We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
Registers cannot be index with negative integers or slices
<!-- ⚠️ If you do not respect this template, your issue will be closed -->
<!-- ⚠️ Make sure to browse the opened and closed issues to confirm this idea does not exist. -->

### What is the expected enhancement?

It would be nice if the behavior mimicked python lists more. e.g.

```python
q = QuantumRegister(5)
q[-1]
q[-3:-1]
etc.
```

--- 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/register.py`
Content:
```
1 # -*- coding: utf-8 -*-
2 
3 # Copyright 2017, IBM.
4 #
5 # This source code is licensed under the Apache License, Version 2.0 found in
6 # the LICENSE.txt file in the root directory of this source tree.
7 
8 """
9 Base register reference object.
10 """
11 import re
12 import logging
13 import itertools
14 
15 from qiskit.exceptions import QiskitError, QiskitIndexError
16 
17 logger = logging.getLogger(__name__)
18 
19 
20 class Register:
21     """Implement a generic register."""
22 
23     # Counter for the number of instances in this class.
24     instances_counter = itertools.count()
25     # Prefix to use for auto naming.
26     prefix = 'reg'
27 
28     def __init__(self, size, name=None):
29         """Create a new generic register.
30         """
31 
32         if name is None:
33             name = '%s%i' % (self.prefix, next(self.instances_counter))
34 
35         if not isinstance(name, str):
36             raise QiskitError("The circuit name should be a string "
37                               "(or None for autogenerate a name).")
38 
39         test = re.compile('[a-z][a-zA-Z0-9_]*')
40         if test.match(name) is None:
41             raise QiskitError("%s is an invalid OPENQASM register name." % name)
42 
43         self.name = name
44         self.size = size
45         if size <= 0:
46             raise QiskitError("register size must be positive")
47 
48     def __repr__(self):
49         """Return the official string representing the register."""
50         return "%s(%d, '%s')" % (self.__class__.__qualname__,
51                                  self.size, self.name)
52 
53     def __len__(self):
54         """Return register size"""
55         return self.size
56 
57     def check_range(self, j):
58         """Check that j is a valid index into self."""
59         if isinstance(j, int):
60             if j < 0 or j >= self.size:
61                 raise QiskitIndexError("register index out of range")
62             elif isinstance(j, slice):
63                 if j.start < 0 or j.stop >= self.size or (j.step is not None and
64                                                           j.step <= 0):
65                     raise QiskitIndexError("register index slice out of range")
66 
67     def __getitem__(self, key):
68         """
69         Arg:
70             key (int|slice|list): index of the bit/qubit to be retrieved.
71 
72         Returns:
73             tuple[Register, int]: a tuple in the form `(self, key)` if key is int.
74                 If key is a slice, return a `list((self,key))`.
75 
76         Raises:
77             QiskitError: if the `key` is not an integer.
78             QiskitIndexError: if the `key` is not in the range
79                 `(0, self.size)`.
80         """
81         if not isinstance(key, (int, slice, list)):
82             raise QiskitError("expected integer or slice index into register")
83         self.check_range(key)
84         if isinstance(key, slice):
85             return [(self, ind) for ind in range(*key.indices(len(self)))]
86         elif isinstance(key, list):  # list of qubit indices
87             if max(key) < len(self):
88                 return [(self, ind) for ind in key]
89             else:
90                 raise QiskitError('register index out of range')
91         else:
92             return self, key
93 
94     def __iter__(self):
95         """
96         Returns:
97             iterator: an iterator over the bits/qubits of the register, in the
98                 form `tuple (Register, int)`.
99         """
100         return zip([self]*self.size, range(self.size))
101 
102     def __eq__(self, other):
103         """Two Registers are the same if they are of the same type
104         (i.e. quantum/classical), and have the same name and size.
105 
106         Args:
107             other (Register): other Register
108 
109         Returns:
110             bool: are self and other equal.
111         """
112         res = False
113         if type(self) is type(other) and \
114                 self.name == other.name and \
115                 self.size == other.size:
116             res = True
117         return res
118 
119     def __hash__(self):
120         """Make object hashable, based on the name and size to hash."""
