Fix phase of cu3 gate to be compatible with u3 gate definition (#2755)

* fix phase of cu3 definition

* update changelog

* update unroller test for new cu3 def

CHANGELOG.md

@@ -71,6 +71,8 @@ The format is based on [Keep a Changelog].
 -   Replaces LegacySwap by faster, more stable StochasticSwap pass (\#2672)
 -   Uses level 1 by default as transpiler optimization level (\#2672)
 -   Change Snapshot signature to match simulator.snapshot (\#2592)
+-   Changed definition of `Cu3Gate` to to equivalent to the canonical
+    definition of a controlled `U3Gate` (\#2755)
 
 ### Removed
 

qiskit/extensions/standard/cu3.py

@@ -33,14 +33,15 @@ def __init__(self, theta, phi, lam):
     def _define(self):
         """
         gate cu3(theta,phi,lambda) c, t
-        { u1((lambda-phi)/2) t; cx c,t;
+        { u1((lambda+phi)/2) c; u1((lambda-phi)/2) t; cx c,t;
           u3(-theta/2,0,-(phi+lambda)/2) t; cx c,t;
           u3(theta/2,phi,0) t;
         }
         """
         definition = []
         q = QuantumRegister(2, "q")
         rule = [
+            (U1Gate((self.params[2] + self.params[1]) / 2), [q[0]], []),
             (U1Gate((self.params[2] - self.params[1]) / 2), [q[1]], []),
             (CnotGate(), [q[0], q[1]], []),
             (U3Gate(-self.params[0] / 2, 0, -(self.params[1] + self.params[2]) / 2), [q[1]], []),

test/python/transpiler/test_unroller.py

@@ -191,6 +191,7 @@ def test_unroll_all_instructions(self):
         ref_circuit.u3(0, 0, -pi/4, qr[0])
         ref_circuit.u3(0, 0, pi/4, qr[1])
         ref_circuit.cx(qr[1], qr[0])
+        ref_circuit.u3(0, 0, 0.05, qr[1])
         ref_circuit.u3(0, 0, pi/4, qr[2])
         ref_circuit.u3(pi/2, 0, pi, qr[2])
         ref_circuit.cx(qr[2], qr[0])