diff --git a/.azure/lint_docs_qpy-linux.yml b/.azure/lint_docs-linux.yml
similarity index 61%
rename from .azure/lint_docs_qpy-linux.yml
rename to .azure/lint_docs-linux.yml
index c08ea702ede5..b9e0c37892df 100644
--- a/.azure/lint_docs_qpy-linux.yml
+++ b/.azure/lint_docs-linux.yml
@@ -4,8 +4,8 @@ parameters:
     displayName: "Version of Python to use"
 
 jobs:
-  - job: 'Lint_Docs_QPY'
-    displayName: 'Lint, documentation and QPY'
+  - job: 'Lint_Docs'
+    displayName: 'Lint and documentation'
     pool: {vmImage: 'ubuntu-latest'}
 
     variables:
@@ -43,24 +43,3 @@ jobs:
           artifactName: 'html_docs'
           Parallel: true
           ParallelCount: 8
-
-      - task: Cache@2
-        inputs:
-          key: 'qpy | test/qpy_compat/test_qpy.py | "$(Build.BuildNumber)"'
-          restoreKeys: |
-            qpy | test/qpy_compat/test_qpy.py
-          path: qpy_files
-        displayName: Cache old QPY files
-
-      - bash: |
-          set -e
-          # Reuse the docs environment to avoid needing to rebuild another
-          # version of Qiskit.
-          source .tox/docs/bin/activate
-          mv qpy_files/* test/qpy_compat || :
-          pushd test/qpy_compat
-          ./run_tests.sh
-          popd
-          mkdir -p qpy_files
-          mv test/qpy_compat/qpy_* qpy_files/.
-        displayName: 'Run QPY backwards compat tests'
diff --git a/.github/workflows/qpy.yml b/.github/workflows/qpy.yml
new file mode 100644
index 000000000000..2c127add907a
--- /dev/null
+++ b/.github/workflows/qpy.yml
@@ -0,0 +1,39 @@
+name: QPY
+
+on:
+  push:
+    branches:
+      - 'main'
+      - 'stable/*'
+  pull_request:
+  merge_group:
+concurrency:
+  group: ${{ github.repository }}-${{ github.ref }}-${{ github.head_ref }}-${{ github.workflow }}
+  cancel-in-progress: ${{ github.event_name == 'pull_request' }}
+
+jobs:
+  backward_compat:
+    if: github.repository_owner == 'Qiskit'
+    name: Backwards compatibility
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v4
+
+      - uses: actions/setup-python@v5
+        with:
+          python-version: '3.9'
+
+      - uses: dtolnay/rust-toolchain@stable
+
+      - uses: actions/cache@v4
+        with:
+          path: test/qpy_compat/qpy_cache
+          # The hashing is this key can be too eager to invalidate the cache,
+          # but since we risk the QPY tests failing to update if they're not in
+          # sync, it's better safe than sorry.
+          key: qpy-${{ hashFiles('test/qpy_compat/**') }}
+
+      - name: Run QPY backwards compatibility tests
+        working-directory: test/qpy_compat
+        run: ./run_tests.sh
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index d182ba32f1b3..94ed7d1fad7f 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -144,7 +144,7 @@ stages:
     - stage: "Lint_Docs_Prelim_Tests"
       displayName: "Preliminary tests"
       jobs:
-        - template: ".azure/lint_docs_qpy-linux.yml"
+        - template: ".azure/lint_docs-linux.yml"
           parameters:
             pythonVersion: ${{ parameters.minimumPythonVersion }}
 
@@ -208,7 +208,7 @@ stages:
     - stage: "Merge_Queue"
       displayName: "Merge queue"
       jobs:
-        - template: ".azure/lint_docs_qpy-linux.yml"
+        - template: ".azure/lint_docs-linux.yml"
           parameters:
             pythonVersion: ${{ parameters.minimumPythonVersion }}
 
diff --git a/requirements.txt b/requirements.txt
index 4c13eb6dc60a..6eb5902ae9fd 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -6,4 +6,7 @@ dill>=0.3
 python-dateutil>=2.8.0
 stevedore>=3.0.0
 typing-extensions
+
+# If updating the version range here, consider updating 'test/qpy_compat/run_tests.sh' to update the
+# list of symengine dependencies used in the cross-version tests.
 symengine>=0.11,<0.14
diff --git a/test/qpy_compat/process_version.sh b/test/qpy_compat/process_version.sh
index c56c44f554bb..01998e01667f 100755
--- a/test/qpy_compat/process_version.sh
+++ b/test/qpy_compat/process_version.sh
@@ -42,14 +42,14 @@ package="$1"
 version="$2"
 
 our_dir="$(realpath -- "$(dirname -- "${BASH_SOURCE[0]}")")"
-cache_dir="$(pwd -P)/qpy_$version"
-venv_dir="$(pwd -P)/${version}"
+cache_dir="$(pwd -P)/qpy_cache/$version"
+venv_dir="$(pwd -P)/venvs/$package-$version"
 
 if [[ ! -d $cache_dir ]] ; then
     echo "Building venv for $package==$version"
     "$python" -m venv "$venv_dir"
     "$venv_dir/bin/pip" install -c "${our_dir}/qpy_test_constraints.txt" "${package}==${version}"
-    mkdir "$cache_dir"
+    mkdir -p "$cache_dir"
     pushd "$cache_dir"
     echo "Generating QPY files with $package==$version"
     "$venv_dir/bin/python" "${our_dir}/test_qpy.py" generate --version="$version"
diff --git a/test/qpy_compat/run_tests.sh b/test/qpy_compat/run_tests.sh
index 979306a83784..a6ff67b14a94 100755
--- a/test/qpy_compat/run_tests.sh
+++ b/test/qpy_compat/run_tests.sh
@@ -14,6 +14,7 @@
 set -e
 set -o pipefail
 set -x
+shopt -s nullglob
 
 # Set fixed hash seed to ensure set orders are identical between saving and
 # loading.
@@ -21,35 +22,72 @@ export PYTHONHASHSEED=$(python -S -c "import random; print(random.randint(1, 429
 echo "PYTHONHASHSEED=$PYTHONHASHSEED"
 
 our_dir="$(realpath -- "$(dirname -- "${BASH_SOURCE[0]}")")"
+repo_root="$(realpath -- "$our_dir/../..")"
 
