Fix RotationXY gate (#88)

* Fix RotationXY bug

* Fix unit test

* Add parenthesis for gate definition

* Update unit tests

Author: gnbaker

src/qureg_apply1qubitgate.cpp

@@ -461,8 +461,8 @@ void QubitRegister<Type>::ApplyHadamard(unsigned const qubit)
 ///
 ///     R_XY(phi, theta) = cos(theta/2) I -i sin(theta/2) (cos(phi) X + sin(phi) Y)
 ///
-///                      = | c(t/2)         -i s(t/2) (c(p) -i s(p) |
-///                        | -i s(t/2) (c(p) +i s(p)         c(t/2) |
+///                      = | c(t/2)         -i s(t/2) (c(p) -i s(p)) |
+///                        | -i s(t/2) (c(p) +i s(p))         c(t/2) |
 ///
 /// Or, in other format:
 ///
@@ -475,7 +475,7 @@ void QubitRegister<Type>::ApplyRotationXY(unsigned const qubit, BaseType phi, Ba
   iqs::TinyMatrix<Type, 2, 2, 32> rxy;
   rxy(0, 0) = Type(std::cos(theta / 2.), 0);
   rxy(0, 1) = Type(-std::sin(theta / 2.) * std::sin(phi), -std::sin(theta / 2.) * std::cos(phi) );
-  rxy(0, 1) = Type( std::sin(theta / 2.) * std::sin(phi), -std::sin(theta / 2.) * std::cos(phi) );
+  rxy(1, 0) = Type( std::sin(theta / 2.) * std::sin(phi), -std::sin(theta / 2.) * std::cos(phi) );
   rxy(1, 1) = Type(std::cos(theta / 2.), 0);
   Apply1QubitGate(qubit, rxy);
 }

unit_test/include/apply_1q_gate_test.hpp

@@ -203,7 +203,9 @@ TEST_F(Apply1QGateTest, RotationXY)
   psi.ApplyRotationZ(qubit, -phi);
   psi.ApplyRotationX(qubit, -theta);
   psi.ApplyRotationZ(qubit,  phi);
-  ASSERT_TRUE( psi.ComputeOverlap(psi_0).real() < 1.-accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).real() - 1) < accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).imag() - 0) < accepted_error_);
+  ASSERT_TRUE( psi.ComputeOverlap(psi_0).real() > 1.-accepted_error_);
   // Apply rotation in the XY plane and then cancel it with two rotations.
   phi = 1.1;
   theta = 0.13;
@@ -212,20 +214,23 @@ TEST_F(Apply1QGateTest, RotationXY)
   psi.ApplyRotationZ(qubit, -phi);
   psi.ApplyRotationX(qubit, -theta);
   psi.ApplyRotationZ(qubit,  phi);
-  ASSERT_TRUE( psi.ComputeOverlap(psi_0).real() < 1.-accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).real() - 1) < accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).imag() - 0) < accepted_error_);
   // Special case phi=0 corresponding to a X rotation.
   phi = 0.;
   theta = 0.28;
   qubit = 1;
   psi.ApplyRotationXY(qubit, phi, theta);
   psi.ApplyRotationX(qubit, -theta);
-  ASSERT_TRUE( psi.ComputeOverlap(psi_0).real() < 1.-accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).real() - 1) < accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).imag() - 0) < accepted_error_);
   // Special case phi=pi/2 corresponding to a Y rotation.
   phi = M_PI/2;
   qubit = 2;
   psi.ApplyRotationXY(qubit, phi, theta);
   psi.ApplyRotationY(qubit, -theta);
-  ASSERT_TRUE( psi.ComputeOverlap(psi_0).real() < 1.-accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).real() - 1) < accepted_error_);
+  ASSERT_TRUE( std::abs(psi.ComputeOverlap(psi_0).imag() - 0) < accepted_error_);
 }
 
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