diff --git a/CMakeLists.txt b/CMakeLists.txt
index 2e7679f..0311658 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -4,7 +4,25 @@
 cmake_minimum_required(VERSION 3.20)
 
 # Project config
-project(cupdlpx LANGUAGES C CXX CUDA)
+project(cupdlpx LANGUAGES C CXX)
+
+# Default CUDA architectures: SASS for every current arch, PTX only for the newest one as a forward-compat fallback.
+find_package(CUDAToolkit REQUIRED)
+if(NOT DEFINED CMAKE_CUDA_ARCHITECTURES AND NOT DEFINED ENV{CUDAARCHS})
+  if(CUDAToolkit_VERSION VERSION_GREATER_EQUAL 13)
+    set(CMAKE_CUDA_ARCHITECTURES 75-real 80-real 86-real 89-real 90-real
+        100-real 120-real 120-virtual)
+  elseif(CUDAToolkit_VERSION VERSION_GREATER_EQUAL 12.8)
+    set(CMAKE_CUDA_ARCHITECTURES 60-real 70-real 75-real 80-real 86-real
+        89-real 90-real 100-real 120-real 120-virtual)
+  else()
+    set(CMAKE_CUDA_ARCHITECTURES 60-real 70-real 75-real 80-real 86-real
+        89-real 90-real 90-virtual)
+  endif()
+endif()
+
+enable_language(CUDA)
+message(STATUS "CUDA architectures: ${CMAKE_CUDA_ARCHITECTURES}")
 
 set(CUPDLPX_VERSION_MAJOR 0)
 set(CUPDLPX_VERSION_MINOR 2)
@@ -32,10 +50,6 @@ if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
     set_property(CACHE CMAKE_BUILD_TYPE PROPERTY STRINGS "Debug" "Release" "MinSizeRel" "RelWithDebInfo")
 endif()
 
-if(NOT DEFINED CMAKE_CUDA_ARCHITECTURES)
-  set(CMAKE_CUDA_ARCHITECTURES 60 70 75 80 86 89 90)
-endif()
-
 # -----------------------------------------------------------------------------
 # [ELEGANT DESIGN] Target-based Compile Flags
 # -----------------------------------------------------------------------------
@@ -85,7 +99,6 @@ endif()
 # -----------------------------------------------------------------------------
 # FIND DEPENDENCIES
 # -----------------------------------------------------------------------------
-find_package(CUDAToolkit REQUIRED)
 include(FetchContent)
 
 # 1. ZLIB Configuration
diff --git a/README.md b/README.md
index 919e8e0..4cd6a31 100644
--- a/README.md
+++ b/README.md
@@ -30,8 +30,8 @@ Our work is presented in two papers:
 * **Build Tools:** CMake (≥ 3.20), GCC, NVCC.
 
 > **SpMV backend** is selected automatically at compile time based on cuSPARSE version:
-> - `cusparseSpMV` — CUDA 12.4 – 13.1 (cuSPARSE < 12.7.3)
-> - `cusparseSpMVOp` — CUDA 13.1 Update 1+ (cuSPARSE ≥ 12.7.3)
+> - `cusparseSpMV` — CUDA 12.4 – 13.2 (cuSPARSE < 12.8.1)
+> - `cusparseSpMVOp` — CUDA 13.3+ (cuSPARSE ≥ 12.8.1)
 
 ### Build from Source
 Clone the repository and compile the project using CMake.
diff --git a/internal/cusparse_compat.h b/internal/cusparse_compat.h
index 9eaecb2..6d84034 100644
--- a/internal/cusparse_compat.h
+++ b/internal/cusparse_compat.h
@@ -3,19 +3,11 @@
 #include <cusparse.h>
 
 // cusparseSpMVOp_bufferSize was introduced in cuSPARSE 12.7.3 (CUDA 13.1 Update 1).
+// cuSPARSE 12.8.1 (CUDA 13.3.0) introduced the SpMVOp ALG1/ALG2 algorithms and
+// added a cusparseSpMVOpAlg_t parameter to cusparseSpMVOp_bufferSize/createDescr.
 // CUSPARSE_VERSION encoding: major*1000 + minor*100 + patch.
-#if defined(CUSPARSE_VERSION) && CUSPARSE_VERSION >= 12703
+#if defined(CUSPARSE_VERSION) && CUSPARSE_VERSION >= 12801
 #define CUPDLPX_HAS_SPMVOP 1
 #else
 #define CUPDLPX_HAS_SPMVOP 0
 #endif
-
-#if !CUPDLPX_HAS_SPMVOP
-// The SpMVOp types were added to cusparse.h before the functions
-// (e.g. CUDA 13.1 base has the types but not the functions).
-// Only provide fallback typedefs for cuSPARSE versions that lack them entirely.
-#if !defined(CUSPARSE_VERSION) || CUSPARSE_VERSION < 12700
-typedef void *cusparseSpMVOpDescr_t;
-typedef void *cusparseSpMVOpPlan_t;
-#endif
-#endif
diff --git a/src/spmv_backend.cu b/src/spmv_backend.cu
index 4b7618a..dd797ec 100644
--- a/src/spmv_backend.cu
+++ b/src/spmv_backend.cu
@@ -47,8 +47,15 @@ void cupdlpx_spmv_buffer_size(cusparseHandle_t sparse_handle,
                               size_t *buffer_size)
 {
 #if CUPDLPX_HAS_SPMVOP
-    CUSPARSE_CHECK(cusparseSpMVOp_bufferSize(
-        sparse_handle, CUSPARSE_OPERATION_NON_TRANSPOSE, mat, vec_x, vec_y, vec_y, CUDA_R_64F, buffer_size));
+    CUSPARSE_CHECK(cusparseSpMVOp_bufferSize(sparse_handle,
+                                             CUSPARSE_OPERATION_NON_TRANSPOSE,
+                                             mat,
+                                             vec_x,
+                                             vec_y,
+                                             vec_y,
+                                             CUDA_R_64F,
+                                             CUSPARSE_SPMVOP_ALG2,
+                                             buffer_size));
 #else
     CUSPARSE_CHECK(cusparseSpMV_bufferSize(sparse_handle,
                                            CUSPARSE_OPERATION_NON_TRANSPOSE,
@@ -74,8 +81,16 @@ void cupdlpx_spmv_prepare(cusparseHandle_t sparse_handle,
 #if CUPDLPX_HAS_SPMVOP
     cusparseSpMVOpDescr_t local_descr = NULL;
     cusparseSpMVOpPlan_t local_plan = NULL;
-    CUSPARSE_CHECK(cusparseSpMVOp_createDescr(
-        sparse_handle, &local_descr, CUSPARSE_OPERATION_NON_TRANSPOSE, mat, vec_x, vec_y, vec_y, CUDA_R_64F, buffer));
+    CUSPARSE_CHECK(cusparseSpMVOp_createDescr(sparse_handle,
+                                              &local_descr,
+                                              CUSPARSE_OPERATION_NON_TRANSPOSE,
+                                              mat,
+                                              vec_x,
+                                              vec_y,
+                                              vec_y,
+                                              CUDA_R_64F,
+                                              CUSPARSE_SPMVOP_ALG2,
+                                              buffer));
     CUSPARSE_CHECK(cusparseSpMVOp_createPlan(sparse_handle, local_descr, &local_plan, NULL, 0));
     *descr = (void *)local_descr;
     *plan = (void *)local_plan;