diff --git a/libs/pika/algorithms/CMakeLists.txt b/libs/pika/algorithms/CMakeLists.txt
index e1d3bf74f1..8dd34e943f 100644
--- a/libs/pika/algorithms/CMakeLists.txt
+++ b/libs/pika/algorithms/CMakeLists.txt
@@ -175,6 +175,12 @@ set(algorithms_headers
     pika/parallel/util/detail/scoped_executor_parameters.hpp
     pika/parallel/util/detail/select_partitioner.hpp
     pika/parallel/util/detail/sender_util.hpp
+    pika/parallel/util/detail/simd/vector_pack_alignment_size.hpp
+    pika/parallel/util/detail/simd/vector_pack_all_any_none.hpp
+    pika/parallel/util/detail/simd/vector_pack_count_bits.hpp
+    pika/parallel/util/detail/simd/vector_pack_find.hpp
+    pika/parallel/util/detail/simd/vector_pack_load_store.hpp
+    pika/parallel/util/detail/simd/vector_pack_type.hpp
     pika/parallel/util/foreach_partitioner.hpp
     pika/parallel/util/invoke_projected.hpp
     pika/parallel/util/loop.hpp
@@ -192,6 +198,12 @@ set(algorithms_headers
     pika/parallel/util/scan_partitioner.hpp
     pika/parallel/util/transfer.hpp
     pika/parallel/util/transform_loop.hpp
+    pika/parallel/util/vector_pack_alignment_size.hpp
+    pika/parallel/util/vector_pack_all_any_none.hpp
+    pika/parallel/util/vector_pack_count_bits.hpp
+    pika/parallel/util/vector_pack_find.hpp
+    pika/parallel/util/vector_pack_load_store.hpp
+    pika/parallel/util/vector_pack_type.hpp
     pika/parallel/util/zip_iterator.hpp
 )
 
diff --git a/libs/pika/algorithms/include/pika/algorithms/traits/projected.hpp b/libs/pika/algorithms/include/pika/algorithms/traits/projected.hpp
index 6048cc9837..237566939d 100644
--- a/libs/pika/algorithms/include/pika/algorithms/traits/projected.hpp
+++ b/libs/pika/algorithms/include/pika/algorithms/traits/projected.hpp
@@ -8,11 +8,11 @@
 
 #include <pika/config.hpp>
 #include <pika/execution/traits/is_execution_policy.hpp>
-#include <pika/execution/traits/vector_pack_load_store.hpp>
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/functional/invoke_result.hpp>
 #include <pika/functional/traits/is_invocable.hpp>
 #include <pika/iterator_support/traits/is_iterator.hpp>
+#include <pika/parallel/util/vector_pack_load_store.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 #include <pika/type_support/pack.hpp>
 
 #include <iterator>
diff --git a/libs/pika/algorithms/include/pika/parallel/algorithms/count.hpp b/libs/pika/algorithms/include/pika/parallel/algorithms/count.hpp
index c8f19e4ffa..0f93cd1eef 100644
--- a/libs/pika/algorithms/include/pika/parallel/algorithms/count.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/algorithms/count.hpp
@@ -162,7 +162,6 @@ namespace pika {
 #include <pika/parallel/util/detail/sender_util.hpp>
 
 #include <pika/algorithms/traits/projected.hpp>
-#include <pika/execution/traits/vector_pack_count_bits.hpp>
 #include <pika/executors/execution_policy.hpp>
 #include <pika/parallel/algorithms/detail/dispatch.hpp>
 #include <pika/parallel/algorithms/detail/distance.hpp>
@@ -170,6 +169,7 @@ namespace pika {
 #include <pika/parallel/util/invoke_projected.hpp>
 #include <pika/parallel/util/loop.hpp>
 #include <pika/parallel/util/partitioner.hpp>
+#include <pika/parallel/util/vector_pack_count_bits.hpp>
 
 #include <algorithm>
 #include <cstddef>
diff --git a/libs/pika/algorithms/include/pika/parallel/datapar/find.hpp b/libs/pika/algorithms/include/pika/parallel/datapar/find.hpp
index 1784322ca7..f2d52d22fe 100644
--- a/libs/pika/algorithms/include/pika/parallel/datapar/find.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/datapar/find.hpp
@@ -10,14 +10,14 @@
 
