# This code is part of Qiskit. # # (C) Copyright IBM 2017, 2023. # # This code is licensed under the Apache License, Version 2.0. You may # obtain a copy of this license in the LICENSE.txt file in the root directory # of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. # # Any modifications or derivative works of this code must retain this # copyright notice, and modified files need to carry a notice indicating # that they have been altered from the originals. """Dictionary containing commutation relations of unparameterizable standard gates. The dictionary key is defined by a pair of gates and, optionally, their relative placement to each other, i.e.: ┌───┐┌───┐ q: ┤ X ├┤ Z ├ -> standard_gates_commutations["x", "z"] = False └───┘└───┘ or ┌───┐ q_0: ──■──┤ X ├ ┌─┴─┐└─┬─┘ -> standard_gates_commutations["cx", "cy"][1, 0] = False q_1: ┤ Y ├──■── └───┘ or q_0: ──■─────── ┌─┴─┐ q_1: ┤ X ├──■── -> standard_gates_commutations['cx', 'cx'][None, 0] = False └───┘┌─┴─┐ q_2: ─────┤ X ├ └───┘ Note that the commutation of a pair of gates is only stored in one specific order, i.e. the commutation of a pair of cy and cx gates is only stored in standard_gates_commutations["cx", "cy"]. The order of the gates is derived from the number of qubits in each gate and the value of the integer representation of the gate name. The values of standard_gates_commutations can be a Boolean value denoting whether the pair of gates commute or another dictionary if the relative placement of the pair of gates has an impact on the commutation. The relative placement is defined by the gate qubit arrangements as q2^{-1}[q1[i]] where q1[i] is the ith qubit of the first gate and q2^{-1}[q] returns the qubit index of qubit q in the second gate (possibly 'None'). In the second example, the zeroth qubit of cy overlaps with qubit 1 of cx. Non- overlapping qubits are specified as 'None' in the dictionary key, e.g. example 3, there is no overlap on the zeroth qubit of the first cx but the zeroth qubit of the second gate overlaps with qubit 1 of the first cx. """ standard_gates_commutations = { ("id", "id"): True, ("id", "sx"): True, ("id", "cx"): True, ("id", "c3sx"): True, ("id", "ccx"): True, ("id", "dcx"): True, ("id", "ch"): True, ("id", "cswap"): True, ("id", "csx"): True, ("id", "cy"): True, ("id", "cz"): True, ("id", "ccz"): True, ("id", "rccx"): True, ("id", "rcccx"): True, ("id", "ecr"): True, ("id", "sdg"): True, ("id", "cs"): True, ("id", "csdg"): True, ("id", "swap"): True, ("id", "iswap"): True, ("id", "sxdg"): True, ("id", "tdg"): True, ("sx", "sx"): True, ("sx", "cx"): { (0,): False, (1,): True, }, ("sx", "c3sx"): { (0,): False, (1,): False, (2,): False, (3,): True, }, ("sx", "ccx"): { (0,): False, (1,): False, (2,): True, }, ("sx", "dcx"): False, ("sx", "ch"): False, ("sx", "cswap"): False, ("sx", "csx"): { (0,): False, (1,): True, }, ("sx", "cy"): False, ("sx", "cz"): False, ("sx", "ccz"): False, ("sx", "rccx"): False, ("sx", "rcccx"): False, ("sx", "ecr"): { (0,): False, (1,): True, }, ("sx", "sdg"): False, ("sx", "cs"): False, ("sx", "csdg"): False, ("sx", "swap"): False, ("sx", "iswap"): False, ("sx", "sxdg"): True, ("sx", "tdg"): False, ("x", "id"): True, ("x", "sx"): True, ("x", "x"): True, ("x", "cx"): { (0,): False, (1,): True, }, ("x", "c3sx"): { (0,): False, (1,): False, (2,): False, (3,): True, }, ("x", "ccx"): { (0,): False, (1,): False, (2,): True, }, ("x", "dcx"): False, ("x", "ch"): False, ("x", "cswap"): False, ("x", "csx"): { (0,): False, (1,): True, }, ("x", "cy"): False, ("x", "cz"): False, ("x", "ccz"): False, ("x", "rccx"): False, ("x", "rcccx"): False, ("x", "ecr"): { (0,): False, (1,): True, }, ("x", "sdg"): False, ("x", "cs"): False, ("x", "csdg"): False, ("x", "swap"): False, ("x", "iswap"): False, ("x", "sxdg"): True, ("x", "tdg"): False, ("x", "y"): False, ("x", "z"): False, ("cx", "cx"): { (0, 1): True, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("cx", "c3sx"): { (0, 1): False, (0, 2): False, (0, 3): True, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): True, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): True, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): True, }, ("cx", "ccx"): { (0, 1): False, (0, 2): True, (0, None): True, (1, 0): False, (1, 2): True, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): True, }, ("cx", "dcx"): False, ("cx", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cx", "csx"): { (0, 1): True, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("cx", "cy"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): False, }, ("cx", "cz"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("cx", "ccz"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): True, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cx", "rccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cx", "rcccx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("cx", "ecr"): { (0, 1): False, (0, None): False, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("cx", "csdg"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("cx", "swap"): False, ("cx", "iswap"): False, ("c3sx", "c3sx"): { (0, 