diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 20c40dc38321..39439f7dd059 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -20,7 +20,7 @@ jobs:
       matrix:
         # Normally we test min and max version but we can't run python
         # 3.9 on arm64 until actions/setup-python#808 is resolved
-        python-version: ["3.10", "3.12"]
+        python-version: ["3.10", "3.13"]
     steps:
       - uses: actions/checkout@v4
       - name: Install Rust toolchain
@@ -44,7 +44,7 @@ jobs:
           python -m pip install -U -r requirements.txt -c constraints.txt
           python -m pip install -U -r requirements-dev.txt -c constraints.txt
           python -m pip install -c constraints.txt -e .
-        if: matrix.python-version == '3.12'
+        if: matrix.python-version == '3.13'
       - name: 'Install optionals'
         run: |
           python -m pip install -r requirements-optional.txt -c constraints.txt
diff --git a/.github/workflows/wheels-build.yml b/.github/workflows/wheels-build.yml
index 30fdcd84bbb5..a7453eb05568 100644
--- a/.github/workflows/wheels-build.yml
+++ b/.github/workflows/wheels-build.yml
@@ -27,7 +27,7 @@ on:
         default: "default"
         required: false
 
-      wheels-32bit: 
+      wheels-32bit:
         description: >-
           The action to take for Tier 1 wheels.
           Choose from 'default', 'build' or 'skip'.
@@ -36,7 +36,7 @@ on:
         default: "default"
         required: false
 
-      wheels-linux-s390x: 
+      wheels-linux-s390x:
         description: >-
           The action to take for Linux s390x wheels.
           Choose from 'default', 'build' or 'skip'.
@@ -44,7 +44,7 @@ on:
         default: "default"
         required: false
 
-      wheels-linux-ppc64le: 
+      wheels-linux-ppc64le:
         description: >-
           The action to take for Linux ppc64le wheels.
           Choose from 'default', 'build' or 'skip'.
@@ -52,7 +52,7 @@ on:
         default: "default"
         required: false
 
-      wheels-linux-aarch64: 
+      wheels-linux-aarch64:
         description: >-
           The action to take for Linux AArch64 wheels.
           Choose from 'default', 'build' or 'skip'.
@@ -77,7 +77,7 @@ on:
         type: boolean
         default: true
         required: false
-      
+
 
 jobs:
   wheels-tier-1:
@@ -126,7 +126,7 @@ jobs:
         env:
           PGO_WORK_DIR: ${{ github.workspace }}/pgo-data
           PGO_OUT_PATH: ${{ github.workspace }}/merged.profdata
-      - uses: pypa/cibuildwheel@v2.19.2
+      - uses: pypa/cibuildwheel@v2.21.3
       - uses: actions/upload-artifact@v4
         with:
           path: ./wheelhouse/*.whl
@@ -151,7 +151,7 @@ jobs:
         with:
           components: llvm-tools-preview
       - name: Build wheels
-        uses: pypa/cibuildwheel@v2.19.2
+        uses: pypa/cibuildwheel@v2.21.3
         env:
           CIBW_SKIP: 'pp* cp36-* cp37-* cp38-* *musllinux* *amd64 *x86_64'
       - uses: actions/upload-artifact@v4
@@ -173,7 +173,7 @@ jobs:
       - uses: docker/setup-qemu-action@v3
         with:
           platforms: all
-      - uses: pypa/cibuildwheel@v2.19.2
+      - uses: pypa/cibuildwheel@v2.21.3
         env:
           CIBW_ARCHS_LINUX: s390x
           CIBW_TEST_SKIP: "cp*"
@@ -196,7 +196,7 @@ jobs:
       - uses: docker/setup-qemu-action@v3
         with:
           platforms: all
-      - uses: pypa/cibuildwheel@v2.19.2
+      - uses: pypa/cibuildwheel@v2.21.3
         env:
           CIBW_ARCHS_LINUX: ppc64le
           CIBW_TEST_SKIP: "cp*"
@@ -218,7 +218,7 @@ jobs:
       - uses: docker/setup-qemu-action@v3
         with:
           platforms: all
-      - uses: pypa/cibuildwheel@v2.19.2
+      - uses: pypa/cibuildwheel@v2.21.3
         env:
           CIBW_ARCHS_LINUX: aarch64
           CIBW_TEST_COMMAND: cp -r {project}/test . && QISKIT_PARALLEL=FALSE stestr --test-path test/python run --abbreviate -n test.python.compiler.test_transpiler
diff --git a/asv.conf.json b/asv.conf.json
index a75bc0c59c3a..379a01cd7edd 100644
--- a/asv.conf.json
+++ b/asv.conf.json
@@ -17,7 +17,7 @@
     "dvcs": "git",
     "environment_type": "virtualenv",
     "show_commit_url": "http://github.com/Qiskit/qiskit/commit/",
-    "pythons": ["3.9", "3.10", "3.11", "3.12"],
+    "pythons": ["3.9", "3.10", "3.11", "3.12", "3.13"],
     "benchmark_dir": "test/benchmarks",
     "env_dir": ".asv/env",
     "results_dir": ".asv/results"
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 49df19808498..d182ba32f1b3 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -37,7 +37,7 @@ parameters:
   - name: "supportedPythonVersions"
     displayName: "All supported versions of Python"
     type: object
-    default: ["3.9", "3.10", "3.11", "3.12"]
+    default: ["3.9", "3.10", "3.11", "3.12", "3.13"]
 