121         return hash((type(self), self.name, self.size))
122
```
--- 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/register.py b/qiskit/circuit/register.py
--- a/qiskit/circuit/register.py
+++ b/qiskit/circuit/register.py
@@ -80,6 +80,8 @@
         """
         if not isinstance(key, (int, slice, list)):
             raise QiskitError("expected integer or slice index into register")
+        if isinstance(key, int) and key < 0:
+            key = self.size + key
         self.check_range(key)
         if isinstance(key, slice):
             return [(self, ind) for ind in range(*key.indices(len(self)))]

{"golden_diff": "diff --git a/qiskit/circuit/register.py b/qiskit/circuit/register.py\n--- a/qiskit/circuit/register.py\n+++ b/qiskit/circuit/register.py\n@@ -80,6 +80,8 @@\n         \"\"\"\n         if not isinstance(key, (int, slice, list)):\n             raise QiskitError(\"expected integer or slice index into register\")\n+        if isinstance(key, int) and key < 0:\n+            key = self.size + key\n         self.check_range(key)\n         if isinstance(key, slice):\n             return [(self, ind) for ind in range(*key.indices(len(self)))]\n", "issue": "Registers cannot be index with negative integers or slices\n<!-- \u26a0\ufe0f If you do not respect this template, your issue will be closed -->\r\n<!-- \u26a0\ufe0f Make sure to browse the opened and closed issues to confirm this idea does not exist. -->\r\n\r\n### What is the expected enhancement?\r\n\r\nIt would be nice if the behavior mimicked python lists more. e.g.\r\n\r\n```python\r\nq = QuantumRegister(5)\r\nq[-1]\r\nq[-3:-1]\r\netc.\r\n```\n", "before_files": [{"content": "# -*- coding: utf-8 -*-\n\n# Copyright 2017, IBM.\n#\n# This source code is licensed under the Apache License, Version 2.0 found in\n# the LICENSE.txt file in the root directory of this source tree.\n\n\"\"\"\nBase register reference object.\n\"\"\"\nimport re\nimport logging\nimport itertools\n\nfrom qiskit.exceptions import QiskitError, QiskitIndexError\n\nlogger = logging.getLogger(__name__)\n\n\nclass Register:\n    \"\"\"Implement a generic register.\"\"\"\n\n    # Counter for the number of instances in this class.\n    instances_counter = itertools.count()\n    # Prefix to use for auto naming.\n    prefix = 'reg'\n\n    def __init__(self, size, name=None):\n        \"\"\"Create a new generic register.\n        \"\"\"\n\n        if name is None:\n            name = '%s%i' % (self.prefix, next(self.instances_counter))\n\n        if not isinstance(name, str):\n            raise QiskitError(\"The circuit name should be a string \"\n                              \"(or None for autogenerate a name).\")\n\n        test = re.compile('[a-z][a-zA-Z0-9_]*')\n        if test.match(name) is None:\n            raise QiskitError(\"%s is an invalid OPENQASM register name.\" % name)\n\n        self.name = name\n        self.size = size\n        if size <= 0:\n            raise QiskitError(\"register size must be positive\")\n\n    def __repr__(self):\n        \"\"\"Return the official string representing the register.\"\"\"\n        return \"%s(%d, '%s')\" % (self.__class__.__qualname__,\n                                 self.size, self.name)\n\n    def __len__(self):\n        \"\"\"Return register size\"\"\"\n        return self.size\n\n    def check_range(self, j):\n        \"\"\"Check that j is a valid index into self.\"\"\"\n        if isinstance(j, int):\n            if j < 0 or j >= self.size:\n                raise QiskitIndexError(\"register index out of range\")\n            elif isinstance(j, slice):\n                if j.start < 0 or j.stop >= self.size or (j.step is not None and\n                                                          j.step <= 0):\n                    raise QiskitIndexError(\"register index slice out of range\")\n\n    def __getitem__(self, key):\n        \"\"\"\n        Arg:\n            key (int|slice|list): index of the bit/qubit to be retrieved.\n\n        Returns:\n            tuple[Register, int]: a tuple in the form `(self, key)` if key is int.\n                If key is a slice, return a `list((self,key))`.\n\n        Raises:\n            QiskitError: if the `key` is not an integer.\n            QiskitIndexError: if the `key` is not in the range\n                `(0, self.size)`.\n        \"\"\"\n        if not isinstance(key, (int, slice, list)):\n            raise QiskitError(\"expected integer or slice index into register\")\n        self.check_range(key)\n        if isinstance(key, slice):\n            return [(self, ind) for ind in range(*key.indices(len(self)))]\n        elif isinstance(key, list):  # list of qubit indices\n            if max(key) < len(self):\n                return [(self, ind) for ind in key]\n            else:\n                raise QiskitError('register index out of range')\n        else:\n            return self, key\n\n    def __iter__(self):\n        \"\"\"\n        Returns:\n            iterator: an iterator over the bits/qubits of the register, in the\n                form `tuple (Register, int)`.