diff --git a/CMakeLists.txt b/CMakeLists.txt
index 1fd914848..6ab70455a 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -195,19 +195,87 @@ option(DEV_MODE "Build testing dev_test.cpp with cytnx" OFF)
 # #####################################################################
 project(CYTNX VERSION ${CYTNX_VERSION} LANGUAGES CXX C)
 
+# #####################################################################
+# ## HOST COMPILER REQUIREMENT
+# #####################################################################
+# Cytnx targets C++20 (CMAKE_CXX_STANDARD 20). The GCC floor is 13: earlier
+# releases lack the C++20 library/feature support the codebase relies on. Only
+# enforce this for GNU; Clang/AppleClang are validated separately on macOS.
+if(CMAKE_CXX_COMPILER_ID STREQUAL "GNU" AND CMAKE_CXX_COMPILER_VERSION VERSION_LESS 13)
+  message(FATAL_ERROR
+    "GCC >= 13 is required (C++20 support), but found GCC "
+    "${CMAKE_CXX_COMPILER_VERSION} at ${CMAKE_CXX_COMPILER}.\n"
+    "Install GCC 13+ and point CMake at it, e.g. "
+    "-DCMAKE_CXX_COMPILER=g++-13 (and -DCMAKE_C_COMPILER=gcc-13), "
+    "or set the CXX/CC environment variables.")
+endif()
+
 set(CMAKE_EXPORT_COMPILE_COMMANDS ON)
 if(USE_CUDA)
+  # Resolve the CUDA toolkit up front (before enable_language) so we can both
+  # enforce the version requirement early and choose an architecture list the
+  # toolkit can actually compile. find_package(CUDAToolkit) does not require the
+  # CUDA language to be enabled; the later find_package in CytnxBKNDCMakeLists
+  # re-uses this cached result.
+  find_package(CUDAToolkit QUIET)
+
+  # enable_language(CUDA) finds the compiler ONLY via CMAKE_CUDA_COMPILER, the
+  # CUDACXX environment variable, or nvcc on PATH -- it does not reuse the
+  # toolkit located above. Catch the "no usable nvcc" case here with an
+  # actionable message instead of CMake's terse "No CMAKE_CUDA_COMPILER could be
+  # found". Skip the check when the user pinned a compiler explicitly.
+  if(NOT CUDAToolkit_FOUND OR (NOT CUDAToolkit_NVCC_EXECUTABLE
+      AND NOT CMAKE_CUDA_COMPILER AND NOT DEFINED ENV{CUDACXX}))
+    message(FATAL_ERROR
+      "USE_CUDA is ON but no usable CUDA compiler (nvcc) could be found.\n"
+      "enable_language(CUDA) searches only CMAKE_CUDA_COMPILER, the CUDACXX "
+      "environment variable, and nvcc on PATH; it does not reuse the libraries "
+      "found by find_package(CUDAToolkit), so installed CUDA runtime/dev "
+      "packages alone are not enough.\n"
+      "Do one of the following, then delete the build directory (a stale "
+      "CMakeCache.txt caches the failed detection) and re-configure:\n"
+      "  * pass -DCMAKE_CUDA_COMPILER=/path/to/nvcc "
+      "(e.g. /usr/local/cuda-12/bin/nvcc), or\n"
+      "  * export CUDACXX=/path/to/nvcc, or\n"
+      "  * put the CUDA bin directory first on PATH "
