diff --git a/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h b/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
--- a/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
+++ b/mlir/include/mlir/Dialect/SparseTensor/Utils/Merger.h
@@ -31,14 +31,18 @@
   kIndex,
   // Unary operations.
   kAbsF,
+  kAbsC,
   kCeilF,
   kFloorF,
   kSqrtF,
   kExpm1F,
   kLog1pF,
+  kLog1pC,
   kSinF,
+  kSinC,
   kTanhF,
   kNegF,
+  kNegC,
   kNegI,
   kTruncF,
   kExtF,
@@ -60,12 +64,14 @@
   kMulC,
   kMulI,
   kDivF,
+  kDivC, // complex
   kDivS, // signed
   kDivU, // unsigned
   kAddF,
   kAddC,
   kAddI,
   kSubF,
+  kSubC,
   kSubI,
   kAndI,
   kOrI,
diff --git a/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp b/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
--- a/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Utils/Merger.cpp
@@ -37,14 +37,18 @@
     index = x;
     break;
   case kAbsF:
+  case kAbsC:
   case kCeilF:
   case kFloorF:
   case kSqrtF:
   case kExpm1F:
   case kLog1pF:
+  case kLog1pC:
   case kSinF:
+  case kSinC:
   case kTanhF:
   case kNegF:
+  case kNegC:
   case kNegI:
   case kCIm:
   case kCRe:
@@ -151,6 +155,8 @@
   // TODO: move this if-else logic into buildLattices
   if (kind == kSubF)
     s1 = mapSet(kNegF, s1);
+  else if (kind == kSubC)
+    s1 = mapSet(kNegC, s1);
   else if (kind == kSubI)
     s1 = mapSet(kNegI, s1);
   // Followed by all in s1.
@@ -274,14 +280,18 @@
   case kTensor:
     return tensorExps[e].tensor == t;
   case kAbsF:
+  case kAbsC:
   case kCeilF:
   case kFloorF:
   case kSqrtF:
   case kExpm1F:
   case kLog1pF:
+  case kLog1pC:
   case kSinF:
+  case kSinC:
   case kTanhF:
   case kNegF:
+  case kNegC:
   case kNegI:
   case kTruncF:
   case kExtF:
@@ -298,6 +308,7 @@
   case kBitCast:
     return isSingleCondition(t, tensorExps[e].children.e0);
   case kDivF: // note: x / c only
+  case kDivC:
   case kDivS:
   case kDivU:
     assert(!maybeZero(tensorExps[e].children.e1));
@@ -342,6 +353,7 @@
   case kIndex:
     return "index";
   case kAbsF:
+  case kAbsC:
     return "abs";
   case kCeilF:
     return "ceil";
@@ -352,13 +364,15 @@
   case kExpm1F:
     return "expm1";
   case kLog1pF:
+  case kLog1pC:
     return "log1p";
   case kSinF:
+  case kSinC:
     return "sin";
   case kTanhF:
     return "tanh";
   case kNegF:
-    return "-";
+  case kNegC:
   case kNegI:
     return "-";
   case kTruncF:
@@ -386,6 +400,7 @@
   case kMulI:
     return "*";
   case kDivF:
+  case kDivC:
   case kDivS:
   case kDivU:
     return "/";
@@ -394,6 +409,7 @@
   case kAddI:
     return "+";
   case kSubF:
+  case kSubC:
   case kSubI:
     return "-";
   case kAndI:
@@ -533,6 +549,7 @@
     return s;
   }
   case kAbsF:
+  case kAbsC:
   case kCeilF:
   case kCIm:
   case kCRe:
@@ -540,9 +557,12 @@
   case kSqrtF:
   case kExpm1F:
   case kLog1pF:
+  case kLog1pC:
   case kSinF:
+  case kSinC:
   case kTanhF:
   case kNegF:
+  case kNegC:
   case kNegI:
   case kTruncF:
   case kExtF:
@@ -607,6 +627,7 @@
                     buildLattices(tensorExps[e].children.e0, i),
                     buildLattices(tensorExps[e].children.e1, i));
   case kDivF:
+  case kDivC:
   case kDivS:
   case kDivU:
     // A division is tricky, since 0/0, 0/c, c/0 all have
@@ -630,6 +651,7 @@
   case kAddC:
   case kAddI:
   case kSubF:
+  case kSubC:
   case kSubI:
   case kOrI:
   case kXorI:
@@ -696,6 +718,11 @@
 /// Only returns false if we are certain this is a nonzero.
