diff --git a/CMakeLists.txt b/CMakeLists.txt
index dcc44be87..3a37040ed 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -861,7 +861,7 @@ if(VLLM_GPU_LANG STREQUAL "CUDA")
   endif()
 
   # Hadacore kernels
-  cuda_archs_loose_intersection(HADACORE_ARCHS "8.0;8.9;9.0" "${CUDA_ARCHS}")
+  cuda_archs_loose_intersection(HADACORE_ARCHS "8.0+PTX;9.0+PTX" "${CUDA_ARCHS}")
   if(HADACORE_ARCHS)
     set(SRCS "csrc/quantization/hadamard/hadacore/hadamard_transform_cuda.cu")
     set_gencode_flags_for_srcs(