diff --git a/qiskit/circuit/instruction.py b/qiskit/circuit/instruction.py
index b1278b4c0e22..55a640a832a5 100644
--- a/qiskit/circuit/instruction.py
+++ b/qiskit/circuit/instruction.py
@@ -35,6 +35,7 @@
 
 import copy
 from itertools import zip_longest
+import math
 from typing import List, Type
 
 import numpy
@@ -628,3 +629,13 @@ def num_clbits(self):
     def num_clbits(self, num_clbits):
         """Set num_clbits."""
         self._num_clbits = num_clbits
+
+    def _compare_parameters(self, other):
+        for x, y in zip(self.params, other.params):
+            try:
+                if not math.isclose(x, y, rel_tol=0, abs_tol=1e-10):
+                    return False
+            except TypeError:
+                if x != y:
+                    return False
+        return True
diff --git a/qiskit/circuit/library/standard_gates/dcx.py b/qiskit/circuit/library/standard_gates/dcx.py
index e917b6874d57..6455bea2779e 100644
--- a/qiskit/circuit/library/standard_gates/dcx.py
+++ b/qiskit/circuit/library/standard_gates/dcx.py
@@ -69,3 +69,6 @@ def _define(self):
             qc._append(instr, qargs, cargs)
 
         self.definition = qc
+
+    def __eq__(self, other):
+        return isinstance(other, DCXGate)
diff --git a/qiskit/circuit/library/standard_gates/ecr.py b/qiskit/circuit/library/standard_gates/ecr.py
index 1b38f7ad08e7..939f96f9e5b2 100644
--- a/qiskit/circuit/library/standard_gates/ecr.py
+++ b/qiskit/circuit/library/standard_gates/ecr.py
@@ -112,3 +112,6 @@ def _define(self):
     def inverse(self):
         """Return inverse ECR gate (itself)."""
         return ECRGate()  # self-inverse
+
+    def __eq__(self, other):
+        return isinstance(other, ECRGate)
diff --git a/qiskit/circuit/library/standard_gates/global_phase.py b/qiskit/circuit/library/standard_gates/global_phase.py
index 55625f6f3e44..7cda9c49ffbc 100644
--- a/qiskit/circuit/library/standard_gates/global_phase.py
+++ b/qiskit/circuit/library/standard_gates/global_phase.py
@@ -13,7 +13,9 @@
 """Global Phase Gate"""
 
 from typing import Optional
+
 import numpy
+
 from qiskit.circuit.gate import Gate
 from qiskit.circuit.quantumregister import QuantumRegister
 from qiskit.circuit.quantumcircuit import QuantumCircuit
@@ -61,3 +63,8 @@ def __array__(self, dtype=complex):
         """Return a numpy.array for the global_phase gate."""
         theta = self.params[0]
         return numpy.array([[numpy.exp(1j * theta)]], dtype=dtype)
+
+    def __eq__(self, other):
+        if isinstance(other, GlobalPhaseGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/h.py b/qiskit/circuit/library/standard_gates/h.py
index b738548cd444..ab58194b0c04 100644
--- a/qiskit/circuit/library/standard_gates/h.py
+++ b/qiskit/circuit/library/standard_gates/h.py
@@ -101,6 +101,9 @@ def inverse(self):
         r"""Return inverted H gate (itself)."""
         return HGate()  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, HGate)
+
 