 #if defined(PIKA_HAVE_DATAPAR)
 #include <pika/execution/traits/is_execution_policy.hpp>
-#include <pika/execution/traits/vector_pack_all_any_none.hpp>
-#include <pika/execution/traits/vector_pack_find.hpp>
 #include <pika/functional/tag_invoke.hpp>
 #include <pika/parallel/algorithms/detail/find.hpp>
 #include <pika/parallel/datapar/iterator_helpers.hpp>
 #include <pika/parallel/datapar/loop.hpp>
 #include <pika/parallel/datapar/zip_iterator.hpp>
 #include <pika/parallel/util/result_types.hpp>
+#include <pika/parallel/util/vector_pack_all_any_none.hpp>
+#include <pika/parallel/util/vector_pack_find.hpp>
 
 #include <cstddef>
 #include <type_traits>
diff --git a/libs/pika/algorithms/include/pika/parallel/datapar/generate.hpp b/libs/pika/algorithms/include/pika/parallel/datapar/generate.hpp
index 7a26670b89..24ff077379 100644
--- a/libs/pika/algorithms/include/pika/parallel/datapar/generate.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/datapar/generate.hpp
@@ -10,13 +10,13 @@
 
 #if defined(PIKA_HAVE_DATAPAR)
 #include <pika/execution/traits/is_execution_policy.hpp>
-#include <pika/execution/traits/vector_pack_alignment_size.hpp>
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/functional/tag_invoke.hpp>
 #include <pika/parallel/algorithms/detail/generate.hpp>
 #include <pika/parallel/datapar/iterator_helpers.hpp>
 #include <pika/parallel/datapar/loop.hpp>
 #include <pika/parallel/util/result_types.hpp>
+#include <pika/parallel/util/vector_pack_alignment_size.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 
 #include <cstddef>
 #include <cstdint>
diff --git a/libs/pika/algorithms/include/pika/parallel/datapar/iterator_helpers.hpp b/libs/pika/algorithms/include/pika/parallel/datapar/iterator_helpers.hpp
index b948dfb33f..b6b09dd311 100644
--- a/libs/pika/algorithms/include/pika/parallel/datapar/iterator_helpers.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/datapar/iterator_helpers.hpp
@@ -10,12 +10,12 @@
 
 #if defined(PIKA_HAVE_DATAPAR)
 #include <pika/assert.hpp>
-#include <pika/execution/traits/vector_pack_alignment_size.hpp>
-#include <pika/execution/traits/vector_pack_load_store.hpp>
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/functional/detail/invoke.hpp>
 #include <pika/functional/invoke_result.hpp>
 #include <pika/iterator_support/traits/is_iterator.hpp>
+#include <pika/parallel/util/vector_pack_alignment_size.hpp>
+#include <pika/parallel/util/vector_pack_load_store.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 
 #include <cstddef>
 #include <iterator>
diff --git a/libs/pika/algorithms/include/pika/parallel/datapar/loop.hpp b/libs/pika/algorithms/include/pika/parallel/datapar/loop.hpp
index 40d844f920..553aa99532 100644
--- a/libs/pika/algorithms/include/pika/parallel/datapar/loop.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/datapar/loop.hpp
@@ -10,15 +10,15 @@
 
 #if defined(PIKA_HAVE_DATAPAR)
 #include <pika/execution/traits/is_execution_policy.hpp>
-#include <pika/execution/traits/vector_pack_alignment_size.hpp>
-#include <pika/execution/traits/vector_pack_load_store.hpp>
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/executors/datapar/execution_policy.hpp>
 #include <pika/executors/execution_policy.hpp>
 #include <pika/functional/tag_invoke.hpp>
 #include <pika/parallel/algorithms/detail/predicates.hpp>
 #include <pika/parallel/datapar/iterator_helpers.hpp>
 #include <pika/parallel/util/loop.hpp>
+#include <pika/parallel/util/vector_pack_alignment_size.hpp>
+#include <pika/parallel/util/vector_pack_load_store.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 
 #include <algorithm>
 #include <cstddef>
diff --git a/libs/pika/algorithms/include/pika/parallel/datapar/zip_iterator.hpp b/libs/pika/algorithms/include/pika/parallel/datapar/zip_iterator.hpp
index 893e0f86b8..8fe597dbfb 100644
--- a/libs/pika/algorithms/include/pika/parallel/datapar/zip_iterator.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/datapar/zip_iterator.hpp
@@ -14,10 +14,10 @@
 #include <pika/iterator_support/zip_iterator.hpp>
 #include <pika/type_support/pack.hpp>
 
