diff --git a/.github/workflows/test_latest_versions.yml b/.github/workflows/test_latest_versions.yml
index 44ec39b7d..7d1e43822 100644
--- a/.github/workflows/test_latest_versions.yml
+++ b/.github/workflows/test_latest_versions.yml
@@ -20,7 +20,7 @@ jobs:
       max-parallel: 4
       matrix:
         os: [ubuntu-latest]
-        python-version: ["3.8", "3.11"]
+        python-version: ["3.8", "3.12"]
         include:
           - os: macos-latest
             python-version: "3.8"
@@ -47,4 +47,8 @@ jobs:
           pver=${{ matrix.python-version }}
           tox -epy${pver/./} -- --run-slow
           notebook_flags=""
+          if [ "$pver" = "3.12" ]; then
+            echo Skipping tutorials that require cplex
+            notebook_flags="${notebook_flags} --ignore=docs/circuit_cutting/cutqc/tutorials/tutorial_1_automatic_cut_finding.ipynb"
+          fi
           tox -epy${pver/./}-notebook -- ${notebook_flags}
diff --git a/INSTALL.rst b/INSTALL.rst
index 47ad3e2e4..068f40e2b 100644
--- a/INSTALL.rst
+++ b/INSTALL.rst
@@ -177,7 +177,8 @@ take care when installing the toolbox, depending on which tools they
 intend to use.
   
   - The automatic wire cut search in the ``cutqc`` package depends
-    on CPLEX, which is only available on Intel chips.
+    on CPLEX, which is only available on Intel chips and is not yet available
+    for Python 3.12.
 
 In each case, one method that is guaranteed to work is to :ref:`use
 the toolbox within Docker <Option 3>`.  Other methods include:
diff --git a/pyproject.toml b/pyproject.toml
index 195d384ab..01950bfb2 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -20,6 +20,7 @@ classifiers = [
     "Programming Language :: Python :: 3.9",
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
+    "Programming Language :: Python :: 3.12",
     "Topic :: Scientific/Engineering :: Physics",
 ]
 
@@ -38,8 +39,8 @@ dependencies = [
 cplex = [
     # We use the same restrictions in both of the following lines, as there
     # is no reason for us to install docplex without cplex.
-    "docplex>=2.23.222; platform_machine != 'arm64'",
-    "cplex>=22.1.0.0; platform_machine != 'arm64'",
+    "docplex>=2.23.222; python_version < '3.12' and platform_machine != 'arm64'",
+    "cplex>=22.1.0.0; python_version < '3.12' and platform_machine != 'arm64'",
 ]
 dev = [
     "circuit-knitting-toolbox[test,nbtest,lint]",
diff --git a/tox.ini b/tox.ini
index a16dc1864..d9c84a716 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 3.25
-envlist = py{38,39,310,311}{,-notebook}, lint, coverage, docs
+envlist = py{38,39,310,311,312}{,-notebook}, lint, coverage, docs
 isolated_build = True
 
 [testenv]
@@ -34,7 +34,7 @@ commands =
   pylint -rn --py-version=3.8 --disable=all --enable=reimported,no-self-use,no-else-raise,redefined-argument-from-local,redefined-builtin,raise-missing-from,cyclic-import,unused-argument circuit_knitting/ test/ tools/
   nbqa pylint -rn --py-version=3.8 --disable=all --enable=reimported,no-self-use,no-else-raise,redefined-argument-from-local,redefined-builtin,raise-missing-from,cyclic-import,unused-argument docs/
 
-[testenv:{,py-,py3-,py38-,py39-,py310-,py311-}notebook]
+[testenv:{,py-,py3-,py38-,py39-,py310-,py311-,py312-}notebook]
 extras =
   nbtest
   notebook-dependencies