1, 2, 3): True, (0, 1, 2, None): True, (0, 1, 3, 2): False, (0, 1, 3, None): False, (0, 1, None, 2): False, (0, 1, None, 3): True, (0, 1, None, None): True, (0, 2, 1, 3): True, (0, 2, 1, None): True, (0, 2, 3, 1): False, (0, 2, 3, None): False, (0, 2, None, 1): False, (0, 2, None, 3): True, (0, 2, None, None): True, (0, 3, 1, 2): False, (0, 3, 1, None): False, (0, 3, 2, 1): False, (0, 3, 2, None): False, (0, 3, None, 1): False, (0, 3, None, 2): False, (0, 3, None, None): False, (0, None, 1, 2): False, (0, None, 1, 3): True, (0, None, 1, None): True, (0, None, 2, 1): False, (0, None, 2, 3): True, (0, None, 2, None): True, (0, None, 3, 1): False, (0, None, 3, 2): False, (0, None, 3, None): False, (0, None, None, 1): False, (0, None, None, 2): False, (0, None, None, 3): True, (0, None, None, None): True, (1, 0, 2, 3): True, (1, 0, 2, None): True, (1, 0, 3, 2): False, (1, 0, 3, None): False, (1, 0, None, 2): False, (1, 0, None, 3): True, (1, 0, None, None): True, (1, 2, 0, 3): True, (1, 2, 0, None): True, (1, 2, 3, 0): False, (1, 2, 3, None): False, (1, 2, None, 0): False, (1, 2, None, 3): True, (1, 2, None, None): True, (1, 3, 0, 2): False, (1, 3, 0, None): False, (1, 3, 2, 0): False, (1, 3, 2, None): False, (1, 3, None, 0): False, (1, 3, None, 2): False, (1, 3, None, None): False, (1, None, 0, 2): False, (1, None, 0, 3): True, (1, None, 0, None): True, (1, None, 2, 0): False, (1, None, 2, 3): True, (1, None, 2, None): True, (1, None, 3, 0): False, (1, None, 3, 2): False, (1, None, 3, None): False, (1, None, None, 0): False, (1, None, None, 2): False, (1, None, None, 3): True, (1, None, None, None): True, (2, 0, 1, 3): True, (2, 0, 1, None): True, (2, 0, 3, 1): False, (2, 0, 3, None): False, (2, 0, None, 1): False, (2, 0, None, 3): True, (2, 0, None, None): True, (2, 1, 0, 3): True, (2, 1, 0, None): True, (2, 1, 3, 0): False, (2, 1, 3, None): False, (2, 1, None, 0): False, (2, 1, None, 3): True, (2, 1, None, None): True, (2, 3, 0, 1): False, (2, 3, 0, None): False, (2, 3, 1, 0): False, (2, 3, 1, None): False, (2, 3, None, 0): False, (2, 3, None, 1): False, (2, 3, None, None): False, (2, None, 0, 1): False, (2, None, 0, 3): True, (2, None, 0, None): True, (2, None, 1, 0): False, (2, None, 1, 3): True, (2, None, 1, None): True, (2, None, 3, 0): False, (2, None, 3, 1): False, (2, None, 3, None): False, (2, None, None, 0): False, (2, None, None, 1): False, (2, None, None, 3): True, (2, None, None, None): True, (3, 0, 1, 2): False, (3, 0, 1, None): False, (3, 0, 2, 1): False, (3, 0, 2, None): False, (3, 0, None, 1): False, (3, 0, None, 2): False, (3, 0, None, None): False, (3, 1, 0, 2): False, (3, 1, 0, None): False, (3, 1, 2, 0): False, (3, 1, 2, None): False, (3, 1, None, 0): False, (3, 1, None, 2): False, (3, 1, None, None): False, (3, 2, 0, 1): False, (3, 2, 0, None): False, (3, 2, 1, 0): False, (3, 2, 1, None): False, (3, 2, None, 0): False, (3, 2, None, 1): False, (3, 2, None, None): False, (3, None, 0, 1): False, (3, None, 0, 2): False, (3, None, 0, None): False, (3, None, 1, 0): False, (3, None, 1, 2): False, (3, None, 1, None): False, (3, None, 2, 0): False, (3, None, 2, 1): False, (3, None, 2, None): False, (3, None, None, 0): False, (3, None, None, 1): False, (3, None, None, 2): False, (3, None, None, None): False, (None, 0, 1, 2): False, (None, 0, 1, 3): True, (None, 0, 1, None): True, (None, 0, 2, 1): False, (None, 0, 2, 3): True, (None, 0, 2, None): True, (None, 0, 3, 1): False, (None, 0, 3, 2): False, (None, 0, 3, None): False, (None, 0, None, 1): False, (None, 0, None, 2): False, (None, 0, None, 3): True, (None, 0, None, None): True, (None, 1, 0, 2): False, (None, 1, 0, 3): True, (None, 1, 0, None): True, (None, 1, 2, 0): False, (None, 1, 2, 3): True, (None, 1, 2, None): True, (None, 1, 3, 0): False, (None, 1, 3, 2): False, (None, 1, 3, None): False, (None, 1, None, 0): False, (None, 1, None, 2): False, (None, 1, None, 3): True, (None, 1, None, None): True, (None, 2, 0, 1): False, (None, 2, 0, 3): True, (None, 2, 0, None): True, (None, 2, 1, 0): False, (None, 2, 1, 3): True, (None, 2, 1, None): True, (None, 2, 3, 0): False, (None, 2, 3, 1): False, (None, 2, 3, None): False, (None, 2, None, 0): False, (None, 2, None, 1): False, (None, 2, None, 3): True, (None, 2, None, None): True, (None, 3, 0, 1): False, (None, 3, 0, 2): False, (None, 3, 0, None): False, (None, 3, 1, 0): False, (None, 3, 1, 2): False, (None, 3, 1, None): False, (None, 3, 2, 0): False, (None, 3, 2, 1): False, (None, 3, 2, None): False, (None, 3, None, 0): False, (None, 3, None, 1): False, (None, 3, None, 2): False, (None, 3, None, None): False, (None, None, 0, 1): False, (None, None, 0, 2): False, (None, None, 0, 3): True, (None, None, 0, None): True, (None, None, 1, 0): False, (None, None, 1, 2): False, (None, None, 1, 3): True, (None, None, 1, None): True, (None, None, 2, 0): False, (None, None, 2, 1): False, (None, None, 2, 3): True, (None, None, 2, None): True, (None, None, 3, 0): False, (None, None, 3, 1): False, (None, None, 3, 2): False, (None, None, 3, None): False, (None, None, None, 0): False, (None, None, None, 