We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Deepcopy of control flow with standalone clbit results in invalid circuit
### Environment

- **Qiskit Terra version**: 0.24.1 (but also on main)
- **Python version**: 3.11
- **Operating system**:  Linux


### What is happening?

When running a deepcopy of a circuit object using a clbit as a standalone bit as the condition for a control flow operation results in the deepcopied circuit being invalid so that qasm3 or qpy serialization, and visualization will fail because the internal state of the circuit is corrupted and not valid in the copy.

### How can we reproduce the issue?

```python
import copy

from qiskit.circuit import QuantumCircuit, Qubit, Clbit, ClassicalRegister, QuantumRegister, Gate, Parameter

bits = [Qubit(), Qubit(), Clbit()]
qc = QuantumCircuit(bits)
with qc.if_test((qc.clbits[0], 1)):
    qc.x(0)

copy_qc = copy.deepcopy(qc)
print(copy_qc)
```

### What should happen?

It should print the visualization of the circuit. This will stack trace though during the circuit to dag conversion. You can also replace `print(copy_qc)` with something like:

```
import io
from qiskit.qpy import dump

with io.BytesIO() as fd:
    dump(copy_qc, fd)
```
this will also fail on a lookup of the clbit.

### Any suggestions?

I think the special `__deepcopy__` handling in the `qiskit.circuit.Instruction` class is not valid for the `ControlFlowOp` when the `.condition` attribute is a clbit. It might just be simplest to revert to the default deepcopy behavior for `ControlFlowOp`.