-#include <pika/execution/traits/vector_pack_alignment_size.hpp>
-#include <pika/execution/traits/vector_pack_load_store.hpp>
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/parallel/datapar/iterator_helpers.hpp>
+#include <pika/parallel/util/vector_pack_alignment_size.hpp>
+#include <pika/parallel/util/vector_pack_load_store.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 
 #include <algorithm>
 #include <cstddef>
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_alignment_size.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_alignment_size.hpp
similarity index 96%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_alignment_size.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_alignment_size.hpp
index 858073994f..ef4e189da8 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_alignment_size.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_alignment_size.hpp
@@ -67,7 +67,7 @@ namespace pika::parallel::traits::detail {
 }    // namespace pika::parallel::traits::detail
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_alignment_size.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_alignment_size.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_all_any_none.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_all_any_none.hpp
similarity index 82%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_all_any_none.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_all_any_none.hpp
index 9dbbad4559..87f156b179 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_all_any_none.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_all_any_none.hpp
@@ -11,7 +11,7 @@
 #if defined(PIKA_HAVE_DATAPAR)
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_all_any_none.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_all_any_none.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_count_bits.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_count_bits.hpp
similarity index 90%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_count_bits.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_count_bits.hpp
index 504f96ec76..0fa546e2c8 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_count_bits.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_count_bits.hpp
@@ -21,7 +21,7 @@ namespace pika::parallel::traits::detail {
 #if defined(PIKA_HAVE_DATAPAR)
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_count_bits.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_count_bits.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_find.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_find.hpp
similarity index 84%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_find.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_find.hpp
index e2596ce3b9..b8dcfc3ac1 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_find.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_find.hpp
@@ -11,7 +11,7 @@
 #if defined(PIKA_HAVE_DATAPAR)
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_find.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_find.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_load_store.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_load_store.hpp
similarity index 91%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_load_store.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_load_store.hpp
index 106b644e5c..65548d6551 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_load_store.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_load_store.hpp
@@ -23,7 +23,7 @@ namespace pika::parallel::traits::detail {
 }    // namespace pika::parallel::traits::detail
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_load_store.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_load_store.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/execution/include/pika/execution/traits/vector_pack_type.hpp b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_type.hpp
similarity index 93%
rename from libs/pika/execution/include/pika/execution/traits/vector_pack_type.hpp
rename to libs/pika/algorithms/include/pika/parallel/util/vector_pack_type.hpp
index 94cae43c57..0c84b7f03c 100644
--- a/libs/pika/execution/include/pika/execution/traits/vector_pack_type.hpp
+++ b/libs/pika/algorithms/include/pika/parallel/util/vector_pack_type.hpp
@@ -32,7 +32,7 @@ namespace pika::parallel::traits::detail {
 }    // namespace pika::parallel::traits::detail
 
 #if !defined(__CUDACC__)
-#include <pika/execution/traits/detail/simd/vector_pack_type.hpp>
+#include <pika/parallel/util/detail/simd/vector_pack_type.hpp>
 #endif
 
 #endif
diff --git a/libs/pika/algorithms/tests/unit/datapar_algorithms/generate_tests.hpp b/libs/pika/algorithms/tests/unit/datapar_algorithms/generate_tests.hpp
index 9041b2bfcf..6943b09db9 100644
--- a/libs/pika/algorithms/tests/unit/datapar_algorithms/generate_tests.hpp
+++ b/libs/pika/algorithms/tests/unit/datapar_algorithms/generate_tests.hpp
@@ -8,10 +8,10 @@
 