1): False, (None, None, None, 2): False, (None, None, None, 3): True, }, ("c3sx", "rcccx"): { (0, 1, 2, 3): False, (0, 1, 2, None): True, (0, 1, 3, 2): False, (0, 1, 3, None): False, (0, 1, None, 2): False, (0, 1, None, 3): False, (0, 1, None, None): True, (0, 2, 1, 3): False, (0, 2, 1, None): True, (0, 2, 3, 1): False, (0, 2, 3, None): False, (0, 2, None, 1): False, (0, 2, None, 3): False, (0, 2, None, None): True, (0, 3, 1, 2): False, (0, 3, 1, None): False, (0, 3, 2, 1): False, (0, 3, 2, None): False, (0, 3, None, 1): False, (0, 3, None, 2): False, (0, 3, None, None): False, (0, None, 1, 2): False, (0, None, 1, 3): False, (0, None, 1, None): True, (0, None, 2, 1): False, (0, None, 2, 3): False, (0, None, 2, None): True, (0, None, 3, 1): False, (0, None, 3, 2): False, (0, None, 3, None): False, (0, None, None, 1): False, (0, None, None, 2): False, (0, None, None, 3): False, (0, None, None, None): True, (1, 0, 2, 3): False, (1, 0, 2, None): True, (1, 0, 3, 2): False, (1, 0, 3, None): False, (1, 0, None, 2): False, (1, 0, None, 3): False, (1, 0, None, None): True, (1, 2, 0, 3): False, (1, 2, 0, None): True, (1, 2, 3, 0): False, (1, 2, 3, None): False, (1, 2, None, 0): False, (1, 2, None, 3): False, (1, 2, None, None): True, (1, 3, 0, 2): False, (1, 3, 0, None): False, (1, 3, 2, 0): False, (1, 3, 2, None): False, (1, 3, None, 0): False, (1, 3, None, 2): False, (1, 3, None, None): False, (1, None, 0, 2): False, (1, None, 0, 3): False, (1, None, 0, None): True, (1, None, 2, 0): False, (1, None, 2, 3): False, (1, None, 2, None): True, (1, None, 3, 0): False, (1, None, 3, 2): False, (1, None, 3, None): False, (1, None, None, 0): False, (1, None, None, 2): False, (1, None, None, 3): False, (1, None, None, None): True, (2, 0, 1, 3): False, (2, 0, 1, None): True, (2, 0, 3, 1): False, (2, 0, 3, None): False, (2, 0, None, 1): False, (2, 0, None, 3): False, (2, 0, None, None): True, (2, 1, 0, 3): False, (2, 1, 0, None): True, (2, 1, 3, 0): False, (2, 1, 3, None): False, (2, 1, None, 0): False, (2, 1, None, 3): False, (2, 1, None, None): True, (2, 3, 0, 1): False, (2, 3, 0, None): False, (2, 3, 1, 0): False, (2, 3, 1, None): False, (2, 3, None, 0): False, (2, 3, None, 1): False, (2, 3, None, None): False, (2, None, 0, 1): False, (2, None, 0, 3): False, (2, None, 0, None): True, (2, None, 1, 0): False, (2, None, 1, 3): False, (2, None, 1, None): True, (2, None, 3, 0): False, (2, None, 3, 1): False, (2, None, 3, None): False, (2, None, None, 0): False, (2, None, None, 1): False, (2, None, None, 3): False, (2, None, None, None): True, (3, 0, 1, 2): False, (3, 0, 1, None): False, (3, 0, 2, 1): False, (3, 0, 2, None): False, (3, 0, None, 1): False, (3, 0, None, 2): False, (3, 0, None, None): False, (3, 1, 0, 2): False, (3, 1, 0, None): False, (3, 1, 2, 0): False, (3, 1, 2, None): False, (3, 1, None, 0): False, (3, 1, None, 2): False, (3, 1, None, None): False, (3, 2, 0, 1): False, (3, 2, 0, None): False, (3, 2, 1, 0): False, (3, 2, 1, None): False, (3, 2, None, 0): False, (3, 2, None, 1): False, (3, 2, None, None): False, (3, None, 0, 1): False, (3, None, 0, 2): False, (3, None, 0, None): False, (3, None, 1, 0): False, (3, None, 1, 2): False, (3, None, 1, None): False, (3, None, 2, 0): False, (3, None, 2, 1): False, (3, None, 2, None): False, (3, None, None, 0): False, (3, None, None, 1): False, (3, None, None, 2): False, (3, None, None, None): False, (None, 0, 1, 2): False, (None, 0, 1, 3): False, (None, 0, 1, None): True, (None, 0, 2, 1): False, (None, 0, 2, 3): False, (None, 0, 2, None): True, (None, 0, 3, 1): False, (None, 0, 3, 2): False, (None, 0, 3, None): False, (None, 0, None, 1): False, (None, 0, None, 2): False, (None, 0, None, 3): False, (None, 0, None, None): True, (None, 1, 0, 2): False, (None, 1, 0, 3): False, (None, 1, 0, None): True, (None, 1, 2, 0): False, (None, 1, 2, 3): False, (None, 1, 2, None): True, (None, 1, 3, 0): False, (None, 1, 3, 2): False, (None, 1, 3, None): False, (None, 1, None, 0): False, (None, 1, None, 2): False, (None, 1, None, 3): False, (None, 1, None, None): True, (None, 2, 0, 1): False, (None, 2, 0, 3): False, (None, 2, 0, None): True, (None, 2, 1, 0): False, (None, 2, 1, 3): False, (None, 2, 1, None): True, (None, 2, 3, 0): False, (None, 2, 3, 1): False, (None, 2, 3, None): False, (None, 2, None, 0): False, (None, 2, None, 1): False, (None, 2, None, 3): False, (None, 2, None, None): True, (None, 3, 0, 1): False, (None, 3, 0, 2): False, (None, 3, 0, None): False, (None, 3, 1, 0): False, (None, 3, 1, 2): False, (None, 3, 1, None): False, (None, 3, 2, 0): False, (None, 3, 2, 1): False, (None, 3, 2, None): False, (None, 3, None, 0): False, (None, 3, None, 1): False, (None, 3, None, 2): False, (None, 3, None, None): False, (None, None, 0, 1): False, (None, None, 0, 2): False, (None, None, 0, 3): False, (None, None, 0, None): True, (None, None, 1, 0): False, (None, None, 1, 2): False, (None, None, 1, 3): False, (None, None, 1, None): True, (None, None, 2, 0): False, (None, None, 2, 1): False, (None, None, 2, 3): False, (None, None, 2, None): True, (None, None, 3, 0): False, (None, None, 3, 1): False, (None, None, 3, 