diff --git a/.github/workflows/weekly.yml b/.github/workflows/weekly.yml
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+# The name is short because we mostly care how it appears in the pull request
+# "checks" dialogue box - it looks like
+#     Tests / ubuntu-latest, python-3.9, defaults
+# or similar.
+name: Tests
+
+on:
+  schedule:
+    - cron "0 12 * * 0"
+
+defaults:
+  run:
+    # The slightly odd shell call is to force bash to read .bashrc, which is
+    # necessary for having conda behave sensibly.  We use bash as the shell even
+    # on Windows, since we don't run anything much complicated, and it makes
+    # things much simpler.
+    shell: bash -l {0}
+
+jobs:
+  cases:
+    name: ${{ matrix.os }}, ${{ matrix.case-name }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        os: [ubuntu-latest]
+        python-version: [3.9]
+        case-name: [defaults]
+
+    steps:
+      - uses: actions/checkout@v2
+
+      - uses: conda-incubator/setup-miniconda@v2
+        with:
+          auto-update-conda: true
+          python-version: ${{ matrix.python-version }}
+
+      - name: Install QuTiP from GitHub
+        run: |
+          python -mpip install git+https://github.com/qutip/qutip.git@master
+          python -c 'import qutip; qutip.about()'
+
+      - name: Install qutip-jax and dependencies
+        # Install in editable mode so Coveralls detects the tree structure
+        # relative to the git repository root as well.
+        run: |
+            python -mpip install -e .[full]
+            python -mpip install pytest-cov coveralls
+
+      - name: Package information
+        run: |
+          conda list
+          python -c 'import qutip_jax; print(qutip_jax.__version__)'
+
+      - name: Run tests
+        # If our tests are running for longer than an hour, _something_ is wrong
+        # somewhere.  The GitHub default is 6 hours, which is a bit long to wait
+        # to see if something hung.
+        timeout-minutes: 60
+        run: |
+          pytest --durations=0 --durations-min=1.0 --verbosity=1 --cov=qutip_jax --color=yes -W ignore::UserWarning:qutip
+          # Above flags are:
+          #  --durations=0 --durations-min=1.0
+          #     at the end, show a list of all the tests that took longer than a
+          #     second to run
+          #  --verbosity=1
+          #     turn the verbosity up so pytest prints the names of the tests
+          #     it's currently working on
+          #  --cov=qutip_jax
+          #     limit coverage reporting to code that's within the qutip_jax package
+          #  --color=yes
+          #     force coloured output in the terminal
+          #  -W ignore::UserWarning:qutip
+          #     Ignore matplotlib missing warnings
+          # These flags are added to those in pyproject.toml.
+
+      - name: Upload to Coveralls
+        env:
+          GITHUB_TOKEN: ${{ secrets.github_token }}
+          COVERALLS_FLAG_NAME: ${{ matrix.os }}-${{ matrix.python-version }}-${{ matrix.case-name }}
+          COVERALLS_PARALLEL: true
+        run: coveralls --service=github
+
+  finalise:
+    name: Finalise coverage reporting
+    needs: cases
+    runs-on: ubuntu-latest
+    container: python:3-slim
+    steps:
+      - name: Finalise coverage reporting
+        env:
+          GITHUB_TOKEN: ${{ secrets.github_token }}
+        run: |
+          python -mpip install coveralls
+          coveralls --service=github --finish