 #pragma once
 
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/init.hpp>
 #include <pika/parallel/algorithms/generate.hpp>
 #include <pika/parallel/datapar.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 #include <pika/testing.hpp>
 
 #include <cstddef>
diff --git a/libs/pika/algorithms/tests/unit/datapar_algorithms/generaten_tests.hpp b/libs/pika/algorithms/tests/unit/datapar_algorithms/generaten_tests.hpp
index 7d75155bd5..8dd26606a7 100644
--- a/libs/pika/algorithms/tests/unit/datapar_algorithms/generaten_tests.hpp
+++ b/libs/pika/algorithms/tests/unit/datapar_algorithms/generaten_tests.hpp
@@ -7,10 +7,10 @@
 
 #pragma once
 
-#include <pika/execution/traits/vector_pack_type.hpp>
 #include <pika/init.hpp>
 #include <pika/parallel/algorithms/generate.hpp>
 #include <pika/parallel/datapar.hpp>
+#include <pika/parallel/util/vector_pack_type.hpp>
 #include <pika/testing.hpp>
 
 #include <cstddef>
diff --git a/libs/pika/execution/CMakeLists.txt b/libs/pika/execution/CMakeLists.txt
index 1692ace86b..1591b365ed 100644
--- a/libs/pika/execution/CMakeLists.txt
+++ b/libs/pika/execution/CMakeLists.txt
@@ -46,21 +46,9 @@ set(execution_headers
     pika/execution/executors/rebind_executor.hpp
     pika/execution/executors/static_chunk_size.hpp
     pika/execution/scheduler_queries.hpp
-    pika/execution/traits/detail/simd/vector_pack_alignment_size.hpp
-    pika/execution/traits/detail/simd/vector_pack_all_any_none.hpp
-    pika/execution/traits/detail/simd/vector_pack_count_bits.hpp
-    pika/execution/traits/detail/simd/vector_pack_find.hpp
-    pika/execution/traits/detail/simd/vector_pack_load_store.hpp
-    pika/execution/traits/detail/simd/vector_pack_type.hpp
     pika/execution/traits/executor_traits.hpp
     pika/execution/traits/future_then_result_exec.hpp
     pika/execution/traits/is_execution_policy.hpp
-    pika/execution/traits/vector_pack_alignment_size.hpp
-    pika/execution/traits/vector_pack_all_any_none.hpp
-    pika/execution/traits/vector_pack_count_bits.hpp
-    pika/execution/traits/vector_pack_find.hpp
-    pika/execution/traits/vector_pack_load_store.hpp
-    pika/execution/traits/vector_pack_type.hpp
 )
 