2): False, (None, None, 3, None): False, (None, None, None, 0): False, (None, None, None, 1): False, (None, None, None, 2): False, (None, None, None, 3): False, }, ("ccx", "c3sx"): { (0, 1, 2): False, (0, 1, 3): True, (0, 1, None): True, (0, 2, 1): False, (0, 2, 3): True, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): True, (0, None, None): True, (1, 0, 2): False, (1, 0, 3): True, (1, 0, None): True, (1, 2, 0): False, (1, 2, 3): True, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): True, (1, None, None): True, (2, 0, 1): False, (2, 0, 3): True, (2, 0, None): True, (2, 1, 0): False, (2, 1, 3): True, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): True, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, 3): True, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, 3): True, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, 3): True, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): True, }, ("ccx", "ccx"): { (0, 1, 2): True, (0, 1, None): True, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): False, (0, None, 2): True, (0, None, None): True, (1, 0, 2): True, (1, 0, None): True, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): False, (1, None, 2): True, (1, None, None): True, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): True, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): True, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): True, }, ("ccx", "cswap"): { (0, 1, 2): False, (0, 1, None): False, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): False, (1, 2, 0): True, (1, 2, None): True, (1, None, 0): False, (1, None, 2): False, (1, None, None): False, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): True, (2, 1, None): True, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, None): False, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("ccx", "ccz"): { (0, 1, 2): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, None): True, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, None): True, (1, None, 0): False, (1, None, 2): False, (1, None, None): True, (2, 0, 1): False, (2, 0, None): True, (2, 1, 0): False, (2, 1, None): True, (2, None, 0): False, (2, None, 1): False, (2, None, None): True, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): True, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("ccx", "rccx"): { (0, 1, 2): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, None): True, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("ccx", "rcccx"): { (0, 1, 2): False, (0, 1, 3): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, 3): False, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): False, (0, None, None): True, (1, 0, 2): False, (1, 0, 3): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, 3): False, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): False, (1, None, None): True, (2, 0, 1): False, (2, 0, 3): False, (2, 0, None): True, (2, 1, 0): False, (2, 1, 3): False, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): False, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, 3): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, 3): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, 3): False, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): False, }, ("dcx", "c3sx"): False, ("dcx", "ccx"): False, ("dcx", "dcx"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("dcx", "cswap"): False, ("dcx", "ccz"): False, ("dcx", "rccx"): False, ("dcx", "rcccx"): False, ("dcx", "ecr"): False, ("dcx", "csdg"): False, ("dcx", "swap"): False, ("dcx", "iswap"): False, ("ch", "cx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): False, }, ("ch", "c3sx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("ch", "ccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("ch", "dcx"): False, ("ch", "ch"): { (0, 1): True, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("ch", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("ch", "csx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): False, }, ("ch", "cy"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): False, }, ("ch", "cz"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("ch", "ccz"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): True, (None, 0): False, (None, 1): False, (None, 2): False, }, ("ch", "rccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("ch", "rcccx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("ch", "ecr"): False, ("ch", "cs"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("ch", "csdg"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("ch", "swap"): False, ("ch", "iswap"): False, ("cswap", "c3sx"): { (0, 1, 2): True, (0, 1, 3): False, (0, 1, None): False, (0, 2, 1): True, (0, 2, 3): False, (0, 2, None): False, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): False, (0, None, None): True, (1, 0, 2): True, (1, 0, 3): False, (1, 0, None): False, (1, 2, 0): True, (1, 2, 3): False, (1, 2, None): False, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): False, (1, None, None): True, (2, 0, 1): True, (2, 0, 3): False, (2, 0, None): False, (2, 1, 0): True, (2, 1, 3): False, (2, 