 bool Merger::maybeZero(unsigned e) const {
   if (tensorExps[e].kind == kInvariant) {
+    if (auto c = tensorExps[e].val.getDefiningOp<complex::ConstantOp>()) {
+      ArrayAttr arrayAttr = c.getValue();
+      return arrayAttr[0].cast<FloatAttr>().getValue().isZero() &&
+             arrayAttr[0].cast<FloatAttr>().getValue().isZero();
+    }
     if (auto c = tensorExps[e].val.getDefiningOp<arith::ConstantIntOp>())
       return c.value() == 0;
     if (auto c = tensorExps[e].val.getDefiningOp<arith::ConstantFloatOp>())
@@ -750,6 +777,8 @@
       unsigned e = x.getValue();
       if (isa<math::AbsOp>(def))
         return addExp(kAbsF, e);
+      if (isa<complex::AbsOp>(def))
+        return addExp(kAbsC, e);
       if (isa<math::CeilOp>(def))
         return addExp(kCeilF, e);
       if (isa<math::FloorOp>(def))
@@ -760,12 +789,18 @@
         return addExp(kExpm1F, e);
       if (isa<math::Log1pOp>(def))
         return addExp(kLog1pF, e);
+      if (isa<complex::Log1pOp>(def))
+        return addExp(kLog1pC, e);
       if (isa<math::SinOp>(def))
         return addExp(kSinF, e);
+      if (isa<complex::SinOp>(def))
+        return addExp(kSinC, e);
       if (isa<math::TanhOp>(def))
         return addExp(kTanhF, e);
       if (isa<arith::NegFOp>(def))
         return addExp(kNegF, e); // no negi in std
+      if (isa<complex::NegOp>(def))
+        return addExp(kNegC, e);
       if (isa<arith::TruncFOp>(def))
         return addExp(kTruncF, e, v);
       if (isa<arith::ExtFOp>(def))
@@ -813,6 +848,8 @@
         return addExp(kMulI, e0, e1);
       if (isa<arith::DivFOp>(def) && !maybeZero(e1))
         return addExp(kDivF, e0, e1);
+      if (isa<complex::DivOp>(def) && !maybeZero(e1))
+        return addExp(kDivC, e0, e1);
       if (isa<arith::DivSIOp>(def) && !maybeZero(e1))
         return addExp(kDivS, e0, e1);
       if (isa<arith::DivUIOp>(def) && !maybeZero(e1))
@@ -825,6 +862,8 @@
         return addExp(kAddI, e0, e1);
       if (isa<arith::SubFOp>(def))
         return addExp(kSubF, e0, e1);
+      if (isa<complex::SubOp>(def))
+        return addExp(kSubC, e0, e1);
       if (isa<arith::SubIOp>(def))
         return addExp(kSubI, e0, e1);
       if (isa<arith::AndIOp>(def))
@@ -902,6 +941,11 @@
   // Unary ops.
