diff --git a/.github/CHANGELOG.md b/.github/CHANGELOG.md
index c69337b9..b0cd32fb 100644
--- a/.github/CHANGELOG.md
+++ b/.github/CHANGELOG.md
@@ -2,10 +2,11 @@
 
 ### New features since last release
 
-* Running CMake with `-DBUILD_PYTHON=ON` now generates Python bindings within a `jet` package. [(#1)](https://github.com/XanaduAI/jet/pull/1)
-
 ### Improvements
 
+* `Tensor` class now checks data type at compile-time. [(#4)](https://github.com/XanaduAI/jet/pull/4)
+* Running CMake with `-DBUILD_PYTHON=ON` now generates Python bindings within a `jet` package. [(#1)](https://github.com/XanaduAI/jet/pull/1)
+
 ### Breaking Changes
 
 ### Bug Fixes
@@ -16,7 +17,7 @@
 
 This release contains contributions from (in alphabetical order):
 
-[Mikhail Andrenkov](https://github.com/Mandrenkov) and [Jack Brown](https://github.com/brownj85).
+[Mikhail Andrenkov](https://github.com/Mandrenkov), [Jack Brown](https://github.com/brownj85).
 
 ## Release 0.1.0 (current release)
 
diff --git a/include/jet/Tensor.hpp b/include/jet/Tensor.hpp
index b58203bc..0c091f1f 100644
--- a/include/jet/Tensor.hpp
+++ b/include/jet/Tensor.hpp
@@ -37,6 +37,10 @@ namespace Jet {
  */
 template <class T = std::complex<float>> class Tensor {
 
+    static_assert(TensorHelpers::is_supported_data_type<T>,
+                  "Tensor data type must be one of std::complex<float>, "
+                  "std::complex<double>");
+
   private:
     std::vector<std::string> indices_;
     std::vector<size_t> shape_;
@@ -679,4 +683,4 @@ inline std::ostream &operator<<(std::ostream &out, const Tensor<T> &tensor)
     return out;
 }
 
-}; // namespace Jet
\ No newline at end of file
+}; // namespace Jet
diff --git a/include/jet/TensorHelpers.hpp b/include/jet/TensorHelpers.hpp
index 19d9947c..99074f1d 100644
--- a/include/jet/TensorHelpers.hpp
+++ b/include/jet/TensorHelpers.hpp
@@ -17,6 +17,19 @@
 namespace Jet {
 namespace TensorHelpers {
 
+/**
+ * If T is a supported data type for tensors, this expression will
+ * evaluate to `true`. Otherwise, it will evaluate to `false`.
+ *
+ * Supported data types are std::complex<float> and std::complex<double>.
+ *
+ * @tparam T candidate data type
+ */
+template <class T>
+constexpr bool is_supported_data_type =
+    std::is_same_v<T, std::complex<float>> ||
+    std::is_same_v<T, std::complex<double>>;
+
 /**
  * @brief Compile-time binding for BLAS GEMM operation (matrix-matrix product).
  *
@@ -45,9 +58,6 @@ gemmBinding(size_t m, size_t n, size_t k, ComplexPrecision alpha,
         cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, m, n, k, &alpha,
                     A_data, std::max(1ul, k), B_data, std::max(1ul, n), &beta,
                     C_data, std::max(1ul, n));
-    else
-        JET_ABORT(
-            "Please use complex<float> or complex<double for Tensor data");
 };
 
 /**
@@ -75,9 +85,6 @@ gemvBinding(size_t m, size_t k, ComplexPrecision alpha, ComplexPrecision beta,
     else if constexpr (std::is_same_v<ComplexPrecision, std::complex<double>>)
         cblas_zgemv(CblasRowMajor, CblasNoTrans, m, k, (&alpha), (A_data),
                     std::max(1ul, k), (B_data), 1, (&beta), (C_data), 1);
-    else
-        JET_ABORT(
-            "Please use complex<float> or complex<double for Tensor data");
 };
 
 /**
@@ -100,9 +107,6 @@ constexpr void dotuBinding(size_t k, const ComplexPrecision *A_data,
         cblas_cdotu_sub(k, (A_data), 1, (B_data), 1, (C_data));
     else if constexpr (std::is_same_v<ComplexPrecision, std::complex<double>>)
         cblas_zdotu_sub(k, (A_data), 1, (B_data), 1, (C_data));
-    else
-        JET_ABORT(
-            "Please use complex<float> or complex<double for Tensor data");
 };
 
 /**
@@ -120,7 +124,9 @@ constexpr void dotuBinding(size_t k, const ComplexPrecision *A_data,
  * @param right_dim Columns in right tensor B and resulting tensor C.
  * @param common_dim Rows in left tensor A and columns in right tensor B.
  */
-template <typename ComplexPrecision>
+template <
+    typename ComplexPrecision,
+    std::enable_if_t<is_supported_data_type<ComplexPrecision>, bool> = true>
 inline void MultiplyTensorData(const std::vector<ComplexPrecision> &A,
                                const std::vector<ComplexPrecision> &B,
                                std::vector<ComplexPrecision> &C,