1, None): False, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): False, (2, None, None): True, (3, 0, 1): True, (3, 0, 2): True, (3, 0, None): False, (3, 1, 0): True, (3, 1, 2): True, (3, 1, None): False, (3, 2, 0): True, (3, 2, 1): True, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): True, (None, 0, 2): True, (None, 0, 3): False, (None, 0, None): False, (None, 1, 0): True, (None, 1, 2): True, (None, 1, 3): False, (None, 1, None): False, (None, 2, 0): True, (None, 2, 1): True, (None, 2, 3): False, (None, 2, None): False, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): False, }, ("cswap", "cswap"): { (0, 1, 2): True, (0, 1, None): False, (0, 2, 1): True, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): False, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, None): False, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): False, (None, 1, 0): False, (None, 1, 2): True, (None, 1, None): False, (None, 2, 0): False, (None, 2, 1): True, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("cswap", "rcccx"): { (0, 1, 2): False, (0, 1, 3): False, (0, 1, None): False, (0, 2, 1): False, (0, 2, 3): False, (0, 2, None): False, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): False, (0, None, None): True, (1, 0, 2): False, (1, 0, 3): False, (1, 0, None): False, (1, 2, 0): False, (1, 2, 3): False, (1, 2, None): False, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): False, (1, None, None): True, (2, 0, 1): True, (2, 0, 3): False, (2, 0, None): False, (2, 1, 0): True, (2, 1, 3): False, (2, 1, None): False, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): False, (2, None, None): True, (3, 0, 1): True, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): True, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): True, (None, 0, 2): False, (None, 0, 3): False, (None, 0, None): False, (None, 1, 0): True, (None, 1, 2): False, (None, 1, 3): False, (None, 1, None): False, (None, 2, 0): False, (None, 2, 1): False, (None, 2, 3): False, (None, 2, None): False, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): False, }, ("csx", "c3sx"): { (0, 1): False, (0, 2): False, (0, 3): True, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): True, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): True, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): True, }, ("csx", "ccx"): { (0, 1): False, (0, 2): True, (0, None): True, (1, 0): False, (1, 2): True, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): True, }, ("csx", "dcx"): False, ("csx", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("csx", "csx"): { (0, 1): True, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("csx", "ccz"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): True, (None, 0): False, (None, 1): False, (None, 2): False, }, ("csx", "rccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("csx", "rcccx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("csx", "ecr"): { (0, 1): False, (0, None): False, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("csx", "csdg"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("csx", "swap"): False, ("csx", "iswap"): False, ("cy", "c3sx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("cy", "ccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cy", "dcx"): False, ("cy", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cy", "csx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): False, }, ("cy", "cy"): { (0, 1): True, (0, None): True, (1, 0): False, (1, None): False, (None, 0): False, (None, 1): True, }, ("cy", "cz"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("cy", "ccz"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): True, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cy", "rccx"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): True, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("cy", "rcccx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): True, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): True, (2, 0): False, (2, 1): False, (2, 3): True, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("cy", "ecr"): False, ("cy", "csdg"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): True, (None, 0): False, (None, 1): False, }, ("cy", "swap"): False, ("cy", "iswap"): False, ("cz", "c3sx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("cz", "ccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("cz", "dcx"): False, ("cz", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): True, (1, None): False, (2, 0): False, (2, 1): True, (2, None): False, (None, 0): True, (None, 1): False, (None, 2): False, }, ("cz", "csx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): True, (None, 1): False, }, ("cz", "cz"): True, ("cz", "ccz"): True, ("cz", "rccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("cz", "rcccx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("cz", "ecr"): False, ("cz", "csdg"): True, ("cz", "swap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("cz", "iswap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("ccz", "c3sx"): { (0, 1, 2): True, (0, 1, 3): False, (0, 