 set(execution_sources execution_parameter_callbacks.cpp)
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_alignment_size.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_alignment_size.hpp
deleted file mode 100644
index 233d84210d..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_alignment_size.hpp
+++ /dev/null
@@ -1,123 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//  Copyright (c) 2016-2017 Hartmut Kaiser
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-#include <cstddef>
-#include <type_traits>
-
-#include <experimental/simd>
-
-namespace pika::parallel::traits::detail {
-    template <typename T>
-    struct is_vector_pack<std::experimental::native_simd<T>> : std::true_type
-    {
-    };
-
-    template <typename T>
-    struct is_vector_pack<
-        std::experimental::simd<T, std::experimental::simd_abi::fixed_size<1>>>
-      : std::false_type
-    {
-    };
-
-    template <typename T>
-    struct is_vector_pack<
-        std::experimental::simd<T, std::experimental::simd_abi::scalar>>
-      : std::false_type
-    {
-    };
-
-    ///////////////////////////////////////////////////////////////////////////
-    template <typename T>
-    struct is_scalar_vector_pack<std::experimental::native_simd<T>>
-      : std::false_type
-    {
-    };
-
-    template <typename T>
-    struct is_scalar_vector_pack<
-        std::experimental::simd<T, std::experimental::simd_abi::fixed_size<1>>>
-      : std::true_type
-    {
-    };
-
-    template <typename T>
-    struct is_scalar_vector_pack<
-        std::experimental::simd<T, std::experimental::simd_abi::scalar>>
-      : std::true_type
-    {
-    };
-
-    ///////////////////////////////////////////////////////////////////////////
-    template <typename T, typename Enable>
-    struct vector_pack_alignment
-    {
-        static std::size_t const value = std::experimental::memory_alignment_v<
-            std::experimental::native_simd<T>>;
-    };
-
-    template <typename T, typename Abi>
-    struct vector_pack_alignment<std::experimental::simd<T, Abi>>
-    {
-        static std::size_t const value = std::experimental::memory_alignment_v<
-            std::experimental::simd<T, Abi>>;
-    };
-
-    template <typename T>
-    struct vector_pack_alignment<
-        std::experimental::simd<T, std::experimental::simd_abi::scalar>>
-    {
-        static std::size_t const value = std::experimental::memory_alignment_v<
-            std::experimental::simd<T, std::experimental::simd_abi::scalar>>;
-    };
-
-    template <typename T>
-    struct vector_pack_alignment<
-        std::experimental::simd<T, std::experimental::simd_abi::fixed_size<1>>>
-    {
-        static std::size_t const value =
-            std::experimental::memory_alignment_v<std::experimental::simd<T,
-                std::experimental::simd_abi::fixed_size<1>>>;
-    };
-
-    ///////////////////////////////////////////////////////////////////////////
-    template <typename T, typename Enable>
-    struct vector_pack_size
-    {
-        static std::size_t const value =
-            std::experimental::native_simd<T>::size();
-    };
-
-    template <typename T, typename Abi>
-    struct vector_pack_size<std::experimental::simd<T, Abi>>
-    {
-        static std::size_t const value =
-            std::experimental::simd<T, Abi>::size();
-    };
-
-    template <typename T>
-    struct vector_pack_size<
-        std::experimental::simd<T, std::experimental::simd_abi::scalar>>
-    {
-        static std::size_t const value = std::experimental::simd<T,
-            std::experimental::simd_abi::scalar>::size();
-    };
-
-    template <typename T>
-    struct vector_pack_size<
-        std::experimental::simd<T, std::experimental::simd_abi::fixed_size<1>>>
-    {
-        static std::size_t const value = std::experimental::simd<T,
-            std::experimental::simd_abi::fixed_size<1>>::size();
-    };
-}    // namespace pika::parallel::traits::detail
-
-#endif
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_all_any_none.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_all_any_none.hpp
deleted file mode 100644
index 51a12e1cca..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_all_any_none.hpp
+++ /dev/null
@@ -1,41 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-#include <cstddef>
-
-#include <experimental/simd>
-
-namespace pika::parallel::traits::detail {
-    template <typename T, typename Abi>
-    PIKA_HOST_DEVICE PIKA_FORCEINLINE std::size_t
-    all_of(std::experimental::simd_mask<T, Abi> const& msk)
-    {
-        return std::experimental::all_of(msk);
-    }
-
-    ///////////////////////////////////////////////////////////////////////
-    template <typename T, typename Abi>
-    PIKA_HOST_DEVICE PIKA_FORCEINLINE std::size_t
-    any_of(std::experimental::simd_mask<T, Abi> const& msk)
-    {
-        return std::experimental::any_of(msk);
-    }
-
-    ///////////////////////////////////////////////////////////////////////
-    template <typename T, typename Abi>
-    PIKA_HOST_DEVICE PIKA_FORCEINLINE std::size_t
-    none_of(std::experimental::simd_mask<T, Abi> const& msk)
-    {