+      "(export PATH=/usr/local/cuda-12/bin:$PATH).")
+  endif()
+
+  # CUDA requirement: >= 12.0, with 12.x and 13.x explicitly supported. The
+  # 12.0 floor comes from device-side C++20 (nvcc gained -std=c++20 in CUDA
+  # 12.0; 11.x tops out at C++17), matching CMAKE_CUDA_STANDARD 20. Fail early
+  # with an actionable message instead of a cryptic later C++20/arch error.
+  if(CUDAToolkit_VERSION VERSION_LESS 12.0)
+    message(FATAL_ERROR
+      "CUDA Toolkit >= 12.0 is required (device-side C++20 support), but found "
+      "${CUDAToolkit_VERSION} at ${CUDAToolkit_BIN_DIR}.\n"
+      "Install CUDA 12 or 13 and select it with "
+      "-DCMAKE_CUDA_COMPILER=/path/to/cuda-12+/bin/nvcc (or set CUDACXX / put "
+      "the desired nvcc first on PATH).")
+  elseif(CUDAToolkit_VERSION VERSION_GREATER_EQUAL 14.0)
+    message(WARNING
+      "CUDA Toolkit ${CUDAToolkit_VERSION} is newer than the versions Cytnx is "
+      "tested against (12.x and 13.x). The build will proceed; please report "
+      "any issues.")
+  endif()
+  message(STATUS " CUDA Toolkit: ${CUDAToolkit_VERSION} (supported: 12.x, 13.x)")
+
   # Default to a portable fat binary unless the caller picked architectures via
   # -D, the cache, a preset's cacheVariables, or the CUDAARCHS environment
   # variable. This must run before enable_language(CUDA): afterwards
   # CMAKE_CUDA_ARCHITECTURES is never empty (CMake fills in its own default), so
   # the "not specified" case can no longer be detected. enable_language(CUDA)
   # reads CUDAARCHS on its own, so we only avoid shadowing it here, not copy it.
-  # The default embeds SASS for each supported real architecture (Volta sm_70 is
-  # the floor required by cuTENSOR/cuQuantum, up through Hopper sm_90) plus PTX
-  # of the newest (90-virtual) so the driver can JIT for newer/unknown GPUs.
+  # The default embeds SASS for each supported real architecture plus PTX of the
+  # newest (90-virtual) so the driver can JIT for newer/unknown GPUs. CUDA 13.0
+  # removed offline support for compute capability < 7.5, so Volta sm_70 is only
+  # included for CUDA 12.x.
   if(NOT CMAKE_CUDA_ARCHITECTURES AND NOT DEFINED ENV{CUDAARCHS})
-    set(CMAKE_CUDA_ARCHITECTURES 70-real 75-real 80-real 86-real 89-real 90-real 90-virtual)
+    if(CUDAToolkit_VERSION VERSION_GREATER_EQUAL 13.0)
+      set(CMAKE_CUDA_ARCHITECTURES 75-real 80-real 86-real 89-real 90-real 90-virtual)
+    else()
+      set(CMAKE_CUDA_ARCHITECTURES 70-real 75-real 80-real 86-real 89-real 90-real 90-virtual)
+    endif()
   endif()
   enable_language(CUDA)
   # Disable generation of "--option-file" flag in compile_commands.json.
diff --git a/CytnxBKNDCMakeLists.cmake b/CytnxBKNDCMakeLists.cmake
index 9bfafb669..caa4b68ca 100644
--- a/CytnxBKNDCMakeLists.cmake
+++ b/CytnxBKNDCMakeLists.cmake
@@ -135,6 +135,9 @@ if(USE_CUDA)
     set(CYTNX_VARIANT_INFO "${CYTNX_VARIANT_INFO} UNI_CUDA")
 
