diff --git a/release/setup.py b/release/setup.py
index e2b392eaf..4c15f1393 100644
--- a/release/setup.py
+++ b/release/setup.py
@@ -50,6 +50,14 @@ def finalize_options(self):
     "cirq-google==1.3.0",
     "sympy==1.14",
     "tf-keras~=2.16.0",
+    # The following are transitive dependencies that need to be constrained to
+    # avoid incompatible versions or because some (e.g., contourpy 1.3.3)
+    # require Python 3.11+ and we want to maintain Python 3.10 compatibility.
+    # TODO: revisit after we reach compatibility with TensorFlow 2.19+.
+    "contourpy<=1.3.2",
+    "jax<=0.5",
+    "numpy<2.0",
+    "scipy<=1.12.0",
     # The following makes it easier to get the right version on Colab. Once
     # TFQ works with the latest version of TF, this may become unnecessary.
     "protobuf==4.25.8",
diff --git a/requirements-pins.txt b/requirements-pins.txt
new file mode 100644
index 000000000..b7847c708
--- /dev/null
+++ b/requirements-pins.txt
@@ -0,0 +1,12 @@
+# Summary: requirements constraints for TensorFlow Quantum.
+#
+# This file is used to constrain the versions of transitive dependencies during
+# the 'pip-compile' process. This is the recommended way to apply security
+# patches without polluting requirements.in.
+#
+# This file currently requires manual updates when necessary, such as when
+# Dependabot opens PRs to update a transitive dependency in requirements.txt.
+
+fonttools>=4.60.2
+urllib3>=2.6.0
+werkzeug>=3.1.4
diff --git a/requirements.in b/requirements.in
index 92c987272..18e52d8f7 100644
--- a/requirements.in
+++ b/requirements.in
@@ -18,14 +18,18 @@
 # scripts/generate_requirements.sh.
 cirq-core~=1.3.0
 cirq-google~=1.3.0
+numpy<2.0
 tensorflow>=2.16,<2.17
 tf-keras~=2.16.0
+scipy<=1.12.0
+sympy==1.14
 