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `qiskit/circuit/bit.py`
Content:
```
1 # This code is part of Qiskit.
2 #
3 # (C) Copyright IBM 2019.
4 #
5 # This code is licensed under the Apache License, Version 2.0. You may
6 # obtain a copy of this license in the LICENSE.txt file in the root directory
7 # of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
8 #
9 # Any modifications or derivative works of this code must retain this
10 # copyright notice, and modified files need to carry a notice indicating
11 # that they have been altered from the originals.
12 
13 """
14 Quantum bit and Classical bit objects.
15 """
16 
17 from qiskit.circuit.exceptions import CircuitError
18 from qiskit.utils.deprecation import deprecate_func
19 
20 
21 class Bit:
22     """Implement a generic bit.
23 
24     .. note::
25         This class should not be instantiated directly. This is just a superclass
26         for :class:`~.Clbit` and :class:`~.Qubit`.
27 
28     """
29 
30     __slots__ = {"_register", "_index", "_hash", "_repr"}
31 
32     def __init__(self, register=None, index=None):
33         """Create a new generic bit."""
34         if (register, index) == (None, None):
35             self._register = None
36             self._index = None
37             # To sidestep the overridden Bit.__hash__ and use the default hash
38             # algorithm (only new-style Bits), call default object hash method.
39             self._hash = object.__hash__(self)
40         else:
41             try:
42                 index = int(index)
43             except Exception as ex:
44                 raise CircuitError(
45                     f"index needs to be castable to an int: type {type(index)} was provided"
46                 ) from ex
47 
48             if index < 0:
49                 index += register.size
50 
51             if index >= register.size:
52                 raise CircuitError(
53                     f"index must be under the size of the register: {index} was provided"
54                 )
55 
56             self._register = register
57             self._index = index
58             self._hash = hash((self._register, self._index))
59             self._repr = f"{self.__class__.__name__}({self._register}, {self._index})"
60 
61     @property
62     @deprecate_func(
63         is_property=True,
64         since="0.17",
65         additional_msg=(
66             "Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find "
67             "all the containing registers within a circuit and the index of the bit within the "
68             "circuit."
69         ),
70     )
71     def register(self):  # pylint: disable=bad-docstring-quotes
72         """Get the register of an old-style bit.
73 
74         In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are
75         aliases to collections of bits.  A bit can be in many registers depending on the circuit, so
76         a single containing register is no longer a property of a bit.  It is an error to access
77         this attribute on bits that were not constructed as "owned" by a register."""
78         if (self._register, self._index) == (None, None):
79             raise CircuitError("Attempt to query register of a new-style Bit.")
80 
81         return self._register
82 
83     @property
84     @deprecate_func(
85         is_property=True,
86         since="0.17",
87         additional_msg=(
88             "Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find "
89             "all the containing registers within a circuit and the index of the bit within the "
90             "circuit."
91         ),
92     )
93     def index(self):  # pylint: disable=bad-docstring-quotes
94         """Get the index of an old-style bit in the register that owns it.
95 
96         In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are
97         aliases to collections of bits.  A bit can be in many registers depending on the circuit, so
98         a single containing register is no longer a property of a bit.  It is an error to access
99         this attribute on bits that were not constructed as "owned" by a register."""
100         if (self._register, self._index) == (None, None):
101             raise CircuitError("Attempt to query index of a new-style Bit.")
102 
103         return self._index
104 
105     def __repr__(self):
106         """Return the official string representing the bit."""
107         if (self._register, self._index) == (None, None):
108             # Similar to __hash__, use default repr method for new-style Bits.
109             return object.__repr__(self)
110         return self._repr
111 
112     def __hash__(self):
113         return self._hash
114 
115     def __eq__(self, other):
116         if (self._register, self._index) == (None, None):
117             return other is self
118 
119         try:
120             return self._repr == other._repr
121         except AttributeError:
122             return False
123
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/qiskit/circuit/bit.py b/qiskit/circuit/bit.py
--- a/qiskit/circuit/bit.py
+++ b/qiskit/circuit/bit.py
@@ -13,6 +13,7 @@
 """
 Quantum bit and Classical bit objects.
 """
+import copy
 
 from qiskit.circuit.exceptions import CircuitError
 from qiskit.utils.deprecation import deprecate_func
@@ -120,3 +121,20 @@
             return self._repr == other._repr
         except AttributeError:
             return False
+
+    def __copy__(self):
+        # Bits are immutable.
+        return self
+
+    def __deepcopy__(self, memo=None):
+        if (self._register, self._index) == (None, None):
+            return self
+
+        # Old-style bits need special handling for now, since some code seems
+        # to rely on their registers getting deep-copied.
+        bit = type(self).__new__(type(self))
+        bit._register = copy.deepcopy(self._register, memo)
+        bit._index = self._index
+        bit._hash = self._hash
+        bit._repr = self._repr
+        return bit

