Simplify cz circuit even more

Co-authored-by: Shelly Garion <46566946+ShellyGarion@users.noreply.github.com>
Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

qiskit/circuit/library/standard_gates/equivalence_library.py

@@ -881,36 +881,23 @@ def _cnot_rxx_decompose(plus_ry: bool = True, plus_rxx: bool = True):
 #       │   ≡
 # q_1: ─X─
 #
-# global phase: 7π/4
-#      ┌─────────┐    ┌────┐      ┌────┐   ┌────────┐┌────┐┌──────────┐   »
-# q_0: ┤ Rz(π/2) ├────┤ √X ├────■─┤ √X ├─■─┤ Rz(-π) ├┤ √X ├┤ Rz(-π/2) ├─■─»
-#      └──┬────┬─┘┌───┴────┴──┐ │ ├────┤ │ └─┬────┬─┘└────┘└──────────┘ │ »
-# q_1: ───┤ √X ├──┤ Rz(-3π/2) ├─■─┤ √X ├─■───┤ √X ├─────────────────────■─»
-#         └────┘  └───────────┘   └────┘     └────┘                       »
-# «        ┌────┐  ┌─────────┐
-# «q_0: ───┤ √X ├──┤ Rz(π/2) ├
-# «     ┌──┴────┴─┐└─────────┘
-# «q_1: ┤ Rz(π/2) ├───────────
-# «     └─────────┘
-#
+# global phase: 3π/2
+#      ┌────┐   ┌────┐   ┌────┐
+# q_0: ┤ √X ├─■─┤ √X ├─■─┤ √X ├─■─
+#      ├────┤ │ ├────┤ │ ├────┤ │
+# q_1: ┤ √X ├─■─┤ √X ├─■─┤ √X ├─■─
+#      └────┘   └────┘   └────┘
 q = QuantumRegister(2, "q")
-def_swap_cz = QuantumCircuit(q, global_phase=7 * pi / 4)
-def_swap_cz.rz(pi / 2, 0)
+def_swap_cz = QuantumCircuit(q, global_phase=-pi / 2)
 def_swap_cz.sx(0)
 def_swap_cz.sx(1)
-def_swap_cz.rz(-3 * pi / 2, 1)
 def_swap_cz.cz(0, 1)
 def_swap_cz.sx(0)
 def_swap_cz.sx(1)
 def_swap_cz.cz(0, 1)
-def_swap_cz.rz(-pi, 0)
 def_swap_cz.sx(0)
-def_swap_cz.rz(-pi / 2, 0)
 def_swap_cz.sx(1)
 def_swap_cz.cz(0, 1)
-def_swap_cz.sx(0)
-def_swap_cz.rz(pi / 2, 0)
-def_swap_cz.rz(pi / 2, 1)
 _sel.add_equivalence(SwapGate(), def_swap_cz)
 
 # iSwapGate