     enable_language(CUDA)
+    # CUDA toolkit version is validated at the top level (CMakeLists.txt, before
+    # enable_language) so the architecture defaults can adapt to it; this call
+    # re-uses that cached result.
     find_package(CUDAToolkit REQUIRED)
     if(NOT DEFINED CMAKE_CUDA_STANDARD)
         set(CMAKE_CUDA_STANDARD 20)
@@ -231,8 +234,12 @@ if(USE_CUDA)
 
 
     message( STATUS " Build CUDA Support: YES")
-    message( STATUS "  - CUDA Version: ${CUDA_VERSION_STRING}")
-    message( STATUS "  - CUDA Toolkit Root: ${CUDA_TOOLKIT_ROOT_DIR}")
+    # Use the modern CUDAToolkit_* variables: the legacy FindCUDA variables
+    # (CUDA_VERSION_STRING / CUDA_TOOLKIT_ROOT_DIR) are not set by
+    # find_package(CUDAToolkit) and would print blank.
+    message( STATUS "  - CUDA Version: ${CUDAToolkit_VERSION}")
+    message( STATUS "  - CUDA Toolkit bin dir: ${CUDAToolkit_BIN_DIR}")
+    message( STATUS "  - CUDA compiler (nvcc): ${CMAKE_CUDA_COMPILER}")
     message( STATUS "  - Internal macro switch: GPU/CUDA")
     FILE(APPEND "${CMAKE_BINARY_DIR}/cxxflags.tmp" "-DUNI_GPU\n" "")
     message( STATUS "  - Cudatoolkit include dir: ${CUDAToolkit_INCLUDE_DIRS}")
diff --git a/cmake/Modules/FindCUQUANTUM.cmake b/cmake/Modules/FindCUQUANTUM.cmake
index dc134ad93..057870fe1 100644
--- a/cmake/Modules/FindCUQUANTUM.cmake
+++ b/cmake/Modules/FindCUQUANTUM.cmake
@@ -49,6 +49,18 @@ find_library(
 )
 message(STATUS "CUQUANTUM_TENSORNET_LIB: ${CUQUANTUM_TENSORNET_LIB}")
 message(STATUS "CUQUANTUM_CUSTATEVEC_LIB: ${CUQUANTUM_CUSTATEVEC_LIB}")
-set(CUQUANTUM_LIBRARIES "${CUQUANTUM_TENSORNET_LIB};${CUQUANTUM_CUSTATEVEC_LIB}")
-message(STATUS "ok")
-set(CUQUANTUM_FOUND TRUE)
+set(CUQUANTUM_LIBRARIES "")
+if(CUQUANTUM_TENSORNET_LIB)
+    list(APPEND CUQUANTUM_LIBRARIES "${CUQUANTUM_TENSORNET_LIB}")
+endif()
+if(CUQUANTUM_CUSTATEVEC_LIB)
+    list(APPEND CUQUANTUM_LIBRARIES "${CUQUANTUM_CUSTATEVEC_LIB}")
+endif()
+
+# CUQUANTUM_FOUND must reflect whether the libraries were actually located;
+# both cuTensorNet and cuStateVec are linked, so both are required. Setting it
+# unconditionally would let a NOTFOUND (e.g. an "...-NOTFOUND" entry on the link
+# line) silently pass the caller's REQUIRED check.
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(CUQUANTUM
+  REQUIRED_VARS CUQUANTUM_TENSORNET_LIB CUQUANTUM_CUSTATEVEC_LIB CUQUANTUM_INCLUDE_DIRS)
diff --git a/cmake/Modules/FindCUTENSOR.cmake b/cmake/Modules/FindCUTENSOR.cmake
index f9d15e707..c789afeee 100644
--- a/cmake/Modules/FindCUTENSOR.cmake
+++ b/cmake/Modules/FindCUTENSOR.cmake
@@ -27,22 +27,54 @@ else()
 endif()
 