 @with_controlled_gate_array(_H_ARRAY, num_ctrl_qubits=1)
 class CHGate(SingletonControlledGate):
@@ -222,3 +225,6 @@ def _define(self):
     def inverse(self):
         """Return inverted CH gate (itself)."""
         return CHGate(ctrl_state=self.ctrl_state)  # self-inverse
+
+    def __eq__(self, other):
+        return isinstance(other, CHGate) and self.ctrl_state == other.ctrl_state
diff --git a/qiskit/circuit/library/standard_gates/i.py b/qiskit/circuit/library/standard_gates/i.py
index ec7009f37ff5..720e9de20f1a 100644
--- a/qiskit/circuit/library/standard_gates/i.py
+++ b/qiskit/circuit/library/standard_gates/i.py
@@ -58,3 +58,6 @@ def inverse(self):
     def power(self, exponent: float):
         """Raise gate to a power."""
         return IGate()
+
+    def __eq__(self, other):
+        return isinstance(other, IGate)
diff --git a/qiskit/circuit/library/standard_gates/iswap.py b/qiskit/circuit/library/standard_gates/iswap.py
index 7b3168ce0c57..d871f6b8c3de 100644
--- a/qiskit/circuit/library/standard_gates/iswap.py
+++ b/qiskit/circuit/library/standard_gates/iswap.py
@@ -127,3 +127,6 @@ def _define(self):
     def power(self, exponent: float):
         """Raise gate to a power."""
         return XXPlusYYGate(-np.pi * exponent)
+
+    def __eq__(self, other):
+        return isinstance(other, iSwapGate)
diff --git a/qiskit/circuit/library/standard_gates/p.py b/qiskit/circuit/library/standard_gates/p.py
index cc6cb5a464f8..7a354fa4f4ab 100644
--- a/qiskit/circuit/library/standard_gates/p.py
+++ b/qiskit/circuit/library/standard_gates/p.py
@@ -133,6 +133,11 @@ def power(self, exponent: float):
         (theta,) = self.params
         return PhaseGate(exponent * theta)
 
+    def __eq__(self, other):
+        if isinstance(other, PhaseGate):
+            return self._compare_parameters(other)
+        return False
+
 
 class CPhaseGate(ControlledGate):
     r"""Controlled-Phase gate.
@@ -263,6 +268,11 @@ def power(self, exponent: float):
         (theta,) = self.params
         return CPhaseGate(exponent * theta)
 
+    def __eq__(self, other):
+        if isinstance(other, CPhaseGate):
+            return self._compare_parameters(other) and self.ctrl_state == other.ctrl_state
+        return False
+
 
 class MCPhaseGate(ControlledGate):
     r"""Multi-controlled-Phase gate.
diff --git a/qiskit/circuit/library/standard_gates/r.py b/qiskit/circuit/library/standard_gates/r.py
index cfc74d1b2cbf..e7772f043aef 100644
--- a/qiskit/circuit/library/standard_gates/r.py
+++ b/qiskit/circuit/library/standard_gates/r.py
@@ -99,3 +99,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         theta, phi = self.params
         return RGate(exponent * theta, phi)
+
+    def __eq__(self, other):
+        if isinstance(other, RGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/rx.py b/qiskit/circuit/library/standard_gates/rx.py
index 5084834888b4..69b8fe8fa328 100644
--- a/qiskit/circuit/library/standard_gates/rx.py
+++ b/qiskit/circuit/library/standard_gates/rx.py
@@ -113,6 +113,11 @@ def power(self, exponent: float):
         (theta,) = self.params
         return RXGate(exponent * theta)
 
+    def __eq__(self, other):
+        if isinstance(other, RXGate):
+            return self._compare_parameters(other)
+        return False
+
 
 class CRXGate(ControlledGate):
     r"""Controlled-RX gate.
@@ -244,3 +249,8 @@ def __array__(self, dtype=None):
             return numpy.array(
                 [[cos, 0, -isin, 0], [0, 1, 0, 0], [-isin, 0, cos, 0], [0, 0, 0, 1]], dtype=dtype
             )
+
+    def __eq__(self, other):
+        if isinstance(other, CRXGate):
+            return self._compare_parameters(other) and self.ctrl_state == other.ctrl_state
+        return False
diff --git a/qiskit/circuit/library/standard_gates/rxx.py b/qiskit/circuit/library/standard_gates/rxx.py
index 361c6b8a40d0..b9635f293f23 100644
--- a/qiskit/circuit/library/standard_gates/rxx.py
+++ b/qiskit/circuit/library/standard_gates/rxx.py
@@ -126,3 +126,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         (theta,) = self.params
         return RXXGate(exponent * theta)
+
+    def __eq__(self, other):
+        if isinstance(other, RXXGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/ry.py b/qiskit/circuit/library/standard_gates/ry.py
index e0270e4f04c9..6fed9206dcb7 100644
--- a/qiskit/circuit/library/standard_gates/ry.py
+++ b/qiskit/circuit/library/standard_gates/ry.py
@@ -112,6 +112,11 @@ def power(self, exponent: float):
         (theta,) = self.params
         return RYGate(exponent * theta)
 