-# TODO: the next ones are not truly core requirements. A better place should be
-# found for them (long with others needed by scripts/*). They're here as a
-# stop-gap measure until then.
-yapf==0.43.0
-pylint==3.3.3
-nbformat==5.1.3
-nbclient==0.6.5
-tensorflow-docs
+# This needs to match what TensorFlow uses to avoid problems with distutils.
+setuptools==68.2.2
+
+# The rest are transitive dependencies that need to be constrained either
+# because pip may try to install incompatible versions, or the higher versions
+# require Python 3.11+ and we want to maintain Python 3.10 compatibility.
+jax<=0.5
+contourpy<=1.3.2
+networkx<=3.4
diff --git a/requirements.txt b/requirements.txt
index ac86eb121..b6c333b04 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,27 +1,17 @@
 #
-# This file is autogenerated by pip-compile with Python 3.11
+# This file is autogenerated by pip-compile with Python 3.10
 # by the following command:
 #
-#    pip-compile --allow-unsafe --no-strip-extras
+#    ./scripts/generate_requirements.sh
 #
-
-absl-py==2.1.0
+absl-py==2.3.1
     # via
     #   keras
     #   tensorboard
     #   tensorflow
-    #   tensorflow-docs
-astor==0.8.1
-    # via tensorflow-docs
-astroid==3.3.11
-    # via pylint
 astunparse==1.6.3
     # via tensorflow
-attrs==25.4.0
-    # via
-    #   jsonschema
-    #   referencing
-cachetools==6.2.2
+cachetools==6.2.3
     # via google-auth
 certifi==2025.11.12
     # via requests
@@ -34,18 +24,20 @@ cirq-core==1.3.0
 cirq-google==1.3.0
     # via -r requirements.in
 contourpy==1.3.2
-    # via matplotlib
+    # via
+    #   -r requirements.in
+    #   matplotlib
 cycler==0.12.1
     # via matplotlib
-dill==0.4.0
-    # via pylint
 duet==0.2.9
     # via cirq-core
 flatbuffers==25.9.23
     # via tensorflow
-fonttools==4.60.1
-    # via matplotlib
-gast==0.6.0
+fonttools==4.61.1
+    # via
+    #   -c requirements-pins.txt
+    #   matplotlib
+gast==0.7.0
     # via tensorflow
 google-api-core[grpc]==2.28.1
     # via cirq-google
@@ -57,13 +49,13 @@ googleapis-common-protos==1.72.0
     # via
     #   google-api-core
     #   grpcio-status
-grpcio==1.60.2
+grpcio==1.76.0
     # via
     #   google-api-core
     #   grpcio-status
     #   tensorboard
     #   tensorflow
-grpcio-status==1.60.2
+grpcio-status==1.62.3
     # via google-api-core
 h5py==3.15.1
     # via
@@ -71,22 +63,10 @@ h5py==3.15.1
     #   tensorflow
 idna==3.11
     # via requests
-ipython-genutils==0.2.0
-    # via nbformat
-isort==5.13.2
-    # via pylint
-jinja2==3.1.6
-    # via tensorflow-docs
-jsonschema==4.25.1
-    # via nbformat
-jsonschema-specifications==2025.9.1
-    # via jsonschema
-jupyter-client==8.6.3
-    # via nbclient
-jupyter-core==5.9.1
-    # via
-    #   jupyter-client
-    #   nbformat
+jax==0.4.34
+    # via -r requirements.in
+jaxlib==0.4.34
+    # via jax
 keras==3.12.0
     # via tensorflow
 kiwisolver==1.4.9
@@ -98,39 +78,33 @@ markdown==3.10
 markdown-it-py==4.0.0
     # via rich
 markupsafe==3.0.3
-    # via
-    #   jinja2
-    #   werkzeug
-matplotlib==3.10.7
+    # via werkzeug
+matplotlib==3.10.8
     # via cirq-core
-mccabe==0.7.0
-    # via pylint
 mdurl==0.1.2
     # via markdown-it-py
 ml-dtypes==0.3.2
     # via
+    #   jax
+    #   jaxlib
     #   keras
     #   tensorflow
 mpmath==1.3.0
     # via sympy
 namex==0.1.0
     # via keras
-nbclient==0.6.5