   case kAbsF:
     return rewriter.create<math::AbsOp>(loc, v0);
+  case kAbsC: {
+    auto type = v0.getType().template cast<ComplexType>();
+    auto eltType = type.getElementType().template cast<FloatType>();
+    return rewriter.create<complex::AbsOp>(loc, eltType, v0);
+  }
   case kCeilF:
     return rewriter.create<math::CeilOp>(loc, v0);
   case kFloorF:
@@ -912,12 +956,18 @@
     return rewriter.create<math::ExpM1Op>(loc, v0);
   case kLog1pF:
     return rewriter.create<math::Log1pOp>(loc, v0);
+  case kLog1pC:
+    return rewriter.create<complex::Log1pOp>(loc, v0);
   case kSinF:
     return rewriter.create<math::SinOp>(loc, v0);
+  case kSinC:
+    return rewriter.create<complex::SinOp>(loc, v0);
   case kTanhF:
     return rewriter.create<math::TanhOp>(loc, v0);
   case kNegF:
     return rewriter.create<arith::NegFOp>(loc, v0);
+  case kNegC:
+    return rewriter.create<complex::NegOp>(loc, v0);
   case kNegI: // no negi in std
     return rewriter.create<arith::SubIOp>(
         loc,
@@ -964,6 +1014,8 @@
     return rewriter.create<arith::MulIOp>(loc, v0, v1);
   case kDivF:
     return rewriter.create<arith::DivFOp>(loc, v0, v1);
+  case kDivC:
+    return rewriter.create<complex::DivOp>(loc, v0, v1);
   case kDivS:
     return rewriter.create<arith::DivSIOp>(loc, v0, v1);
   case kDivU:
@@ -976,6 +1028,8 @@
     return rewriter.create<arith::AddIOp>(loc, v0, v1);
   case kSubF:
     return rewriter.create<arith::SubFOp>(loc, v0, v1);
+  case kSubC:
+    return rewriter.create<complex::SubOp>(loc, v0, v1);
   case kSubI:
     return rewriter.create<arith::SubIOp>(loc, v0, v1);
   case kAndI:
diff --git a/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_complex_ops.mlir b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_complex_ops.mlir
new file mode 100644
--- /dev/null
+++ b/mlir/test/Integration/Dialect/SparseTensor/CPU/sparse_complex_ops.mlir
@@ -0,0 +1,179 @@
+// RUN: mlir-opt %s --sparse-compiler | \
+// RUN: mlir-cpu-runner \
+// RUN:  -e entry -entry-point-result=void  \
+// RUN:  -shared-libs=%mlir_integration_test_dir/libmlir_c_runner_utils%shlibext | \
+// RUN: FileCheck %s
+
+#SparseVector = #sparse_tensor.encoding<{dimLevelType = ["compressed"]}>
+
+#trait_op1 = {
+  indexing_maps = [
+    affine_map<(i) -> (i)>,  // a (in)
+    affine_map<(i) -> (i)>   // x (out)
+  ],
+  iterator_types = ["parallel"],
+  doc = "x(i) = OP a(i)"
+}
+
+#trait_op2 = {
+  indexing_maps = [
+    affine_map<(i) -> (i)>,  // a (in)
+    affine_map<(i) -> (i)>,  // b (in)
+    affine_map<(i) -> (i)>   // x (out)
+  ],
+  iterator_types = ["parallel"],
+  doc = "x(i) = a(i) OP b(i)"
+}
+
+module {
+  func.func @cops(%arga: tensor<?xcomplex<f64>, #SparseVector>,
+                  %argb: tensor<?xcomplex<f64>, #SparseVector>)
+                 -> tensor<?xcomplex<f64>, #SparseVector> {
+    %c0 = arith.constant 0 : index
+    %d = tensor.dim %arga, %c0 : tensor<?xcomplex<f64>, #SparseVector>
+    %xv = sparse_tensor.init [%d] : tensor<?xcomplex<f64>, #SparseVector>
+    %0 = linalg.generic #trait_op2
+       ins(%arga, %argb: tensor<?xcomplex<f64>, #SparseVector>,
+                         tensor<?xcomplex<f64>, #SparseVector>)
+        outs(%xv: tensor<?xcomplex<f64>, #SparseVector>) {
+        ^bb(%a: complex<f64>, %b: complex<f64>, %x: complex<f64>):