+    def __eq__(self, other):
+        if isinstance(other, RYGate):
+            return self._compare_parameters(other)
+        return False
+
 
 class CRYGate(ControlledGate):
     r"""Controlled-RY gate.
@@ -239,3 +244,8 @@ def __array__(self, dtype=None):
             return numpy.array(
                 [[cos, 0, -sin, 0], [0, 1, 0, 0], [sin, 0, cos, 0], [0, 0, 0, 1]], dtype=dtype
             )
+
+    def __eq__(self, other):
+        if isinstance(other, CRYGate):
+            return self._compare_parameters(other) and self.ctrl_state == other.ctrl_state
+        return False
diff --git a/qiskit/circuit/library/standard_gates/ryy.py b/qiskit/circuit/library/standard_gates/ryy.py
index 40d638aac3cc..bc654d1af437 100644
--- a/qiskit/circuit/library/standard_gates/ryy.py
+++ b/qiskit/circuit/library/standard_gates/ryy.py
@@ -126,3 +126,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         (theta,) = self.params
         return RYYGate(exponent * theta)
+
+    def __eq__(self, other):
+        if isinstance(other, RYYGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/rz.py b/qiskit/circuit/library/standard_gates/rz.py
index 33b7146b44f1..b96fe6183869 100644
--- a/qiskit/circuit/library/standard_gates/rz.py
+++ b/qiskit/circuit/library/standard_gates/rz.py
@@ -124,6 +124,11 @@ def power(self, exponent: float):
         (theta,) = self.params
         return RZGate(exponent * theta)
 
+    def __eq__(self, other):
+        if isinstance(other, RZGate):
+            return self._compare_parameters(other)
+        return False
+
 
 class CRZGate(ControlledGate):
     r"""Controlled-RZ gate.
@@ -259,3 +264,8 @@ def __array__(self, dtype=None):
                 [[exp(-arg), 0, 0, 0], [0, 1, 0, 0], [0, 0, exp(arg), 0], [0, 0, 0, 1]],
                 dtype=dtype,
             )
+
+    def __eq__(self, other):
+        if isinstance(other, CRZGate):
+            return self._compare_parameters(other) and self.ctrl_state == other.ctrl_state
+        return False
diff --git a/qiskit/circuit/library/standard_gates/rzx.py b/qiskit/circuit/library/standard_gates/rzx.py
index 7963d60f9274..bd76d8f0af39 100644
--- a/qiskit/circuit/library/standard_gates/rzx.py
+++ b/qiskit/circuit/library/standard_gates/rzx.py
@@ -172,3 +172,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         (theta,) = self.params
         return RZXGate(exponent * theta)
+
+    def __eq__(self, other):
+        if isinstance(other, RZXGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/rzz.py b/qiskit/circuit/library/standard_gates/rzz.py
index a9b2b01e8afe..d15f5cb70d7a 100644
--- a/qiskit/circuit/library/standard_gates/rzz.py
+++ b/qiskit/circuit/library/standard_gates/rzz.py
@@ -139,3 +139,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         (theta,) = self.params
         return RZZGate(exponent * theta)
+
+    def __eq__(self, other):
+        if isinstance(other, RZZGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/s.py b/qiskit/circuit/library/standard_gates/s.py
index 1a35dc8fdcc7..e31ca8de894e 100644
--- a/qiskit/circuit/library/standard_gates/s.py
+++ b/qiskit/circuit/library/standard_gates/s.py
@@ -90,6 +90,9 @@ def power(self, exponent: float):
 
         return PhaseGate(0.5 * numpy.pi * exponent)
 