   - name: "minimumPythonVersion"
     displayName: "Minimum supported version of Python"
@@ -47,7 +47,7 @@ parameters:
   - name: "maximumPythonVersion"
     displayName: "Maximum supported version of Python"
     type: string
-    default: "3.12"
+    default: "3.13"
 
   # These two versions of Python can be chosen somewhat arbitrarily, but we get
   # slightly better coverage per PR if they're neither the maximum nor minimum
diff --git a/pyproject.toml b/pyproject.toml
index 70a6e7c9d0cf..326d28f2a273 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -31,6 +31,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
     "Topic :: Scientific/Engineering",
 ]
 # These are configured in the `tool.setuptools.dynamic` table.
diff --git a/test/python/utils/test_deprecation.py b/test/python/utils/test_deprecation.py
index 5d3b82e75aa2..08872b9e7a41 100644
--- a/test/python/utils/test_deprecation.py
+++ b/test/python/utils/test_deprecation.py
@@ -14,6 +14,7 @@
 
 from __future__ import annotations
 
+import sys
 from textwrap import dedent
 
 from qiskit.utils.deprecation import (
@@ -409,17 +410,21 @@ def func3():
             to a new line."""
 
         add_deprecation_to_docstring(func3, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func3.__doc__,
-            (
-                f"""Docstring extending
+        expected_doc = f"""Docstring extending
             to a new line.
 {indent}
             .. deprecated:: 9.99
               Deprecated!
 {indent}"""
-            ),
-        )
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """Docstring extending
+to a new line.
+
+.. deprecated:: 9.99
+  Deprecated!
+"""
+
+        self.assertEqual(func3.__doc__, expected_doc)
 
         def func4():
             """
@@ -427,10 +432,7 @@ def func4():
             """
 
         add_deprecation_to_docstring(func4, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func4.__doc__,
-            (
-                f"""\
+        expected_doc = f"""\
 
             Docstring starting on a new line.
 {indent}
@@ -438,7 +440,18 @@ def func4():
             .. deprecated:: 9.99
               Deprecated!
 {indent}"""
-            ),
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """\
+
+Docstring starting on a new line.
+
+.. deprecated:: 9.99
+  Deprecated!
+"""
+
+        self.assertEqual(
+            func4.__doc__,
+            expected_doc,
         )
 
         def func5():
@@ -450,11 +463,7 @@ def func5():
 
             """
 
-        add_deprecation_to_docstring(func5, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func5.__doc__,
-            (
-                f"""\
+        expected_doc = f"""\
 
             Paragraph 1, line 1.
             Line 2.
@@ -466,7 +475,24 @@ def func5():
             .. deprecated:: 9.99
               Deprecated!
 {indent}"""
-            ),
+
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """\
+
+Paragraph 1, line 1.
+Line 2.
+
+Paragraph 2.
+
+
+.. deprecated:: 9.99
+  Deprecated!
+"""
+
+        add_deprecation_to_docstring(func5, msg="Deprecated!", since="9.99", pending=False)
+        self.assertEqual(
+            func5.__doc__,
+            expected_doc,
         )
 
         def func6():
@@ -478,11 +504,7 @@ def func6():
                 continued
             """
 
-        add_deprecation_to_docstring(func6, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func6.__doc__,
-            (
-                f"""Blah.
+        expected_doc = f"""Blah.
 