1, None): True, (0, 2, 1): True, (0, 2, 3): False, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): True, (0, None, 2): True, (0, None, 3): False, (0, None, None): True, (1, 0, 2): True, (1, 0, 3): False, (1, 0, None): True, (1, 2, 0): True, (1, 2, 3): False, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): True, (1, None, 2): True, (1, None, 3): False, (1, None, None): True, (2, 0, 1): True, (2, 0, 3): False, (2, 0, None): True, (2, 1, 0): True, (2, 1, 3): False, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): True, (2, None, 1): True, (2, None, 3): False, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): True, (None, 0, 2): True, (None, 0, 3): False, (None, 0, None): True, (None, 1, 0): True, (None, 1, 2): True, (None, 1, 3): False, (None, 1, None): True, (None, 2, 0): True, (None, 2, 1): True, (None, 2, 3): False, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): True, (None, None, 1): True, (None, None, 2): True, (None, None, 3): False, }, ("ccz", "cswap"): { (0, 1, 2): True, (0, 1, None): False, (0, 2, 1): True, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): True, (1, 0, None): False, (1, 2, 0): True, (1, 2, None): True, (1, None, 0): False, (1, None, 2): True, (1, None, None): False, (2, 0, 1): True, (2, 0, None): False, (2, 1, 0): True, (2, 1, None): True, (2, None, 0): False, (2, None, 1): True, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): True, (None, 1, None): False, (None, 2, 0): False, (None, 2, 1): True, (None, 2, None): False, (None, None, 0): True, (None, None, 1): False, (None, None, 2): False, }, ("ccz", "ccz"): True, ("ccz", "rccx"): { (0, 1, 2): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): True, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): True, (1, None, 2): False, (1, None, None): True, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): True, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): True, (None, 1, 2): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): True, (None, None, 1): True, (None, None, 2): False, }, ("ccz", "rcccx"): { (0, 1, 2): True, (0, 1, 3): False, (0, 1, None): True, (0, 2, 1): True, (0, 2, 3): False, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): True, (0, None, 2): True, (0, None, 3): False, (0, None, None): True, (1, 0, 2): True, (1, 0, 3): False, (1, 0, None): True, (1, 2, 0): True, (1, 2, 3): False, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): True, (1, None, 2): True, (1, None, 3): False, (1, None, None): True, (2, 0, 1): True, (2, 0, 3): False, (2, 0, None): True, (2, 1, 0): True, (2, 1, 3): False, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): True, (2, None, 1): True, (2, None, 3): False, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): True, (None, 0, 2): True, (None, 0, 3): False, (None, 0, None): True, (None, 1, 0): True, (None, 1, 2): True, (None, 1, 3): False, (None, 1, None): True, (None, 2, 0): True, (None, 2, 1): True, (None, 2, 3): False, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): True, (None, None, 1): True, (None, None, 2): True, (None, None, 3): False, }, ("h", "id"): True, ("h", "sx"): False, ("h", "x"): False, ("h", "cx"): False, ("h", "c3sx"): False, ("h", "ccx"): False, ("h", "dcx"): False, ("h", "ch"): { (0,): False, (1,): True, }, ("h", "cswap"): False, ("h", "csx"): False, ("h", "cy"): False, ("h", "cz"): False, ("h", "ccz"): False, ("h", "h"): True, ("h", "rccx"): False, ("h", "rcccx"): False, ("h", "ecr"): False, ("h", "s"): False, ("h", "sdg"): False, ("h", "cs"): False, ("h", "csdg"): False, ("h", "swap"): False, ("h", "iswap"): False, ("h", "sxdg"): False, ("h", "t"): False, ("h", "tdg"): False, ("h", "y"): False, ("h", "z"): False, ("rccx", "c3sx"): { (0, 1, 2): False, (0, 1, 3): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, 3): False, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): False, (0, None, None): True, (1, 0, 2): False, (1, 0, 3): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, 3): False, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): False, (1, None, None): True, (2, 0, 1): False, (2, 0, 3): False, (2, 0, None): True, (2, 1, 0): False, (2, 1, 3): False, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): False, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, 3): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, 3): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, 3): False, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): False, }, ("rccx", "cswap"): { (0, 1, 2): False, (0, 1, None): False, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): False, (1, 0, None): False, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, None): False, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, None): False, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("rccx", "rccx"): { (0, 1, 2): True, (0, 1, None): True, (0, 2, 1): False, (0, 2, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, None): True, (1, 0, 2): True, (1, 0, None): True, (1, 2, 0): False, (1, 2, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, None): True, (2, 0, 1): False, (2, 