+    def __eq__(self, other):
+        return isinstance(other, SGate)
+
 
 @with_gate_array(_SDG_ARRAY)
 class SdgGate(SingletonGate):
@@ -155,6 +158,9 @@ def power(self, exponent: float):
 
         return PhaseGate(-0.5 * numpy.pi * exponent)
 
+    def __eq__(self, other):
+        return isinstance(other, SdgGate)
+
 
 @with_controlled_gate_array(_S_ARRAY, num_ctrl_qubits=1)
 class CSGate(SingletonControlledGate):
@@ -229,6 +235,9 @@ def power(self, exponent: float):
 
         return CPhaseGate(0.5 * numpy.pi * exponent)
 
+    def __eq__(self, other):
+        return isinstance(other, CSGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_controlled_gate_array(_SDG_ARRAY, num_ctrl_qubits=1)
 class CSdgGate(SingletonControlledGate):
@@ -301,3 +310,6 @@ def power(self, exponent: float):
         from .p import CPhaseGate
 
         return CPhaseGate(-0.5 * numpy.pi * exponent)
+
+    def __eq__(self, other):
+        return isinstance(other, CSdgGate) and self.ctrl_state == other.ctrl_state
diff --git a/qiskit/circuit/library/standard_gates/swap.py b/qiskit/circuit/library/standard_gates/swap.py
index 551e760c6932..2a7ccd16d41f 100644
--- a/qiskit/circuit/library/standard_gates/swap.py
+++ b/qiskit/circuit/library/standard_gates/swap.py
@@ -112,6 +112,9 @@ def inverse(self):
         """Return inverse Swap gate (itself)."""
         return SwapGate()  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, SwapGate)
+
 
 @with_controlled_gate_array(_SWAP_ARRAY, num_ctrl_qubits=1)
 class CSwapGate(SingletonControlledGate):
@@ -244,3 +247,6 @@ def _define(self):
     def inverse(self):
         """Return inverse CSwap gate (itself)."""
         return CSwapGate(ctrl_state=self.ctrl_state)  # self-inverse
+
+    def __eq__(self, other):
+        return isinstance(other, CSwapGate) and self.ctrl_state == other.ctrl_state
diff --git a/qiskit/circuit/library/standard_gates/sx.py b/qiskit/circuit/library/standard_gates/sx.py
index 1c8344c6fa59..88a8119e59b2 100644
--- a/qiskit/circuit/library/standard_gates/sx.py
+++ b/qiskit/circuit/library/standard_gates/sx.py
@@ -112,6 +112,9 @@ def control(
             return gate
         return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state)
 
+    def __eq__(self, other):
+        return isinstance(other, SXGate)
+
 
 @with_gate_array(_SXDG_ARRAY)
 class SXdgGate(SingletonGate):
@@ -169,6 +172,9 @@ def inverse(self):
         """Return inverse SXdg gate (i.e. SX)."""
         return SXGate()
 
+    def __eq__(self, other):
+        return isinstance(other, SXdgGate)
+
 
 @with_controlled_gate_array(_SX_ARRAY, num_ctrl_qubits=1)
 class CSXGate(SingletonControlledGate):
@@ -266,3 +272,6 @@ def _define(self):
         for operation, qubits, clbits in rules:
             qc._append(operation, qubits, clbits)
         self.definition = qc
+
+    def __eq__(self, other):
+        return isinstance(other, CSXGate) and self.ctrl_state == other.ctrl_state
diff --git a/qiskit/circuit/library/standard_gates/t.py b/qiskit/circuit/library/standard_gates/t.py
index eaa912456d7c..c1e83f0871a5 100644
--- a/qiskit/circuit/library/standard_gates/t.py
+++ b/qiskit/circuit/library/standard_gates/t.py
@@ -86,6 +86,9 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         return PhaseGate(0.25 * numpy.pi * exponent)
 