 message(STATUS " cudaver: ${CUDAToolkit_VERSION_MAJOR}" )
-if(EXISTS "${CUTENSOR_ROOT}/lib")
-  set(CUTNLIB_DIR "lib/")
-endif()
-if((${CUDAToolkit_VERSION_MAJOR} LESS_EQUAL 10))
-  set(CUTNLIB_DIR "${CUTNLIB_DIR}10.2")
-elseif((${CUDAToolkit_VERSION_MAJOR} GREATER_EQUAL 11) AND (${CUDAToolkit_VERSION_MAJOR} LESS 12) AND (${CUDAToolkit_VERSION_MINOR} LESS_EQUAL 0))
-  set(CUTNLIB_DIR "${CUTNLIB_DIR}11.0")
-elseif((${CUDAToolkit_VERSION_MAJOR} GREATER_EQUAL 11) AND (${CUDAToolkit_VERSION_MAJOR} LESS 12) AND (${CUDAToolkit_VERSION_MINOR} GREATER_EQUAL 1))
-  set(CUTNLIB_DIR "${CUTNLIB_DIR}11")
-elseif((${CUDAToolkit_VERSION_MAJOR} GREATER_EQUAL 12))
-  set(CUTNLIB_DIR "${CUTNLIB_DIR}12")
+# Cytnx requires CUDA >= 12 (enforced in CMakeLists.txt) and cuTENSOR >= 2.0.
+# Search both library layouts: cuTENSOR 2.x tarballs place the libraries
+# directly under lib/, while 1.x tarballs and apt use a per-CUDA subdir
+# (lib/<cuda-major>, e.g. lib/12, lib/13). Listing both as find_library
+# PATH_SUFFIXES lets the supported 2.x flat layout and the legacy versioned
+# layout resolve for both CUDA 12 and 13. The older lib/10.2 and lib/11
+# branches were removed as dead code; apt multiarch paths remain (issue #946).
+if(CUDAToolkit_VERSION_MAJOR GREATER_EQUAL 12)
+  set(CUTNLIB_DIR lib lib/${CUDAToolkit_VERSION_MAJOR})
+else()
+  message(FATAL_ERROR
+    "cuTENSOR support requires CUDA >= 12, but CUDAToolkit_VERSION_MAJOR is "
+    "'${CUDAToolkit_VERSION_MAJOR}'.")
 endif()
 
-set(CUTENSOR_LIBRARY_DIRS ${CUTENSOR_ROOT}/${CUTNLIB_DIR})
 set(CUTENSOR_INCLUDE_DIRS ${CUTENSOR_ROOT}/include)
 
+# Require cuTENSOR >= 2.0. The version macros (CUTENSOR_MAJOR/MINOR/PATCH) live
+# in cutensor.h (older releases) or cutensor/types.h (newer ones); read whichever
+# defines them and fail early on the 1.x API, which Cytnx no longer supports.
+set(_cutensor_version_header "")
+foreach(_hdr "${CUTENSOR_INCLUDE_DIRS}/cutensor.h" "${CUTENSOR_INCLUDE_DIRS}/cutensor/types.h")
+  if(EXISTS "${_hdr}")
+    file(STRINGS "${_hdr}" _cutensor_major_line REGEX "^#define[ \t]+CUTENSOR_MAJOR[ \t]+[0-9]+")
+    if(_cutensor_major_line)
+      set(_cutensor_version_header "${_hdr}")
+      break()
+    endif()
+  endif()
+endforeach()
+
+if(_cutensor_version_header)
+  file(STRINGS "${_cutensor_version_header}" _cutensor_minor_line REGEX "^#define[ \t]+CUTENSOR_MINOR[ \t]+[0-9]+")
+  string(REGEX REPLACE ".*CUTENSOR_MAJOR[ \t]+([0-9]+).*" "\\1" CUTENSOR_VERSION_MAJOR "${_cutensor_major_line}")
+  string(REGEX REPLACE ".*CUTENSOR_MINOR[ \t]+([0-9]+).*" "\\1" CUTENSOR_VERSION_MINOR "${_cutensor_minor_line}")
+  set(CUTENSOR_VERSION "${CUTENSOR_VERSION_MAJOR}.${CUTENSOR_VERSION_MINOR}")
+  message(STATUS "cuTENSOR version: ${CUTENSOR_VERSION} (from ${_cutensor_version_header})")
+  if(CUTENSOR_VERSION_MAJOR LESS 2)
+    message(FATAL_ERROR
+      "cuTENSOR >= 2.0 is required, but found ${CUTENSOR_VERSION} in "
+      "${CUTENSOR_ROOT}. Install cuTENSOR 2.x and point CUTENSOR_ROOT at it.")
+  endif()
+else()
+  message(WARNING
+    "Could not determine the cuTENSOR version from headers under "
+    "${CUTENSOR_INCLUDE_DIRS}; Cytnx requires cuTENSOR >= 2.0.")
+endif()
+
 # set libs:
 find_library(
     CUTENSOR_LIB
@@ -60,6 +92,24 @@ find_library(
 )
 message(STATUS "CUTENSOR_LIB: ${CUTENSOR_LIB}")
 message(STATUS "CUTENSORMg_LIB: ${CUTENSORMg_LIB}")
-set(CUTENSOR_LIBRARIES "${CUTENSOR_LIB};${CUTENSORMg_LIB}")
-message(STATUS "ok")
-set(CUTENSOR_FOUND TRUE)
+# Report the directory the library was actually found in (flat lib/ or the
+# versioned lib/<major>) rather than guessing a subdir, so callers and runtime
+# guidance reference the real location.
+if(CUTENSOR_LIB)
+  get_filename_component(CUTENSOR_LIBRARY_DIRS "${CUTENSOR_LIB}" DIRECTORY)
+endif()
+set(CUTENSOR_LIBRARIES "")
+if(CUTENSOR_LIB)
+    list(APPEND CUTENSOR_LIBRARIES "${CUTENSOR_LIB}")
+endif()
+if(CUTENSORMg_LIB)
+    list(APPEND CUTENSOR_LIBRARIES "${CUTENSORMg_LIB}")
+endif()
+
+# CUTENSOR_FOUND must reflect whether the core library was actually located:
+# the main cutensor lib is mandatory, cutensorMg is optional. Setting it
+# unconditionally would let a NOTFOUND silently pass the caller's REQUIRED check.
+include(FindPackageHandleStandardArgs)
+find_package_handle_standard_args(CUTENSOR
+  REQUIRED_VARS CUTENSOR_LIB CUTENSOR_INCLUDE_DIRS
+  VERSION_VAR CUTENSOR_VERSION)
diff --git a/docs/source/adv_install.rst b/docs/source/adv_install.rst
index 1e928d2cc..f97fd19d0 100644
--- a/docs/source/adv_install.rst
+++ b/docs/source/adv_install.rst
@@ -29,9 +29,9 @@ In addition, you might want to install the following optional dependencies if yo
 