0, None): False, (2, 1, 0): False, (2, 1, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): True, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, }, ("rccx", "rcccx"): { (0, 1, 2): False, (0, 1, 3): False, (0, 1, None): True, (0, 2, 1): False, (0, 2, 3): True, (0, 2, None): True, (0, 3, 1): False, (0, 3, 2): False, (0, 3, None): False, (0, None, 1): False, (0, None, 2): False, (0, None, 3): False, (0, None, None): True, (1, 0, 2): False, (1, 0, 3): False, (1, 0, None): True, (1, 2, 0): False, (1, 2, 3): True, (1, 2, None): True, (1, 3, 0): False, (1, 3, 2): False, (1, 3, None): False, (1, None, 0): False, (1, None, 2): False, (1, None, 3): False, (1, None, None): True, (2, 0, 1): False, (2, 0, 3): True, (2, 0, None): True, (2, 1, 0): False, (2, 1, 3): True, (2, 1, None): True, (2, 3, 0): False, (2, 3, 1): False, (2, 3, None): False, (2, None, 0): False, (2, None, 1): False, (2, None, 3): False, (2, None, None): True, (3, 0, 1): False, (3, 0, 2): False, (3, 0, None): False, (3, 1, 0): False, (3, 1, 2): False, (3, 1, None): False, (3, 2, 0): False, (3, 2, 1): False, (3, 2, None): False, (3, None, 0): False, (3, None, 1): False, (3, None, 2): False, (3, None, None): False, (None, 0, 1): False, (None, 0, 2): False, (None, 0, 3): False, (None, 0, None): True, (None, 1, 0): False, (None, 1, 2): False, (None, 1, 3): False, (None, 1, None): True, (None, 2, 0): False, (None, 2, 1): False, (None, 2, 3): True, (None, 2, None): True, (None, 3, 0): False, (None, 3, 1): False, (None, 3, 2): False, (None, 3, None): False, (None, None, 0): False, (None, None, 1): False, (None, None, 2): False, (None, None, 3): False, }, ("rcccx", "rcccx"): { (0, 1, 2, 3): True, (0, 1, 2, None): True, (0, 1, 3, 2): False, (0, 1, 3, None): False, (0, 1, None, 2): False, (0, 1, None, 3): False, (0, 1, None, None): True, (0, 2, 1, 3): True, (0, 2, 1, None): True, (0, 2, 3, 1): False, (0, 2, 3, None): False, (0, 2, None, 1): False, (0, 2, None, 3): False, (0, 2, None, None): True, (0, 3, 1, 2): False, (0, 3, 1, None): False, (0, 3, 2, 1): False, (0, 3, 2, None): False, (0, 3, None, 1): False, (0, 3, None, 2): False, (0, 3, None, None): False, (0, None, 1, 2): False, (0, None, 1, 3): False, (0, None, 1, None): True, (0, None, 2, 1): False, (0, None, 2, 3): True, (0, None, 2, None): True, (0, None, 3, 1): False, (0, None, 3, 2): False, (0, None, 3, None): False, (0, None, None, 1): False, (0, None, None, 2): False, (0, None, None, 3): False, (0, None, None, None): True, (1, 0, 2, 3): True, (1, 0, 2, None): True, (1, 0, 3, 2): False, (1, 0, 3, None): False, (1, 0, None, 2): False, (1, 0, None, 3): False, (1, 0, None, None): True, (1, 2, 0, 3): True, (1, 2, 0, None): True, (1, 2, 3, 0): False, (1, 2, 3, None): False, (1, 2, None, 0): False, (1, 2, None, 3): False, (1, 2, None, None): True, (1, 3, 0, 2): False, (1, 3, 0, None): False, (1, 3, 2, 0): False, (1, 3, 2, None): False, (1, 3, None, 0): False, (1, 3, None, 2): False, (1, 3, None, None): False, (1, None, 0, 2): False, (1, None, 0, 3): False, (1, None, 0, None): True, (1, None, 2, 0): False, (1, None, 2, 3): True, (1, None, 2, None): True, (1, None, 3, 0): False, (1, None, 3, 2): False, (1, None, 3, None): False, (1, None, None, 0): False, (1, None, None, 2): False, (1, None, None, 3): False, (1, None, None, None): True, (2, 0, 1, 3): True, (2, 0, 1, None): True, (2, 0, 3, 1): False, (2, 0, 3, None): False, (2, 0, None, 1): False, (2, 0, None, 3): False, (2, 0, None, None): True, (2, 1, 0, 3): True, (2, 1, 0, None): True, (2, 1, 3, 0): False, (2, 1, 3, None): False, (2, 1, None, 0): False, (2, 1, None, 3): False, (2, 1, None, None): True, (2, 3, 0, 1): False, (2, 3, 0, None): False, (2, 3, 1, 0): False, (2, 3, 1, None): False, (2, 3, None, 0): False, (2, 3, None, 1): False, (2, 3, None, None): False, (2, None, 0, 1): False, (2, None, 0, 3): True, (2, None, 0, None): True, (2, None, 1, 0): False, (2, None, 1, 3): True, (2, None, 1, None): True, (2, None, 3, 0): False, (2, None, 3, 1): False, (2, None, 3, None): False, (2, None, None, 0): False, (2, None, None, 1): False, (2, None, None, 3): False, (2, None, None, None): True, (3, 0, 1, 2): False, (3, 0, 1, None): False, (3, 0, 2, 1): False, (3, 0, 2, None): False, (3, 0, None, 1): False, (3, 0, None, 2): False, (3, 0, None, None): False, (3, 1, 0, 2): False, (3, 1, 0, None): False, (3, 1, 2, 0): False, (3, 1, 2, None): False, (3, 1, None, 0): False, (3, 1, None, 2): False, (3, 1, None, None): False, (3, 2, 0, 1): False, (3, 2, 0, None): False, (3, 2, 1, 0): False, (3, 2, 1, None): False, (3, 2, None, 0): False, (3, 2, None, 1): False, (3, 2, None, None): False, (3, None, 0, 1): False, (3, None, 0, 2): False, (3, None, 0, None): False, (3, None, 1, 0): False, (3, None, 1, 2): False, (3, None, 1, None): False, (3, None, 2, 0): False, (3, None, 2, 1): False, (3, None, 2, None): False, (3, None, None, 0): False, (3, None, None, 1): False, (3, None, None, 2): False, (3, None, None, None): False, (None, 0, 1, 2): False, (None, 0, 1, 3): False, (None, 0, 1, None): True, (None, 0, 2, 1): False, (None, 0, 2, 3): True, (None, 0, 2, None): True, (None, 0, 3, 