+    def __eq__(self, other):
+        return isinstance(other, TGate)
+
 
 @with_gate_array([[1, 0], [0, (1 - 1j) / math.sqrt(2)]])
 class TdgGate(SingletonGate):
@@ -148,3 +151,6 @@ def inverse(self):
     def power(self, exponent: float):
         """Raise gate to a power."""
         return PhaseGate(-0.25 * numpy.pi * exponent)
+
+    def __eq__(self, other):
+        return isinstance(other, TdgGate)
diff --git a/qiskit/circuit/library/standard_gates/u.py b/qiskit/circuit/library/standard_gates/u.py
index 23a9fc7861ce..30f6ff7f735b 100644
--- a/qiskit/circuit/library/standard_gates/u.py
+++ b/qiskit/circuit/library/standard_gates/u.py
@@ -130,6 +130,11 @@ def __array__(self, dtype=complex):
             dtype=dtype,
         )
 
+    def __eq__(self, other):
+        if isinstance(other, UGate):
+            return self._compare_parameters(other)
+        return False
+
 
 class _CUGateParams(list):
     # This awful class is to let `CUGate.params` have its keys settable (as
diff --git a/qiskit/circuit/library/standard_gates/x.py b/qiskit/circuit/library/standard_gates/x.py
index 7effa675c83c..4ea9712c3dd7 100644
--- a/qiskit/circuit/library/standard_gates/x.py
+++ b/qiskit/circuit/library/standard_gates/x.py
@@ -123,6 +123,9 @@ def inverse(self):
         r"""Return inverted X gate (itself)."""
         return XGate()  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, XGate)
+
 
 @with_controlled_gate_array(_X_ARRAY, num_ctrl_qubits=1)
 class CXGate(SingletonControlledGate):
@@ -244,6 +247,9 @@ def inverse(self):
         """Return inverted CX gate (itself)."""
         return CXGate(ctrl_state=self.ctrl_state)  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, CXGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_controlled_gate_array(_X_ARRAY, num_ctrl_qubits=2, cached_states=(3,))
 class CCXGate(SingletonControlledGate):
@@ -414,6 +420,9 @@ def inverse(self):
         """Return an inverted CCX gate (also a CCX)."""
         return CCXGate(ctrl_state=self.ctrl_state)  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, CCXGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_gate_array(
     [
@@ -486,6 +495,9 @@ def _define(self):
 
         self.definition = qc
 
+    def __eq__(self, other):
+        return isinstance(other, RCCXGate)
+
 
 class C3SXGate(SingletonControlledGate):
     """The 3-qubit controlled sqrt-X gate.
@@ -589,6 +601,9 @@ def _define(self):
 
         self.definition = qc
 
+    def __eq__(self, other):
+        return isinstance(other, C3SXGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_controlled_gate_array(_X_ARRAY, num_ctrl_qubits=3, cached_states=(7,))
 class C3XGate(SingletonControlledGate):
@@ -724,6 +739,9 @@ def inverse(self):
         """Invert this gate. The C4X is its own inverse."""
         return C3XGate(ctrl_state=self.ctrl_state)
 
+    def __eq__(self, other):
+        return isinstance(other, C3XGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_gate_array(
     [
@@ -820,6 +838,9 @@ def _define(self):
 
         self.definition = qc
 
+    def __eq__(self, other):
+        return isinstance(other, RC3XGate)
+
 
 @with_controlled_gate_array(_X_ARRAY, num_ctrl_qubits=4, cached_states=(15,))
 class C4XGate(SingletonControlledGate):
@@ -940,6 +961,9 @@ def inverse(self):
         """Invert this gate. The C4X is its own inverse."""
         return C4XGate(ctrl_state=self.ctrl_state)
 