-    # via -r requirements.in
-nbformat==5.1.3
+networkx==3.4
     # via
     #   -r requirements.in
-    #   nbclient
-    #   tensorflow-docs
-nest-asyncio==1.6.0
-    # via nbclient
-networkx==3.4.2
-    # via cirq-core
+    #   cirq-core
 numpy==1.26.4
     # via
+    #   -r requirements.in
     #   cirq-core
     #   contourpy
     #   h5py
+    #   jax
+    #   jaxlib
     #   keras
     #   matplotlib
     #   ml-dtypes
@@ -139,7 +113,9 @@ numpy==1.26.4
     #   tensorboard
     #   tensorflow
 opt-einsum==3.4.0
-    # via tensorflow
+    # via
+    #   jax
+    #   tensorflow
 optree==0.18.0
     # via keras
 packaging==25.0
@@ -147,15 +123,11 @@ packaging==25.0
     #   keras
     #   matplotlib
     #   tensorflow
+    #   wheel
 pandas==2.3.3
     # via cirq-core
 pillow==12.0.0
     # via matplotlib
-platformdirs==4.5.0
-    # via
-    #   jupyter-core
-    #   pylint
-    #   yapf
 proto-plus==1.26.1
     # via
     #   cirq-google
@@ -169,7 +141,6 @@ protobuf==4.25.8
     #   proto-plus
     #   tensorboard
     #   tensorflow
-    #   tensorflow-docs
 pyasn1==0.6.1
     # via
     #   pyasn1-modules
@@ -178,39 +149,28 @@ pyasn1-modules==0.4.2
     # via google-auth
 pygments==2.19.2
     # via rich
-pylint==3.3.3
-    # via -r requirements.in
 pyparsing==3.2.5
     # via matplotlib
 python-dateutil==2.9.0.post0
     # via
-    #   jupyter-client
     #   matplotlib
     #   pandas
 pytz==2025.2
     # via pandas
-pyyaml
-    # via tensorflow-docs
-pyzmq==27.1.0
-    # via jupyter-client
-referencing==0.37.0
-    # via
-    #   jsonschema
-    #   jsonschema-specifications
 requests==2.32.5
     # via
     #   google-api-core
     #   tensorflow
 rich==14.2.0
     # via keras
-rpds-py==0.29.0
-    # via
-    #   jsonschema
-    #   referencing
 rsa==4.9.1
     # via google-auth
-scipy==1.15.3
-    # via cirq-core
+scipy==1.12.0
+    # via
+    #   -r requirements.in
+    #   cirq-core
+    #   jax
+    #   jaxlib
 six==1.17.0
     # via
     #   astunparse
@@ -221,7 +181,9 @@ six==1.17.0
 sortedcontainers==2.4.0
     # via cirq-core
 sympy==1.14.0
-    # via cirq-core
+    # via
+    #   -r requirements.in
+    #   cirq-core
 tensorboard==2.16.2
     # via tensorflow
 tensorboard-data-server==0.7.2
@@ -230,47 +192,38 @@ tensorflow==2.16.2
     # via
     #   -r requirements.in
     #   tf-keras
-tensorflow-docs==2025.2.19.33219
-    # via -r requirements.in
 tensorflow-io-gcs-filesystem==0.37.1
     # via tensorflow
 termcolor==3.2.0
     # via tensorflow
 tf-keras==2.16.0
     # via -r requirements.in
-tomlkit==0.13.3
-    # via pylint
-tornado==6.5.2
-    # via jupyter-client
 tqdm==4.67.1
     # via cirq-core
-traitlets==5.14.3
-    # via
-    #   jupyter-client
-    #   jupyter-core
-    #   nbclient
-    #   nbformat
 typing-extensions==4.15.0
     # via
     #   cirq-core
+    #   grpcio
     #   optree
-    #   referencing
     #   tensorflow
-tzdata==2025.2
+tzdata==2025.3
     # via pandas
-urllib3==2.5.0
-    # via requests
-werkzeug==3.1.3
-    # via tensorboard
-wheel==0.45.1
+urllib3==2.6.2
+    # via
+    #   -c requirements-pins.txt
+    #   requests
+werkzeug==3.1.4
+    # via
+    #   -c requirements-pins.txt
+    #   tensorboard
+wheel==0.46.1
     # via astunparse
-wrapt==1.17.3
+wrapt==2.0.1
     # via tensorflow
-yapf==0.43.0
-    # via -r requirements.in
 
