diff --git a/src/QuantumClifford.jl b/src/QuantumClifford.jl
index 6b4945b6b..36901ed23 100644
--- a/src/QuantumClifford.jl
+++ b/src/QuantumClifford.jl
@@ -52,7 +52,7 @@ export
     sCNOT, sCPHASE, sSWAP,
     sXCX, sXCY, sXCZ, sYCX, sYCY, sYCZ, sZCX, sZCY, sZCZ,
     sZCrY, sInvZCrY, sSWAPCX, sInvSWAPCX, sCZSWAP, sCXSWAP, sISWAP, sInvISWAP,
-    sSQRTZZ, sInvSQRTZZ,
+    sSQRTZZ, sInvSQRTZZ, sSQRTXX, sInvSQRTXX, sSQRTYY, sInvSQRTYY,
     # Misc Ops
     SparseGate,
     sMX, sMY, sMZ, PauliMeasurement, Reset, sMRX, sMRY, sMRZ,
diff --git a/src/symbolic_cliffords.jl b/src/symbolic_cliffords.jl
index 03f5f2e69..fcff4cb38 100644
--- a/src/symbolic_cliffords.jl
+++ b/src/symbolic_cliffords.jl
@@ -339,6 +339,12 @@ end
 @qubitop2 SQRTZZ    (x1       , x1⊻x2⊻z1 , x2       , x1⊻z2⊻x2 , ~iszero((x1 & z1 & ~x2) | (~x1 & x2 & z2)))
 @qubitop2 InvSQRTZZ (x1       , x1⊻x2⊻z1 , x2       , x1⊻z2⊻x2 , ~iszero((x1 &~z1 & ~x2) | (~x1 & x2 &~z2)))
 
+@qubitop2 SQRTXX    (z1⊻z2⊻x1, z1      , z1⊻x2⊻z2, z2      , ~iszero((~x1 & z1 &~z2) | (~z1 &~x2 & z2)))
+@qubitop2 InvSQRTXX (z1⊻z2⊻x1, z1      , z1⊻x2⊻z2, z2      , ~iszero(( x1 & z1 &~z2) | (~z1 & x2 & z2)))
+
+@qubitop2 SQRTYY    (z1⊻x2⊻z2, x1⊻z2⊻x2, x1⊻z1⊻z2, x1⊻x2⊻z1, ~iszero((~x1 &~z1 & x2 &~z2) | ( x1 &~z1 &~x2 &~z2) | ( x1 &~z1 & x2 & z2) | ( x1 & z1 & x2 &~z2)))
+@qubitop2 InvSQRTYY (z1⊻x2⊻z2, x1⊻z2⊻x2, x1⊻z1⊻z2, x1⊻x2⊻z1, ~iszero(( x1 & z1 &~x2 & z2) | (~x1 & z1 & x2 & z2) | (~x1 & z1 &~x2 &~z2) | (~x1 &~z1 &~x2 & z2)))
+
 #=
 To get the boolean formulas for the phase, it is easiest to first write down the truth table for the phase:
 for i in 0:15
@@ -405,6 +411,10 @@ LinearAlgebra.inv(op::sISWAP)     = sInvISWAP(op.q1, op.q2)
 LinearAlgebra.inv(op::sInvISWAP)  = sISWAP(op.q1, op.q2)
 LinearAlgebra.inv(op::sSQRTZZ)    = sInvSQRTZZ(op.q1, op.q2)
 LinearAlgebra.inv(op::sInvSQRTZZ) = sSQRTZZ(op.q1, op.q2)
+LinearAlgebra.inv(op::sSQRTXX)    = sInvSQRTXX(op.q1, op.q2)
+LinearAlgebra.inv(op::sInvSQRTXX) = sSQRTXX(op.q1, op.q2)
+LinearAlgebra.inv(op::sSQRTYY)    = sInvSQRTYY(op.q1, op.q2)
+LinearAlgebra.inv(op::sInvSQRTYY) = sSQRTYY(op.q1, op.q2)
 
 ##############################
 # Functions that perform direct application of common operators without needing an operator instance
diff --git a/test/test_symcliff.jl b/test/test_symcliff.jl
index 40ed505ac..6bbad80d4 100644
--- a/test/test_symcliff.jl
+++ b/test/test_symcliff.jl
@@ -76,6 +76,7 @@
             @test CliffordOperator(inv(random_op), i) == inv(CliffordOperator(random_op, i))
             @test CliffordOperator(inv(SingleQubitOperator(random_op)), i) == inv(CliffordOperator(random_op, i))
         end
+    end
 
     @testset "Consistency checks with Stim" begin
        # see https://github.com/quantumlib/Stim/blob/main/doc/gates.md
@@ -113,5 +114,9 @@
         @test CliffordOperator(sInvISWAP)  == C"-ZY -YZ IZ ZI"
         @test CliffordOperator(sSQRTZZ)    == C"YZ ZY ZI IZ"
         @test CliffordOperator(sInvSQRTZZ) == C"-YZ -ZY ZI IZ"
+        @test CliffordOperator(sSQRTXX)    == C"XI IX -YX -XY"
+        @test CliffordOperator(sInvSQRTXX) == C"XI IX YX XY"
+        @test CliffordOperator(sSQRTYY)    == C"-ZY -YZ XY YX"
+        @test CliffordOperator(sInvSQRTYY) == C"ZY YZ -XY -YX"
     end
 end