{"golden_diff": "diff --git a/qiskit/circuit/bit.py b/qiskit/circuit/bit.py\n--- a/qiskit/circuit/bit.py\n+++ b/qiskit/circuit/bit.py\n@@ -13,6 +13,7 @@\n \"\"\"\n Quantum bit and Classical bit objects.\n \"\"\"\n+import copy\n \n from qiskit.circuit.exceptions import CircuitError\n from qiskit.utils.deprecation import deprecate_func\n@@ -120,3 +121,20 @@\n             return self._repr == other._repr\n         except AttributeError:\n             return False\n+\n+    def __copy__(self):\n+        # Bits are immutable.\n+        return self\n+\n+    def __deepcopy__(self, memo=None):\n+        if (self._register, self._index) == (None, None):\n+            return self\n+\n+        # Old-style bits need special handling for now, since some code seems\n+        # to rely on their registers getting deep-copied.\n+        bit = type(self).__new__(type(self))\n+        bit._register = copy.deepcopy(self._register, memo)\n+        bit._index = self._index\n+        bit._hash = self._hash\n+        bit._repr = self._repr\n+        return bit\n", "issue": "Deepcopy of control flow with standalone clbit results in invalid circuit\n### Environment\n\n- **Qiskit Terra version**: 0.24.1 (but also on main)\r\n- **Python version**: 3.11\r\n- **Operating system**:  Linux\r\n\n\n### What is happening?\n\nWhen running a deepcopy of a circuit object using a clbit as a standalone bit as the condition for a control flow operation results in the deepcopied circuit being invalid so that qasm3 or qpy serialization, and visualization will fail because the internal state of the circuit is corrupted and not valid in the copy.\n\n### How can we reproduce the issue?\n\n```python\r\nimport copy\r\n\r\nfrom qiskit.circuit import QuantumCircuit, Qubit, Clbit, ClassicalRegister, QuantumRegister, Gate, Parameter\r\n\r\nbits = [Qubit(), Qubit(), Clbit()]\r\nqc = QuantumCircuit(bits)\r\nwith qc.if_test((qc.clbits[0], 1)):\r\n    qc.x(0)\r\n\r\ncopy_qc = copy.deepcopy(qc)\r\nprint(copy_qc)\r\n```\n\n### What should happen?\n\nIt should print the visualization of the circuit. This will stack trace though during the circuit to dag conversion. You can also replace `print(copy_qc)` with something like:\r\n\r\n```\r\nimport io\r\nfrom qiskit.qpy import dump\r\n\r\nwith io.BytesIO() as fd:\r\n    dump(copy_qc, fd)\r\n```\r\nthis will also fail on a lookup of the clbit.\n\n### Any suggestions?\n\nI think the special `__deepcopy__` handling in the `qiskit.circuit.Instruction` class is not valid for the `ControlFlowOp` when the `.condition` attribute is a clbit. It might just be simplest to revert to the default deepcopy behavior for `ControlFlowOp`.\n", "before_files": [{"content": "# This code is part of Qiskit.\n#\n# (C) Copyright IBM 2019.\n#\n# This code is licensed under the Apache License, Version 2.0. You may\n# obtain a copy of this license in the LICENSE.txt file in the root directory\n# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.\n#\n# Any modifications or derivative works of this code must retain this\n# copyright notice, and modified files need to carry a notice indicating\n# that they have been altered from the originals.\n\n\"\"\"\nQuantum bit and Classical bit objects.\n\"\"\"\n\nfrom qiskit.circuit.exceptions import CircuitError\nfrom qiskit.utils.deprecation import deprecate_func\n\n\nclass Bit:\n    \"\"\"Implement a generic bit.\n\n    .. note::\n        This class should not be instantiated directly. This is just a superclass\n        for :class:`~.Clbit` and :class:`~.Qubit`.\n\n    \"\"\"\n\n    __slots__ = {\"_register\", \"_index\", \"_hash\", \"_repr\"}\n\n    def __init__(self, register=None, index=None):\n        \"\"\"Create a new generic bit.\"\"\"\n        if (register, index) == (None, None):\n            self._register = None\n            self._index = None\n            # To sidestep the overridden Bit.__hash__ and use the default hash\n            # algorithm (only new-style Bits), call default object hash method.\n            self._hash = object.__hash__(self)\n        else:\n            try:\n                index = int(index)\n            except Exception as ex:\n                raise CircuitError(\n                    f\"index needs to be castable to an int: type {type(index)} was provided\"\n                ) from ex\n\n            if index < 0:\n                index += register.size\n\n            if index >= register.size:\n                raise CircuitError(\n                    f\"index must be under the size of the register: {index} was provided\"\n                )\n\n            self._register = register\n            self._index = index\n            self._hash = hash((self._register, self._index))\n            self._repr = f\"{self.__class__.__name__}({self._register}, {self._index})\"\n\n    @property\n    @deprecate_func(\n        is_property=True,\n        since=\"0.17\",\n        additional_msg=(\n            \"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n            \"all the containing registers within a circuit and the index of the bit within the \"\n            \"circuit.\"\n        ),\n    )\n    def register(self):  # pylint: disable=bad-docstring-quotes\n        \"\"\"Get the register of an old-style bit.\n\n        In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\n        aliases to collections of bits.  A bit can be in many registers depending on the circuit, so\n        a single containing register is no longer a property of a bit.  It is an error to access\n        this attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\n        if (self._register, self._index) == (None, None):\n            raise CircuitError(\"Attempt to query register of a new-style Bit.\")\n\n        return self._register\n\n    @property\n    @deprecate_func(\n        is_property=True,\n        since=\"0.17\",\n        additional_msg=(\n            \"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n            \"all the containing registers within a circuit and the index of the bit within the \"\n            \"circuit.\"\n        ),\n    )\n    def index(self):  # pylint: disable=bad-docstring-quotes\n        \"\"\"Get the index of an old-style bit in the register that owns it.\n\n        In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\n        aliases to collections of bits.  A bit can be in many registers depending on the circuit, so\n        a single containing register is no longer a property of a bit.  