 # The following packages are considered to be unsafe in a requirements file:
 setuptools==68.2.2
     # via
+    #   -r requirements.in
     #   tensorboard
     #   tensorflow
diff --git a/scripts/generate_requirements.sh b/scripts/generate_requirements.sh
index 8868273e7..bc8da9f23 100755
--- a/scripts/generate_requirements.sh
+++ b/scripts/generate_requirements.sh
@@ -15,29 +15,36 @@
 # ==============================================================================
 
 # Summary: produce requirements.txt using pip-compile & munging the result.
-# Usage: ./generate_requirements.sh
+# Usage: ./scripts/generate_requirements.sh from the top dir of the repo.
 
 set -eu
 
 # Find the top of the local TFQ git tree. Do it early in case this fails.
-thisdir=$(CDPATH="" cd -- "$(dirname -- "$0")" && pwd -P)
+thisdir=$(CDPATH="" cd -- "$(dirname -- "${0}")" && pwd -P)
 repo_dir=$(git -C "${thisdir}" rev-parse --show-toplevel 2>/dev/null || \
   echo "${thisdir}/..")
 
-echo "Running pip-compile in ${repo_dir} …"
-pip-compile -q --no-strip-extras --allow-unsafe
+# Ensure we have pip-compile.
+if ! pip show -qq pip-tools; then
+    echo "Python pip-tools not found. Please run 'pip install pip-tools'."
+    exit 1
+fi
 
-declare -a inplace_edit=(-i)
-if [[ "$(uname -s)" == "Darwin" ]]; then
-  # macOS uses BSD sed, which requires a suffix for -i.
-  inplace_edit+=('')
+declare -a constraint=()
+pins_file="$(realpath --relative-to=. "${repo_dir}/requirements-pins.txt")"
+if [[ -e "${pins_file}" ]]; then
+    constraint+=(--constraint "${pins_file}")
 fi
 
-echo "Adjusting output of pip-compile …"
-sed "${inplace_edit[@]}" \
-  -e '/^--index-url/d' \
-  -e '/^--extra-index-url/d' \
-  -e 's/^pyyaml==.*/pyyaml/' \
-  requirements.txt
+# Tell pip-compile to reference this script in the requirements.txt comments.
+export CUSTOM_COMPILE_COMMAND="${0}"
+
+echo "Running pip-compile in ${repo_dir} …"
+pip-compile -q \
+    --rebuild \
+    --allow-unsafe \
+    --no-strip-extras \
+    --no-emit-index-url \
+     "${constraint[@]}"
 
 echo "Done."
diff --git a/tensorflow_quantum/core/ops/math_ops/fidelity_op.py b/tensorflow_quantum/core/ops/math_ops/fidelity_op.py
index 8f2e87e44..9e704794d 100644
--- a/tensorflow_quantum/core/ops/math_ops/fidelity_op.py
+++ b/tensorflow_quantum/core/ops/math_ops/fidelity_op.py
@@ -25,9 +25,11 @@ def fidelity(programs, symbol_names, symbol_values, other_programs):
     Compute (potentially many) fidelities between the given circuits and
     the symbol free comparison circuits.
 
-    Calculates out[i][j] = $ | \langle \psi_{\text{programs[i]}} \\
-     (\text{symbol\_values[i]}) | \psi_{\text{other\_programs[j]}} \rangle \\
-     |^2 $
+    Calculates out[i][j] as:
+    $$
+    |\langle \psi_{\text{programs[i]}}(\text{symbol_values[i]}) \mid
+    \psi_{\text{other_programs[j]}} \rangle|^2
+    $$
 
 
     >>> symbols = sympy.symbols('alpha beta')
diff --git a/tensorflow_quantum/core/ops/math_ops/inner_product_op.py b/tensorflow_quantum/core/ops/math_ops/inner_product_op.py
index 5d92b7b92..18529ba18 100644
--- a/tensorflow_quantum/core/ops/math_ops/inner_product_op.py
+++ b/tensorflow_quantum/core/ops/math_ops/inner_product_op.py
@@ -75,8 +75,11 @@ def inner_product(programs, symbol_names, symbol_values, other_programs):
     Compute (potentially many) inner products between the given circuits and
     the symbol free comparison circuits.
 
-    Calculates out[i][j] = $ \langle \psi_{\text{programs[i]}} \\
-     (\text{symbol\_values[i]}) | \psi_{\text{other\_programs[j]}} \rangle $
+    Calculates out[i][j] as:
+    $$
+    \langle \psi_{\text{programs[i]}}(\text{symbol_values[i]}) \mid
+    \psi_{\text{other_programs[j]}} \rangle
+    $$
 
 
     >>> symbols = sympy.symbols('alpha beta')