diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml
index a428f4881f..b24105fdb0 100644
--- a/.github/workflows/deploy.yml
+++ b/.github/workflows/deploy.yml
@@ -50,6 +50,8 @@ jobs:
               | jq -nRc '{"only": inputs, "os": "windows-latest"}'
             } | jq -sc
           )
+          # append GPU builds
+          MATRIX="$(echo $MATRIX  | jq '. + [{"only": "qiskit-aer-gpu-cu11", "os": "ubunut-latest"}, {"only": "qiskit-aer-gpu-cu12", "os": "ubunut-latest"}]')"
           echo "MATRIX IS $MATRIX"
           echo "include=$MATRIX" >> $GITHUB_OUTPUT          
     env:
@@ -67,10 +69,10 @@ jobs:
     steps:
       - uses: actions/checkout@v4
 
-      - uses: actions-rs/toolchain@v1
-        if: contains(fromJSON('["aarch64", "ppc64le", "s390x"]'), '${{ matrix.only }}')
-        with:
-          toolchain: stable
+      #- uses: actions-rs/toolchain@v1
+      #  if: contains(fromJSON('["aarch64", "ppc64le", "s390x"]'), '${{ matrix.only }}')
+      #  with:
+      #    toolchain: stable
 
       - name: Set up QEMU
         if: runner.os == 'Linux'
@@ -91,8 +93,6 @@ jobs:
           remove-docker-images: 'true'
 
       - uses: pypa/cibuildwheel@v2.16.0
-        env:
-          CIBW_ENVIRONMENT: AER_CMAKE_OPENMP_BUILD=1
         with:
           only: ${{ matrix.only }}
 
diff --git a/pyproject.toml b/pyproject.toml
index fdfe6f8455..508adc1446 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -22,6 +22,7 @@ test-command = "python {project}/tools/verify_wheels.py"
 # Numpy 1.22 there are no i686 wheels, so we force pip to use older ones without
 # restricting any dependencies that Numpy and Scipy might have.
 before-test = "pip install --only-binary=numpy,scipy numpy scipy"
+environment = { AER_CMAKE_OPENMP_BUILD="1" }
 
 [tool.cibuildwheel.linux]
 before-all = "yum install -y openblas-devel"
@@ -36,10 +37,12 @@ before-all = "yum install -y wget && bash {project}/tools/install_openblas_i686.
 [[tool.cibuildwheel.overrides]]
 select = "cp3{8,9,10,11}-manylinux_{ppc64le,s390x}"
 before-all = "yum install -y epel-release && yum install -y openblas-devel"
+environment = { AER_CMAKE_OPENMP_BUILD="0" }
 
 [[tool.cibuildwheel.overrides]]
 select = "cp3{8,9,10,11}-manylinux_{aarch64}"
-before-all-linux = "yum install -y https://dl.fedoraproject.org/pub/epel/7/aarch64/Packages/e/epel-release-7-12.noarch.rpm && yum install -y openblas-devel"
+before-all = "yum install -y https://dl.fedoraproject.org/pub/epel/7/aarch64/Packages/e/epel-release-7-12.noarch.rpm && yum install -y openblas-devel"
+environment = { AER_CMAKE_OPENMP_BUILD="0" }
 
 [[tool.cibuildwheel.overrides]]
 select = "*-gpu-*"