrl_qubits = 3
+        with self.assertRaises(CircuitError):
+            base_gate.control(num_ctrl_qubits, ctrl_state=-1)
+        with self.assertRaises(CircuitError):
+            base_gate.control(num_ctrl_qubits, ctrl_state=2**num_ctrl_qubits)
+        with self.assertRaises(CircuitError):
+            base_gate.control(num_ctrl_qubits, ctrl_state='201')
 
 
 if __name__ == '__main__':
diff --git a/test/python/pickles/TestsBasicSwap_a_cx_to_map.pickle b/test/python/pickles/TestsBasicSwap_a_cx_to_map.pickle
index 2dc1af8cf877..bf9d7480c7c8 100644
Binary files a/test/python/pickles/TestsBasicSwap_a_cx_to_map.pickle and b/test/python/pickles/TestsBasicSwap_a_cx_to_map.pickle differ
diff --git a/test/python/pickles/TestsBasicSwap_handle_measurement.pickle b/test/python/pickles/TestsBasicSwap_handle_measurement.pickle
index 27eb154a547d..f4fdaab4e45f 100644
Binary files a/test/python/pickles/TestsBasicSwap_handle_measurement.pickle and b/test/python/pickles/TestsBasicSwap_handle_measurement.pickle differ
diff --git a/test/python/pickles/TestsBasicSwap_initial_layout.pickle b/test/python/pickles/TestsBasicSwap_initial_layout.pickle
index dc47de80b9fa..acade011a9e0 100644
Binary files a/test/python/pickles/TestsBasicSwap_initial_layout.pickle and b/test/python/pickles/TestsBasicSwap_initial_layout.pickle differ
diff --git a/test/python/pickles/TestsLookaheadSwap_a_cx_to_map.pickle b/test/python/pickles/TestsLookaheadSwap_a_cx_to_map.pickle
index 1528506f8ca0..2e4333db9551 100644
Binary files a/test/python/pickles/TestsLookaheadSwap_a_cx_to_map.pickle and b/test/python/pickles/TestsLookaheadSwap_a_cx_to_map.pickle differ
diff --git a/test/python/pickles/TestsLookaheadSwap_handle_measurement.pickle b/test/python/pickles/TestsLookaheadSwap_handle_measurement.pickle
index 8b3dc7f56807..b4a70c461dfb 100644
Binary files a/test/python/pickles/TestsLookaheadSwap_handle_measurement.pickle and b/test/python/pickles/TestsLookaheadSwap_handle_measurement.pickle differ
diff --git a/test/python/pickles/TestsLookaheadSwap_initial_layout.pickle b/test/python/pickles/TestsLookaheadSwap_initial_layout.pickle
index 90be0799bc10..ce58363424ba 100644
Binary files a/test/python/pickles/TestsLookaheadSwap_initial_layout.pickle and b/test/python/pickles/TestsLookaheadSwap_initial_layout.pickle differ
diff --git a/test/python/pickles/TestsStochasticSwap_a_cx_to_map.pickle b/test/python/pickles/TestsStochasticSwap_a_cx_to_map.pickle
index 2cfd35193b9a..8ae086d5c19c 100644
Binary files a/test/python/pickles/TestsStochasticSwap_a_cx_to_map.pickle and b/test/python/pickles/TestsStochasticSwap_a_cx_to_map.pickle differ
diff --git a/test/python/pickles/TestsStochasticSwap_handle_measurement.pickle b/test/python/pickles/TestsStochasticSwap_handle_measurement.pickle
index 5491cda0cc0c..392d06808324 100644
Binary files a/test/python/pickles/TestsStochasticSwap_handle_measurement.pickle and b/test/python/pickles/TestsStochasticSwap_handle_measurement.pickle differ
diff --git a/test/python/pickles/TestsStochasticSwap_initial_layout.pickle b/test/python/pickles/TestsStochasticSwap_initial_layout.pickle
index 15fc03083b37..972cd2de297f 100644
Binary files a/test/python/pickles/TestsStochasticSwap_initial_layout.pickle and b/test/python/pickles/TestsStochasticSwap_initial_layout.pickle differ