+          %1 = complex.neg %b : complex<f64>
+          %2 = complex.sub %a, %1 : complex<f64>
+          linalg.yield %2 : complex<f64>
+    } -> tensor<?xcomplex<f64>, #SparseVector>
+    return %0 : tensor<?xcomplex<f64>, #SparseVector>
+  }
+
+  func.func @csin(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+                 -> tensor<?xcomplex<f64>, #SparseVector> {
+    %c0 = arith.constant 0 : index
+    %d = tensor.dim %arga, %c0 : tensor<?xcomplex<f64>, #SparseVector>
+    %xv = sparse_tensor.init [%d] : tensor<?xcomplex<f64>, #SparseVector>
+    %0 = linalg.generic #trait_op1
+       ins(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+        outs(%xv: tensor<?xcomplex<f64>, #SparseVector>) {
+        ^bb(%a: complex<f64>, %x: complex<f64>):
+          %1 = complex.sin %a : complex<f64>
+          linalg.yield %1 : complex<f64>
+    } -> tensor<?xcomplex<f64>, #SparseVector>
+    return %0 : tensor<?xcomplex<f64>, #SparseVector>
+  }
+
+  func.func @cdiv(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+                 -> tensor<?xcomplex<f64>, #SparseVector> {
+    %c0 = arith.constant 0 : index
+    %d = tensor.dim %arga, %c0 : tensor<?xcomplex<f64>, #SparseVector>
+    %xv = sparse_tensor.init [%d] : tensor<?xcomplex<f64>, #SparseVector>
+    %c = complex.constant [2.0 : f64, 0.0 : f64] : complex<f64>
+    %0 = linalg.generic #trait_op1
+       ins(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+        outs(%xv: tensor<?xcomplex<f64>, #SparseVector>) {
+        ^bb(%a: complex<f64>, %x: complex<f64>):
+          %1 = complex.div %a, %c  : complex<f64>
+          linalg.yield %1 : complex<f64>
+    } -> tensor<?xcomplex<f64>, #SparseVector>
+    return %0 : tensor<?xcomplex<f64>, #SparseVector>
+  }
+
+  func.func @cabs(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+                 -> tensor<?xf64, #SparseVector> {
+    %c0 = arith.constant 0 : index
+    %d = tensor.dim %arga, %c0 : tensor<?xcomplex<f64>, #SparseVector>
+    %xv = sparse_tensor.init [%d] : tensor<?xf64, #SparseVector>
+    %0 = linalg.generic #trait_op1
+       ins(%arga: tensor<?xcomplex<f64>, #SparseVector>)
+        outs(%xv: tensor<?xf64, #SparseVector>) {
+        ^bb(%a: complex<f64>, %x: f64):
+          %1 = complex.abs %a : complex<f64>
+          linalg.yield %1 : f64
+    } -> tensor<?xf64, #SparseVector>
+    return %0 : tensor<?xf64, #SparseVector>
+  }
+
+  func.func @dumpc(%arg0: tensor<?xcomplex<f64>, #SparseVector>, %d: index) {
+    %c0 = arith.constant 0 : index
+    %c1 = arith.constant 1 : index
+    %mem = sparse_tensor.values %arg0 : tensor<?xcomplex<f64>, #SparseVector> to memref<?xcomplex<f64>>
+    scf.for %i = %c0 to %d step %c1 {
+       %v = memref.load %mem[%i] : memref<?xcomplex<f64>>
+       %real = complex.re %v : complex<f64>
+       %imag = complex.im %v : complex<f64>
+       vector.print %real : f64
+       vector.print %imag : f64
+    }
+    return
+  }
+
+  func.func @dumpf(%arg0: tensor<?xf64, #SparseVector>) {
+    %c0 = arith.constant 0 : index
+    %d0 = arith.constant 0.0 : f64
+    %values = sparse_tensor.values %arg0 : tensor<?xf64, #SparseVector> to memref<?xf64>
+    %0 = vector.transfer_read %values[%c0], %d0: memref<?xf64>, vector<3xf64>
+    vector.print %0 : vector<3xf64>
+    return
+  }
+
+  // Driver method to call and verify complex kernels.
