Add GHA for docs building

.github/workflows/sphinx_build.yml

@@ -0,0 +1,39 @@
+name: Build and Deploy Docs
+
+on:
+  push:
+    branches:
+      - main
+
+permissions: write-all
+
+jobs:
+  deploy_docs:
+    runs-on: ubuntu-latest
+
+    steps:
+      - uses: actions/checkout@v3
+        with:
+          fetch-depth: 0 # needed for tag/version
+
+      - uses: actions/setup-python@v4
+        with:
+          python-version: '3.11'
+
+      - name: Install package
+        shell: bash -l {0}
+        working-directory: .
+        run: |
+          python -m pip install -r requirements.txt
+
+      - name: Build Documentation
+        shell: bash -l {0}
+        working-directory: .
+        run: |
+          make html
+
+      - name: Deploy Documentation
+        uses: JamesIves/github-pages-deploy-action@v4
+        with:
+          folder: ./_build/html
+          branch: gh-pages