-        return std::experimental::none_of(msk);
-    }
-}    // namespace pika::parallel::traits::detail
-
-#endif
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_count_bits.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_count_bits.hpp
deleted file mode 100644
index d82b2dc4e7..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_count_bits.hpp
+++ /dev/null
@@ -1,26 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//  Copyright (c) 2016-2017 Hartmut Kaiser
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-#include <cstddef>
-
-#include <experimental/simd>
-
-namespace pika::parallel::traits::detail {
-    template <typename T, typename Abi>
-    PIKA_HOST_DEVICE PIKA_FORCEINLINE std::size_t
-    count_bits(std::experimental::simd_mask<T, Abi> const& mask)
-    {
-        return std::experimental::popcount(mask);
-    }
-}    // namespace pika::parallel::traits::detail
-
-#endif
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_find.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_find.hpp
deleted file mode 100644
index a511b9839e..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_find.hpp
+++ /dev/null
@@ -1,29 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-#include <cstddef>
-
-#include <experimental/simd>
-
-namespace pika::parallel::traits::detail {
-    template <typename T, typename Abi>
-    PIKA_HOST_DEVICE PIKA_FORCEINLINE int
-    find_first_of(std::experimental::simd_mask<T, Abi> const& msk)
-    {
-        if (std::experimental::any_of(msk))
-        {
-            return std::experimental::find_first_set(msk);
-        }
-        return -1;
-    }
-}    // namespace pika::parallel::traits::detail
-
-#endif
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_load_store.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_load_store.hpp
deleted file mode 100644
index 1e31d8f56f..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_load_store.hpp
+++ /dev/null
@@ -1,56 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//  Copyright (c) 2016-2017 Hartmut Kaiser
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-#include <cstddef>
-#include <iterator>
-#include <memory>
-
-#include <experimental/simd>
-
-namespace pika::parallel::traits::detail {
-    template <typename V, typename ValueType, typename Enable>
-    struct vector_pack_load
-    {
-        template <typename Iter>
-        static V aligned(Iter const& iter)
-        {
-            return V(std::addressof(*iter), std::experimental::vector_aligned);
-        }
-
-        template <typename Iter>
-        static V unaligned(Iter const& iter)
-        {
-            return V(std::addressof(*iter), std::experimental::element_aligned);
-        }
-    };
-
-    ///////////////////////////////////////////////////////////////////////////
-    template <typename V, typename ValueType, typename Enable>
-    struct vector_pack_store
-    {
-        template <typename Iter>
-        static void aligned(V& value, Iter const& iter)
-        {
-            value.copy_to(
-                std::addressof(*iter), std::experimental::vector_aligned);
-        }
-
-        template <typename Iter>
-        static void unaligned(V& value, Iter const& iter)
-        {
-            value.copy_to(
-                std::addressof(*iter), std::experimental::element_aligned);
-        }
-    };
-}    // namespace pika::parallel::traits::detail
-
-#endif
diff --git a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_type.hpp b/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_type.hpp
deleted file mode 100644
index 95b0450f91..0000000000
--- a/libs/pika/execution/include/pika/execution/traits/detail/simd/vector_pack_type.hpp
+++ /dev/null
@@ -1,49 +0,0 @@
-//  Copyright (c) 2021 Srinivas Yadav
-//  Copyright (c) 2016-2017 Hartmut Kaiser
-//
-//  SPDX-License-Identifier: BSL-1.0
-//  Distributed under the Boost Software License, Version 1.0. (See accompanying
-//  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#pragma once
-
-#include <pika/config.hpp>
-
-#if defined(PIKA_HAVE_CXX20_EXPERIMENTAL_SIMD)
-
-#include <experimental/simd>
-
-#include <cstddef>
-#include <type_traits>
-
-namespace pika::parallel::traits::detail {
-    template <typename T, std::size_t N, typename Abi>
-    struct vector_pack_type_impl
-    {
-        using type = std::experimental::fixed_size_simd<T, N>;
-    };
-
-    template <typename T, typename Abi>
-    struct vector_pack_type_impl<T, 0, Abi>
-    {
-        typedef typename std::conditional<std::is_void<Abi>::value,
-            std::experimental::simd_abi::native<T>, Abi>::type abi_type;
-
-        using type = std::experimental::simd<T, abi_type>;
-    };
-
-    template <typename T, typename Abi>
-    struct vector_pack_type_impl<T, 1, Abi>
-    {
-        typedef std::experimental::simd<T, std::experimental::simd_abi::scalar>
-            type;
-    };
-
-    ///////////////////////////////////////////////////////////////////////////
-    template <typename T, std::size_t N, typename Abi>
-    struct vector_pack_type : vector_pack_type_impl<T, N, Abi>
-    {
-    };
-}    // namespace pika::parallel::traits::detail
-
-#endif