+    def __eq__(self, other):
+        return isinstance(other, C4XGate) and self.ctrl_state == other.ctrl_state
+
 
 class MCXGate(ControlledGate):
     """The general, multi-controlled X gate.
diff --git a/qiskit/circuit/library/standard_gates/xx_minus_yy.py b/qiskit/circuit/library/standard_gates/xx_minus_yy.py
index 4b9597169c30..127c57cee039 100644
--- a/qiskit/circuit/library/standard_gates/xx_minus_yy.py
+++ b/qiskit/circuit/library/standard_gates/xx_minus_yy.py
@@ -177,3 +177,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         theta, beta = self.params
         return XXMinusYYGate(exponent * theta, beta)
+
+    def __eq__(self, other):
+        if isinstance(other, XXMinusYYGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/xx_plus_yy.py b/qiskit/circuit/library/standard_gates/xx_plus_yy.py
index 599d870e0ec1..8b76c21ea375 100644
--- a/qiskit/circuit/library/standard_gates/xx_plus_yy.py
+++ b/qiskit/circuit/library/standard_gates/xx_plus_yy.py
@@ -178,3 +178,8 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         theta, beta = self.params
         return XXPlusYYGate(exponent * theta, beta)
+
+    def __eq__(self, other):
+        if isinstance(other, XXPlusYYGate):
+            return self._compare_parameters(other)
+        return False
diff --git a/qiskit/circuit/library/standard_gates/y.py b/qiskit/circuit/library/standard_gates/y.py
index 1789fed72e10..b57e29b5ed1f 100644
--- a/qiskit/circuit/library/standard_gates/y.py
+++ b/qiskit/circuit/library/standard_gates/y.py
@@ -117,6 +117,9 @@ def inverse(self):
         r"""Return inverted Y gate (:math:`Y^{\dagger} = Y`)"""
         return YGate()  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, YGate)
+
 
 @with_controlled_gate_array(_Y_ARRAY, num_ctrl_qubits=1)
 class CYGate(SingletonControlledGate):
@@ -219,3 +222,6 @@ def _define(self):
     def inverse(self):
         """Return inverted CY gate (itself)."""
         return CYGate(ctrl_state=self.ctrl_state)  # self-inverse
+
+    def __eq__(self, other):
+        return isinstance(other, CYGate) and self.ctrl_state == other.ctrl_state
diff --git a/qiskit/circuit/library/standard_gates/z.py b/qiskit/circuit/library/standard_gates/z.py
index 1df875a81099..e79cfdd6e874 100644
--- a/qiskit/circuit/library/standard_gates/z.py
+++ b/qiskit/circuit/library/standard_gates/z.py
@@ -125,6 +125,9 @@ def power(self, exponent: float):
         """Raise gate to a power."""
         return PhaseGate(numpy.pi * exponent)
 
+    def __eq__(self, other):
+        return isinstance(other, ZGate)
+
 
 @with_controlled_gate_array(_Z_ARRAY, num_ctrl_qubits=1)
 class CZGate(SingletonControlledGate):
@@ -206,6 +209,9 @@ def inverse(self):
         """Return inverted CZ gate (itself)."""
         return CZGate(ctrl_state=self.ctrl_state)  # self-inverse
 
+    def __eq__(self, other):
+        return isinstance(other, CZGate) and self.ctrl_state == other.ctrl_state
+
 
 @with_controlled_gate_array(_Z_ARRAY, num_ctrl_qubits=2, cached_states=(3,))
 class CCZGate(SingletonControlledGate):
@@ -292,3 +298,6 @@ def _define(self):
     def inverse(self):
         """Return inverted CCZ gate (itself)."""
         return CCZGate(ctrl_state=self.ctrl_state)  # self-inverse
+
+    def __eq__(self, other):
+        return isinstance(other, CCZGate) and self.ctrl_state == other.ctrl_state