\n        \"\"\"\n        return zip([self]*self.size, range(self.size))\n\n    def __eq__(self, other):\n        \"\"\"Two Registers are the same if they are of the same type\n        (i.e. quantum/classical), and have the same name and size.\n\n        Args:\n            other (Register): other Register\n\n        Returns:\n            bool: are self and other equal.\n        \"\"\"\n        res = False\n        if type(self) is type(other) and \\\n                self.name == other.name and \\\n                self.size == other.size:\n            res = True\n        return res\n\n    def __hash__(self):\n        \"\"\"Make object hashable, based on the name and size to hash.\"\"\"\n        return hash((type(self), self.name, self.size))\n", "path": "qiskit/circuit/register.py"}], "after_files": [{"content": "# -*- coding: utf-8 -*-\n\n# Copyright 2017, IBM.\n#\n# This source code is licensed under the Apache License, Version 2.0 found in\n# the LICENSE.txt file in the root directory of this source tree.\n\n\"\"\"\nBase register reference object.\n\"\"\"\nimport re\nimport logging\nimport itertools\n\nfrom qiskit.exceptions import QiskitError, QiskitIndexError\n\nlogger = logging.getLogger(__name__)\n\n\nclass Register:\n    \"\"\"Implement a generic register.\"\"\"\n\n    # Counter for the number of instances in this class.\n    instances_counter = itertools.count()\n    # Prefix to use for auto naming.\n    prefix = 'reg'\n\n    def __init__(self, size, name=None):\n        \"\"\"Create a new generic register.\n        \"\"\"\n\n        if name is None:\n            name = '%s%i' % (self.prefix, next(self.instances_counter))\n\n        if not isinstance(name, str):\n            raise QiskitError(\"The circuit name should be a string \"\n                              \"(or None for autogenerate a name).\")\n\n        test = re.compile('[a-z][a-zA-Z0-9_]*')\n        if test.match(name) is None:\n            raise QiskitError(\"%s is an invalid OPENQASM register name.\" % name)\n\n        self.name = name\n        self.size = size\n        if size <= 0:\n            raise QiskitError(\"register size must be positive\")\n\n    def __repr__(self):\n        \"\"\"Return the official string representing the register.\"\"\"\n        return \"%s(%d, '%s')\" % (self.__class__.__qualname__,\n                                 self.size, self.name)\n\n    def __len__(self):\n        \"\"\"Return register size\"\"\"\n        return self.size\n\n    def check_range(self, j):\n        \"\"\"Check that j is a valid index into self.\"\"\"\n        if isinstance(j, int):\n            if j < 0 or j >= self.size:\n                raise QiskitIndexError(\"register index out of range\")\n            elif isinstance(j, slice):\n                if j.start < 0 or j.stop >= self.size or (j.step is not None and\n                                                          j.step <= 0):\n                    raise QiskitIndexError(\"register index slice out of range\")\n\n    def __getitem__(self, key):\n        \"\"\"\n        Arg:\n            key (int|slice|list): index of the bit/qubit to be retrieved.\n\n        Returns:\n            tuple[Register, int]: a tuple in the form `(self, key)` if key is int.\n                If key is a slice, return a `list((self,key))`.\n\n        Raises:\n            QiskitError: if the `key` is not an integer.\n            QiskitIndexError: if the `key` is not in the range\n                `(0, self.size)`.\n        \"\"\"\n        if not isinstance(key, (int, slice, list)):\n            raise QiskitError(\"expected integer or slice index into register\")\n        if isinstance(key, int) and key < 0:\n            key = self.size + key\n        self.check_range(key)\n        if isinstance(key, slice):\n            return [(self, ind) for ind in range(*key.indices(len(self)))]\n        elif isinstance(key, list):  # list of qubit indices\n            if max(key) < len(self):\n                return [(self, ind) for ind in key]\n            else:\n                raise QiskitError('register index out of range')\n        else:\n            return self, key\n\n    def __iter__(self):\n        \"\"\"\n        Returns:\n            iterator: an iterator over the bits/qubits of the register, in the\n                form `tuple (Register, int)`.\n        \"\"\"\n        return zip([self]*self.size, range(self.size))\n\n    def __eq__(self, other):\n        \"\"\"Two Registers are the same if they are of the same type\n        (i.e. quantum/classical), and have the same name and size.\n\n        Args:\n            other (Register): other Register\n\n        Returns:\n            bool: are self and other equal.\n        \"\"\"\n        res = False\n        if type(self) is type(other) and \\\n                self.name == other.name and \\\n                self.size == other.size:\n            res = True\n        return res\n\n    def __hash__(self):\n        \"\"\"Make object hashable, based on the name and size to hash.\"\"\"\n        return hash((type(self), self.name, self.size))\n", "path": "qiskit/circuit/register.py"}]}