             A list.
               * element 1
@@ -493,7 +515,23 @@ def func6():
             .. deprecated:: 9.99
               Deprecated!
 {indent}"""
-            ),
+
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """Blah.
+
+A list.
+  * element 1
+  * element 2
+    continued
+
+.. deprecated:: 9.99
+  Deprecated!
+"""
+
+        add_deprecation_to_docstring(func6, msg="Deprecated!", since="9.99", pending=False)
+        self.assertEqual(
+            func6.__doc__,
+            expected_doc,
         )
 
     def test_add_deprecation_docstring_meta_lines(self) -> None:
@@ -511,10 +549,7 @@ def func1():
             """
 
         add_deprecation_to_docstring(func1, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func1.__doc__,
-            (
-                f"""\
+        expected_doc = f"""\
 {indent}
             .. deprecated:: 9.99
               Deprecated!
@@ -526,7 +561,22 @@ def func1():
             Raises:
                 SomeError
 {indent}"""
-            ),
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """\
+
+.. deprecated:: 9.99
+  Deprecated!
+
+
+Returns:
+    Content.
+
+Raises:
+    SomeError"""
+
+        self.assertEqual(
+            func1.__doc__,
+            expected_doc,
         )
 
         def func2():
@@ -537,10 +587,7 @@ def func2():
             """
 
         add_deprecation_to_docstring(func2, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func2.__doc__,
-            (
-                f"""Docstring.
+        expected_doc = f"""Docstring.
 {indent}
             .. deprecated:: 9.99
               Deprecated!
@@ -549,8 +596,17 @@ def func2():
             Returns:
                 Content.
 {indent}"""
-            ),
-        )
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """Docstring.
+
+.. deprecated:: 9.99
+  Deprecated!
+
+
+Returns:
+    Content."""
+
+        self.assertEqual(func2.__doc__, expected_doc)
 
         def func3():
             """
@@ -562,11 +618,7 @@ def func3():
                 Content.
             """
 
-        add_deprecation_to_docstring(func3, msg="Deprecated!", since="9.99", pending=False)
-        self.assertEqual(
-            func3.__doc__,
-            (
-                f"""\
+        expected_doc = f"""\
 
             Docstring starting on a new line.
 
@@ -579,7 +631,24 @@ def func3():
             Examples:
                 Content.
 {indent}"""
-            ),
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """\
+
+Docstring starting on a new line.
+
+Paragraph 2.
+
+.. deprecated:: 9.99
+  Deprecated!
+
+
+Examples:
+    Content."""
+
+        add_deprecation_to_docstring(func3, msg="Deprecated!", since="9.99", pending=False)
+        self.assertEqual(
+            func3.__doc__,
+            expected_doc,
         )
 
     def test_add_deprecation_docstring_multiple_entries(self) -> None:
@@ -613,10 +682,7 @@ def func2():
 
         add_deprecation_to_docstring(func2, msg="Deprecated #1!", since="9.99", pending=False)
         add_deprecation_to_docstring(func2, msg="Deprecated #2!", since="9.99", pending=False)
-        self.assertEqual(
-            func2.__doc__,
-            (
-                f"""\
+        expected_doc = f"""\
 
             Docstring starting on a new line.
 {indent}
@@ -628,7 +694,21 @@ def func2():
             .. deprecated:: 9.99
               Deprecated #2!
 {indent}"""
-            ),
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """\
+
+Docstring starting on a new line.
+
+.. deprecated:: 9.99
+  Deprecated #1!
+
+.. deprecated:: 9.99
+  Deprecated #2!
+"""
+
+        self.assertEqual(
+            func2.__doc__,
+            expected_doc,
         )
 
         def func3():
@@ -638,12 +718,7 @@ def func3():
                 Content.
             """
 
-        add_deprecation_to_docstring(func3, msg="Deprecated #1!", since="9.99", pending=False)
-        add_deprecation_to_docstring(func3, msg="Deprecated #2!", since="9.99", pending=False)
-        self.assertEqual(
-            func3.__doc__,
-            (
-                f"""Docstring.
+        expected_doc = f"""Docstring.
 {indent}
             .. deprecated:: 9.99
               Deprecated #1!
@@ -656,7 +731,26 @@ def func3():
             Yields:
                 Content.
 {indent}"""
-            ),
+
+        if sys.version_info >= (3, 13, 0):
+            expected_doc = """Docstring.
+
+.. deprecated:: 9.99
+  Deprecated #1!
+
+
+.. deprecated:: 9.99
+  Deprecated #2!
+
+
+Yields:
+    Content."""
+
+        add_deprecation_to_docstring(func3, msg="Deprecated #1!", since="9.99", pending=False)
+        add_deprecation_to_docstring(func3, msg="Deprecated #2!", since="9.99", pending=False)
+        self.assertEqual(
+            func3.__doc__,
+            expected_doc,
         )
 
     def test_add_deprecation_docstring_pending(self) -> None:
diff --git a/tox.ini b/tox.ini
index 5456e7731920..d4d822766675 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 4.0
-envlist = py39, py310, py311, py312, lint-incr
+envlist = py39, py310, py311, py312, py313, lint-incr
 isolated_build = true
 
 [testenv]