Add var support to LTensor

.github/CHANGELOG.md

@@ -2,6 +2,9 @@
 
 ### New features since last release
 
+* Add `var` support to `lightning.tensor`. Note that `var` support is added via `obs**2` and this implementation scales `O(num_obs**2)`.
+  [(#804)](https://github.com/PennyLaneAI/pennylane-lightning/pull/804) 
+
 ### Breaking changes
 
 * Remove `NDpermuter.hpp` which is no longer required.

pennylane_lightning/core/_version.py

@@ -16,4 +16,4 @@
    Version number (major.minor.patch[-label])
 """
 
-__version__ = "0.38.0-dev21"
+__version__ = "0.38.0-dev22"

pennylane_lightning/core/src/bindings/Bindings.hpp

@@ -727,12 +727,19 @@ template <class TensorNetT, class PyClass>
 void registerLightningTensorBackendAgnosticMeasurements(PyClass &pyclass) {
     using MeasurementsT = MeasurementsTNCuda<TensorNetT>;
     using ObservableT = ObservableTNCuda<TensorNetT>;
-    pyclass.def(
-        "expval",
-        [](MeasurementsT &M, const std::shared_ptr<ObservableT> &ob) {
-            return M.expval(*ob);
-        },
-        "Expected value of an observable object.");
+    pyclass
+        .def(
+            "expval",
+            [](MeasurementsT &M, const std::shared_ptr<ObservableT> &ob) {
+                return M.expval(*ob);
+            },
+            "Expected value of an observable object.")
+        .def(
+            "var",
+            [](MeasurementsT &M, const std::shared_ptr<ObservableT> &ob) {
+                return M.var(*ob);
+            },
+            "Variance of an observable object.");
 }
 
 /**

pennylane_lightning/core/src/simulators/lightning_tensor/tncuda/measurements/MeasurementsTNCuda.hpp

@@ -59,7 +59,34 @@ template <class TensorNetT> class MeasurementsTNCuda {
         : tensor_network_(tensor_network){};
 
     /**
-     * @brief Calculate expectation value for a general Observable.
+     * @brief Calculate var value for a general ObservableTNCuda Observable.
+     *
+     * Current implementation ensure that only one cutensornetNetworkOperator_t
+     * object is attached to the circuit.
+     *
+     * @param obs An Observable object.
+     * @param numHyperSamples Number of hyper samples to use in the calculation
+     * and is default as 1.
+     */
+    auto var(ObservableTNCuda<TensorNetT> &obs,
+             const int32_t numHyperSamples = 1) -> PrecisionT {
+        auto expectation_val =
+            expval(obs, numHyperSamples); // The cutensornetNetworkOperator_t
+                                          // object created in expval() will be
+                                          // released after the function call.
+
+        const bool val_cal = true;
+        auto tnObs2Operator =
+            ObservableTNCudaOperator<TensorNetT>(tensor_network_, obs, val_cal);
+        auto expectation_squared_obs =
+            expval_(tnObs2Operator.getTNOperator(), numHyperSamples);
+
+        return expectation_squared_obs - expectation_val * expectation_val;
+    }
+
+    /**
+     * @brief Calculate expectation value for a general ObservableTNCuda
+     * Observable.
      *
      * @param obs An Observable object.
      * @param numHyperSamples Number of hyper samples to use in the calculation
@@ -72,6 +99,24 @@ template <class TensorNetT> class MeasurementsTNCuda {
         auto tnoperator =
             ObservableTNCudaOperator<TensorNetT>(tensor_network_, obs);
 
+        return expval_(tnoperator.getTNOperator(), numHyperSamples);
+    }
+
+  private:
+    /**
+     * @brief Calculate expectation value for a cutensornetNetworkOperator_t
+     * object.
+     *
+     * @param tnoperator A cutensornetNetworkOperator_t object.
+     * @param numHyperSamples Number of hyper samples to use in the calculation
+     * and is default as 1.
+     *
+     * @return Expectation value with respect to the given
+     * cutensornetNetworkOperator_t object.
+     */
+
+    auto expval_(cutensornetNetworkOperator_t tnoperator,
+                 const int32_t numHyperSamples) -> PrecisionT {
         ComplexT expectation_val{0.0, 0.0};
         ComplexT state_norm2{0.0, 0.0};
 
@@ -80,7 +125,7 @@ template <class TensorNetT> class MeasurementsTNCuda {
         PL_CUTENSORNET_IS_SUCCESS(cutensornetCreateExpectation(
             /* const cutensornetHandle_t */ tensor_network_.getTNCudaHandle(),
             /* cutensornetState_t */ tensor_network_.getQuantumState(),
-            /* cutensornetNetworkOperator_t */ tnoperator.getTNOperator(),
+            /* cutensornetNetworkOperator_t */ tnoperator,
             /* cutensornetStateExpectation_t * */ &expectation));
 
         PL_CUTENSORNET_IS_SUCCESS(cutensornetExpectationConfigure(

pennylane_lightning/core/src/simulators/lightning_tensor/tncuda/measurements/tests/CMakeLists.txt

@@ -30,7 +30,8 @@ target_sources(${PL_BACKEND}_measurements_tests INTERFACE runner_${PL_BACKEND}_m
 ################################################################################
 # Define targets
 ################################################################################
-set(TEST_SOURCES    Test_MPSTNCuda_Expval.cpp)
+set(TEST_SOURCES    Test_MPSTNCuda_Expval.cpp
+                    Test_MPSTNCuda_Var.cpp)
 
 add_executable(${PL_BACKEND}_measurements_test_runner ${TEST_SOURCES})
 target_link_libraries(${PL_BACKEND}_measurements_test_runner PRIVATE ${PL_BACKEND}_measurements_tests)