-qiskit_venv="$(pwd -P)/qiskit_venv"
+# First, prepare a wheel file for the dev version.  We install several venvs with this, and while
+# cargo will cache some rust artefacts, it still has to re-link each time, so the wheel build takes
+# a little while.
+wheel_dir="$(pwd -P)/wheels"
+python -m pip wheel --no-deps --wheel-dir "$wheel_dir" "$repo_root"
+all_wheels=("$wheel_dir"/*.whl)
+qiskit_dev_wheel="${all_wheels[0]}"
+
+# Now set up a "base" development-version environment, which we'll use for most of the backwards
+# compatibility checks.
+qiskit_venv="$(pwd -P)/venvs/dev"
 qiskit_python="$qiskit_venv/bin/python"
 python -m venv "$qiskit_venv"
+
 # `packaging` is needed for the `get_versions.py` script.
-#  symengine is pinned to 0.13 to explicitly test the migration path reusing the venv
-"$qiskit_venv/bin/pip" install -c "$our_dir/../../constraints.txt" "$our_dir/../.." packaging "symengine~=0.13"
+"$qiskit_venv/bin/pip" install -c "$repo_root/constraints.txt" "$qiskit_dev_wheel" packaging
 
+# Run all of the tests of cross-Qiskit-version compatibility.
 "$qiskit_python" "$our_dir/get_versions.py" | parallel --colsep=" " bash "$our_dir/process_version.sh" -p "$qiskit_python"
 
-# Test dev compatibility
+# Test dev compatibility with itself.
 dev_version="$("$qiskit_python" -c 'import qiskit; print(qiskit.__version__)')"
+mkdir -p "dev-files/base"
+pushd "dev-files/base"
 "$qiskit_python" "$our_dir/test_qpy.py" generate --version="$dev_version"
 "$qiskit_python" "$our_dir/test_qpy.py" load --version="$dev_version"
-
-# Test dev compatibility with different symengine versions across 0.11 and 0.13
-#
-# NOTE: When symengine >= 0.14.0 is released we will need to modify this to build an explicit
-# symengine 0.13.0 venv instead of reusing $qiskit_venv.
-#
-symengine_11_venv="$(pwd -P)/qiskit_symengine_11_venv"
-symengine_11_python="$symengine_11_venv/bin/python"
-python -m venv "$symengine_11_venv"
-"$symengine_11_venv/bin/pip" install -c "$our_dir/../../constraints.txt" "$our_dir/../.." "symengine==0.11.0"
-# Load symengine 0.13.0 generated payload with symengine 0.11
-"$symengine_11_python" "$our_dir/test_qpy.py" load --version="$dev_version"
-# Load symengine 0.11.0 generated payload with symengine 0.13.0
-mkdir symengine_11_qpy_files
-pushd symengine_11_qpy_files
-"$symengine_11_python" "$our_dir/test_qpy.py" generate --version="$dev_version"
-"$qiskit_python" "$our_dir/test_qpy.py" load --version="$dev_version"
 popd
+
+
+# Test dev compatibility with all supported combinations of symengine between generator and loader.
+# This will likely duplicate the base dev-compatibility test, but the tests are fairly fast, and
+# it's better safe than sorry with the serialisation tests.
+
+symengine_versions=(
+    '>=0.11,<0.12'
+    '>=0.13,<0.14'
+)
+symengine_venv_prefix="$(pwd -P)/venvs/dev-symengine-"
+symengine_files_prefix="$(pwd -P)/dev-files/symengine-"
+
+# Create the venvs and QPY files for each symengine version.
+for i in "${!symengine_versions[@]}"; do
+    specifier="${symengine_versions[$i]}"
+    symengine_venv="$symengine_venv_prefix$i"
+    files_dir="$symengine_files_prefix$i"
+    python -m venv "$symengine_venv"
+    "$symengine_venv/bin/pip" install -c "$repo_root/constraints.txt" "$qiskit_dev_wheel" "symengine$specifier"
+    mkdir -p "$files_dir"
+    pushd "$files_dir"
+    "$symengine_venv/bin/python" -c 'import symengine; print(symengine.__version__)' > "SYMENGINE_VERSION"
+    "$symengine_venv/bin/python" "$our_dir/test_qpy.py" generate --version="$dev_version"
+    popd
+done
+
+# For each symengine version, try loading the QPY files from every other symengine version.
+for loader_num in "${!symengine_versions[@]}"; do
+    loader_venv="$symengine_venv_prefix$loader_num"
+    loader_version="$(< "$symengine_files_prefix$loader_num/SYMENGINE_VERSION")"
+    for generator_num in "${!symengine_versions[@]}"; do
+        generator_files="$symengine_files_prefix$generator_num"
+        generator_version="$(< "$generator_files/SYMENGINE_VERSION")"
+        echo "Using symengine==$loader_version to load files generated with symengine==$generator_version"
+        pushd "$generator_files"
+        "$loader_venv/bin/python" "$our_dir/test_qpy.py" load --version="$dev_version"
+        popd
+    done
+done