 [CUDA]
 
-* Nvidia cuda library v10+
+* Nvidia CUDA toolkit >= 12.0 (12.x and 13.x supported)
 * Nvidia cuDNN library
-* Nvidia cuTensor library
+* Nvidia cuTENSOR library >= 2.0
 * Nvidia cuQuantum library
 
 
@@ -155,6 +155,43 @@ Similarly, cuqauantum (compile option -DUSE_CUTENSOR=ON), requires:
 
     $conda install -c nvidia cuquantum
 
+.. important::
+
+    **If you install cuTENSOR and/or cuQuantum from NVIDIA tarballs**
+    (instead of conda), you must configure two separate paths -- one for the
+    build and one for runtime:
+
+    1. **Build time** -- point CMake at the extracted directories so the
+       libraries are found during configuration:
+
+       .. code-block:: shell
+
+           $export CUTENSOR_ROOT=/path/to/libcutensor-<version>
+           $export CUQUANTUM_ROOT=/path/to/cuquantum-<version>
+
+    2. **Runtime** -- the dynamic loader must also find the shared libraries
+       when you ``import cytnx`` (or run a C++ binary). Tarball libraries live
+       outside the system loader's default search path, and unlike conda they
+       are **not** registered with ``ldconfig``, so add their library
+       directories to ``LD_LIBRARY_PATH``:
+
+       .. code-block:: shell
+
+           $export LD_LIBRARY_PATH=$CUTENSOR_ROOT/lib:$CUQUANTUM_ROOT/lib:$LD_LIBRARY_PATH
+
+       For cuTENSOR 2.x tarballs the libraries sit directly under ``lib/``, so
+       the path above is sufficient at both build and runtime. Older cuTENSOR
+       1.x tarballs instead use a per-CUDA subdirectory (``lib/<cuda-major>``,
+       e.g. ``lib/12``); on that legacy layout point ``LD_LIBRARY_PATH`` at the
+       subdirectory. Cytnx's ``FindCUTENSOR`` searches both layouts at build
+       time, so the runtime path matches whichever one was found. If
+       ``LD_LIBRARY_PATH`` is not set
+       up, importing/running Cytnx fails with ``error while loading shared
+       libraries: libcutensor.so... cannot open shared object file``, or
+       silently binds to a mismatched system copy of the library if one is
+       present. Add these ``export`` lines to your shell profile (e.g.
+       ``~/.bashrc``) to make them persistent.
+
 **Option B. Install dependencies via system package manager**
 