It is an error to access\n        this attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\n        if (self._register, self._index) == (None, None):\n            raise CircuitError(\"Attempt to query index of a new-style Bit.\")\n\n        return self._index\n\n    def __repr__(self):\n        \"\"\"Return the official string representing the bit.\"\"\"\n        if (self._register, self._index) == (None, None):\n            # Similar to __hash__, use default repr method for new-style Bits.\n            return object.__repr__(self)\n        return self._repr\n\n    def __hash__(self):\n        return self._hash\n\n    def __eq__(self, other):\n        if (self._register, self._index) == (None, None):\n            return other is self\n\n        try:\n            return self._repr == other._repr\n        except AttributeError:\n            return False\n", "path": "qiskit/circuit/bit.py"}], "after_files": [{"content": "# This code is part of Qiskit.\n#\n# (C) Copyright IBM 2019.\n#\n# This code is licensed under the Apache License, Version 2.0. You may\n# obtain a copy of this license in the LICENSE.txt file in the root directory\n# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.\n#\n# Any modifications or derivative works of this code must retain this\n# copyright notice, and modified files need to carry a notice indicating\n# that they have been altered from the originals.\n\n\"\"\"\nQuantum bit and Classical bit objects.\n\"\"\"\nimport copy\n\nfrom qiskit.circuit.exceptions import CircuitError\nfrom qiskit.utils.deprecation import deprecate_func\n\n\nclass Bit:\n    \"\"\"Implement a generic bit.\n\n    .. note::\n        This class should not be instantiated directly. This is just a superclass\n        for :class:`~.Clbit` and :class:`~.Qubit`.\n\n    \"\"\"\n\n    __slots__ = {\"_register\", \"_index\", \"_hash\", \"_repr\"}\n\n    def __init__(self, register=None, index=None):\n        \"\"\"Create a new generic bit.\"\"\"\n        if (register, index) == (None, None):\n            self._register = None\n            self._index = None\n            # To sidestep the overridden Bit.__hash__ and use the default hash\n            # algorithm (only new-style Bits), call default object hash method.\n            self._hash = object.__hash__(self)\n        else:\n            try:\n                index = int(index)\n            except Exception as ex:\n                raise CircuitError(\n                    f\"index needs to be castable to an int: type {type(index)} was provided\"\n                ) from ex\n\n            if index < 0:\n                index += register.size\n\n            if index >= register.size:\n                raise CircuitError(\n                    f\"index must be under the size of the register: {index} was provided\"\n                )\n\n            self._register = register\n            self._index = index\n            self._hash = hash((self._register, self._index))\n            self._repr = f\"{self.__class__.__name__}({self._register}, {self._index})\"\n\n    @property\n    @deprecate_func(\n        is_property=True,\n        since=\"0.17\",\n        additional_msg=(\n            \"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n            \"all the containing registers within a circuit and the index of the bit within the \"\n            \"circuit.\"\n        ),\n    )\n    def register(self):  # pylint: disable=bad-docstring-quotes\n        \"\"\"Get the register of an old-style bit.\n\n        In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\n        aliases to collections of bits.  A bit can be in many registers depending on the circuit, so\n        a single containing register is no longer a property of a bit.  It is an error to access\n        this attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\n        if (self._register, self._index) == (None, None):\n            raise CircuitError(\"Attempt to query register of a new-style Bit.\")\n\n        return self._register\n\n    @property\n    @deprecate_func(\n        is_property=True,\n        since=\"0.17\",\n        additional_msg=(\n            \"Instead, use :meth:`~qiskit.circuit.quantumcircuit.QuantumCircuit.find_bit` to find \"\n            \"all the containing registers within a circuit and the index of the bit within the \"\n            \"circuit.\"\n        ),\n    )\n    def index(self):  # pylint: disable=bad-docstring-quotes\n        \"\"\"Get the index of an old-style bit in the register that owns it.\n\n        In modern Qiskit Terra (version 0.17+), bits are the fundamental object and registers are\n        aliases to collections of bits.  A bit can be in many registers depending on the circuit, so\n        a single containing register is no longer a property of a bit.  It is an error to access\n        this attribute on bits that were not constructed as \"owned\" by a register.\"\"\"\n        if (self._register, self._index) == (None, None):\n            raise CircuitError(\"Attempt to query index of a new-style Bit.\")\n\n        return self._index\n\n    def __repr__(self):\n        \"\"\"Return the official string representing the bit.\"\"\"\n        if (self._register, self._index) == (None, None):\n            # Similar to __hash__, use default repr method for new-style Bits.\n            return object.__repr__(self)\n        return self._repr\n\n    def __hash__(self):\n        return self._hash\n\n    def __eq__(self, other):\n        if (self._register, self._index) == (None, None):\n            return other is self\n\n        try:\n            return self._repr == other._repr\n        except AttributeError:\n            return False\n\n    def __copy__(self):\n        # Bits are immutable.\n        return self\n\n    def __deepcopy__(self, memo=None):\n        if (self._register, self._index) == (None, None):\n            return self\n\n        # Old-style bits need special handling for now, since some code seems\n        # to rely on their registers getting deep-copied.\n        bit = type(self).__new__(type(self))\n        bit._register = copy.deepcopy(self._register, memo)\n        bit._index = self._index\n        bit._hash = self._hash\n        bit._repr = self._repr\n        return bit\n", "path": "qiskit/circuit/bit.py"}]}