+  func.func @entry() {
+    // Setup sparse vectors.
+    %v1 = arith.constant sparse<
+       [ [0], [28], [31] ],
+         [ (-5.13, 2.0), (3.0, 4.0), (5.0, 6.0) ] > : tensor<32xcomplex<f64>>
+    %v2 = arith.constant sparse<
+       [ [1], [28], [31] ],
+         [ (1.0, 0.0), (-2.0, 0.0), (3.0, 0.0) ] > : tensor<32xcomplex<f64>>
+    %sv1 = sparse_tensor.convert %v1 : tensor<32xcomplex<f64>> to tensor<?xcomplex<f64>, #SparseVector>
+    %sv2 = sparse_tensor.convert %v2 : tensor<32xcomplex<f64>> to tensor<?xcomplex<f64>, #SparseVector>
+
+    // Call sparse vector kernels.
+    %0 = call @cops(%sv1, %sv2)
+       : (tensor<?xcomplex<f64>, #SparseVector>,
+          tensor<?xcomplex<f64>, #SparseVector>) -> tensor<?xcomplex<f64>, #SparseVector>
+    %1 = call @csin(%sv1)
+       : (tensor<?xcomplex<f64>, #SparseVector>) -> tensor<?xcomplex<f64>, #SparseVector>
+    %2 = call @cdiv(%sv1)
+       : (tensor<?xcomplex<f64>, #SparseVector>) -> tensor<?xcomplex<f64>, #SparseVector>
+    %3 = call @cabs(%sv1)
+       : (tensor<?xcomplex<f64>, #SparseVector>) -> tensor<?xf64, #SparseVector>
+
+    //
+    // Verify the results.
+    //
+    %d3 = arith.constant 3 : index
+    %d4 = arith.constant 4 : index
+    // CHECK: -5.13
+    // CHECK-NEXT: 2
+    // CHECK-NEXT: 1
+    // CHECK-NEXT: 0
+    // CHECK-NEXT: 1
+    // CHECK-NEXT: 4
+    // CHECK-NEXT: 8
+    // CHECK-NEXT: 6
+    call @dumpc(%0, %d4) : (tensor<?xcomplex<f64>, #SparseVector>, index) -> ()
+    // CHECK-NEXT: 3.43887
+    // CHECK-NEXT: 1.47097
+    // CHECK-NEXT: 3.85374
+    // CHECK-NEXT: -27.0168
+    // CHECK-NEXT: -193.43
+    // CHECK-NEXT: 57.2184
+    call @dumpc(%1, %d3) : (tensor<?xcomplex<f64>, #SparseVector>, index) -> ()
+    // CHECK-NEXT: -2.565
+    // CHECK-NEXT: 1
+    // CHECK-NEXT: 1.5
+    // CHECK-NEXT: 2
+    // CHECK-NEXT: 2.5
+    // CHECK-NEXT: 3
+    call @dumpc(%2, %d3) : (tensor<?xcomplex<f64>, #SparseVector>, index) -> ()
+    // CHECK-NEXT: ( 5.50608, 5, 7.81025 )
+    call @dumpf(%3) : (tensor<?xf64, #SparseVector>) -> ()
+
+    // Release the resources.
+    sparse_tensor.release %sv1 : tensor<?xcomplex<f64>, #SparseVector>
+    sparse_tensor.release %sv2 : tensor<?xcomplex<f64>, #SparseVector>
+    sparse_tensor.release %0 : tensor<?xcomplex<f64>, #SparseVector>
+    sparse_tensor.release %1 : tensor<?xcomplex<f64>, #SparseVector>
+    sparse_tensor.release %2 : tensor<?xcomplex<f64>, #SparseVector>
+    sparse_tensor.release %3 : tensor<?xf64, #SparseVector>
+    return
+  }
+}