 You can also choose to install dependencies directly from the system package manager, but one needs to carefully resolve the dependency path for cmake to capture them successfully.
@@ -345,6 +382,61 @@ In the case that Cytnx is installed locally from binary build, not from anaconda
 Build troubleshooting
 *************************************
 
+Choosing between CUDA 12 and CUDA 13 when both are installed
+-------------------------------------------------------------------------------------
+
+Cytnx supports both CUDA 12.x and 13.x. If more than one CUDA toolkit is present
+(for example CUDA 12 installed via ``apt`` and CUDA 13 unpacked under
+``/usr/local/cuda-13``), you must select the one to build against; otherwise
+CMake picks up whichever ``nvcc`` it finds first on ``PATH``, which may not be
+the one you intended. There are two independent things to pin -- the **build**
+toolkit and the **runtime** libraries.
+
+**1. Build time -- select the compiler.** ``enable_language(CUDA)`` finds the
+compiler only from ``CMAKE_CUDA_COMPILER``, the ``CUDACXX`` environment
+variable, or ``nvcc`` on ``PATH`` (it does *not* reuse the libraries found by
+``find_package(CUDAToolkit)``). Point it at the toolkit you want -- the rest of
+the toolkit (libraries, headers, version) is then derived from that ``nvcc``:
+
+.. code-block:: shell
+
+    # Use CUDA 13:
+    $cmake -S . -B build -DUSE_CUDA=ON -DCMAKE_CUDA_COMPILER=/usr/local/cuda-13/bin/nvcc
+
+    # ...or use CUDA 12:
+    $cmake -S . -B build -DUSE_CUDA=ON -DCMAKE_CUDA_COMPILER=/usr/local/cuda-12/bin/nvcc
+
+Equivalent alternatives are ``export CUDACXX=/usr/local/cuda-13/bin/nvcc`` or
+putting the desired ``bin`` directory first on ``PATH``
+(``export PATH=/usr/local/cuda-13/bin:$PATH``). For the ``pip`` build, pass it
+through scikit-build-core:
+
+.. code-block:: shell
+
+    $pip install . --config-settings=cmake.args="-DUSE_CUDA=ON;-DCMAKE_CUDA_COMPILER=/usr/local/cuda-13/bin/nvcc"
+
+The configure output reports the resolved toolkit (``CUDA Version``,
+``CUDA Toolkit bin dir``, ``CUDA compiler (nvcc)``) -- check these match the
+version you intended. CMake caches the detected compiler, so if you previously
+configured with the wrong one, delete the build directory before reconfiguring;
+a stale ``CMakeCache.txt`` keeps the old choice.
+
+**2. Runtime -- match the shared libraries.** Selecting the compiler does not
+control which CUDA runtime libraries are loaded at run time. The dynamic loader
+resolves ``libcudart.so.<major>`` (and cuTENSOR/cuQuantum, etc.) via
+``LD_LIBRARY_PATH``, then the ``ldconfig`` cache. If a different major version is
+registered with ``ldconfig`` (commonly the ``apt`` copy under
+``/usr/lib/x86_64-linux-gnu``), it can be loaded instead of the toolkit you
+built against, causing version-skew crashes. To force the matching runtime, put
+its library directory first:
+
+.. code-block:: shell
+
+    $export LD_LIBRARY_PATH=/usr/local/cuda-13/lib64:$LD_LIBRARY_PATH
+
+(Adjust the path to the toolkit you built against; append the cuTENSOR/cuQuantum
+``lib`` directories too if you enabled them -- see the tarball note above.)
+
 CUDA device link fails with ``elfLink linker library load error``
 -------------------------------------------------------------------------------------