1): False, (None, 0, 3, 2): False, (None, 0, 3, None): False, (None, 0, None, 1): False, (None, 0, None, 2): False, (None, 0, None, 3): False, (None, 0, None, None): True, (None, 1, 0, 2): False, (None, 1, 0, 3): False, (None, 1, 0, None): True, (None, 1, 2, 0): False, (None, 1, 2, 3): True, (None, 1, 2, None): True, (None, 1, 3, 0): False, (None, 1, 3, 2): False, (None, 1, 3, None): False, (None, 1, None, 0): False, (None, 1, None, 2): False, (None, 1, None, 3): False, (None, 1, None, None): True, (None, 2, 0, 1): False, (None, 2, 0, 3): True, (None, 2, 0, None): True, (None, 2, 1, 0): False, (None, 2, 1, 3): True, (None, 2, 1, None): True, (None, 2, 3, 0): False, (None, 2, 3, 1): False, (None, 2, 3, None): False, (None, 2, None, 0): False, (None, 2, None, 1): False, (None, 2, None, 3): False, (None, 2, None, None): True, (None, 3, 0, 1): False, (None, 3, 0, 2): False, (None, 3, 0, None): False, (None, 3, 1, 0): False, (None, 3, 1, 2): False, (None, 3, 1, None): False, (None, 3, 2, 0): False, (None, 3, 2, 1): False, (None, 3, 2, None): False, (None, 3, None, 0): False, (None, 3, None, 1): False, (None, 3, None, 2): False, (None, 3, None, None): False, (None, None, 0, 1): False, (None, None, 0, 2): False, (None, None, 0, 3): False, (None, None, 0, None): True, (None, None, 1, 0): False, (None, None, 1, 2): False, (None, None, 1, 3): False, (None, None, 1, None): True, (None, None, 2, 0): False, (None, None, 2, 1): False, (None, None, 2, 3): True, (None, None, 2, None): True, (None, None, 3, 0): False, (None, None, 3, 1): False, (None, None, 3, 2): False, (None, None, 3, None): False, (None, None, None, 0): False, (None, None, None, 1): False, (None, None, None, 2): False, (None, None, None, 3): False, }, ("ecr", "c3sx"): { (0, 1): False, (0, 2): False, (0, 3): False, (0, None): False, (1, 0): False, (1, 2): False, (1, 3): False, (1, None): False, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): False, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): True, }, ("ecr", "ccx"): { (0, 1): False, (0, 2): False, (0, None): False, (1, 0): False, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): True, }, ("ecr", "cswap"): False, ("ecr", "ccz"): False, ("ecr", "rccx"): False, ("ecr", "rcccx"): False, ("ecr", "ecr"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): True, }, ("ecr", "csdg"): False, ("ecr", "swap"): False, ("ecr", "iswap"): False, ("s", "id"): True, ("s", "sx"): False, ("s", "x"): False, ("s", "cx"): { (0,): True, (1,): False, }, ("s", "c3sx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("s", "ccx"): { (0,): True, (1,): True, (2,): False, }, ("s", "dcx"): False, ("s", "ch"): { (0,): True, (1,): False, }, ("s", "cswap"): { (0,): True, (1,): False, (2,): False, }, ("s", "csx"): { (0,): True, (1,): False, }, ("s", "cy"): { (0,): True, (1,): False, }, ("s", "cz"): True, ("s", "ccz"): True, ("s", "rccx"): { (0,): True, (1,): True, (2,): False, }, ("s", "rcccx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("s", "ecr"): False, ("s", "s"): True, ("s", "sdg"): True, ("s", "cs"): True, ("s", "csdg"): True, ("s", "swap"): False, ("s", "iswap"): False, ("s", "sxdg"): False, ("s", "t"): True, ("s", "tdg"): True, ("s", "y"): False, ("s", "z"): True, ("sdg", "cx"): { (0,): True, (1,): False, }, ("sdg", "c3sx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("sdg", "ccx"): { (0,): True, (1,): True, (2,): False, }, ("sdg", "dcx"): False, ("sdg", "ch"): { (0,): True, (1,): False, }, ("sdg", "cswap"): { (0,): True, (1,): False, (2,): False, }, ("sdg", "csx"): { (0,): True, (1,): False, }, ("sdg", "cy"): { (0,): True, (1,): False, }, ("sdg", "cz"): True, ("sdg", "ccz"): True, ("sdg", "rccx"): { (0,): True, (1,): True, (2,): False, }, ("sdg", "rcccx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("sdg", "ecr"): False, ("sdg", "sdg"): True, ("sdg", "cs"): True, ("sdg", "csdg"): True, ("sdg", "swap"): False, ("sdg", "iswap"): False, ("sdg", "sxdg"): False, ("sdg", "tdg"): True, ("cs", "cx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): True, (None, 1): False, }, ("cs", "c3sx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("cs", "ccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("cs", "dcx"): False, ("cs", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): True, (1, None): False, (2, 0): False, (2, 1): True, (2, None): False, (None, 0): True, (None, 1): False, (None, 2): False, }, ("cs", "csx"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): True, (None, 1): False, }, ("cs", "cy"): { (0, 1): False, (0, None): True, (1, 0): False, (1, None): False, (None, 0): True, (None, 1): False, }, ("cs", "cz"): True, ("cs", "ccz"): True, ("cs", "rccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("cs", "rcccx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("cs", "ecr"): False, ("cs", "cs"): True, ("cs", "csdg"): True, ("cs", "swap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("cs", "iswap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("csdg", "c3sx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("csdg", "ccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("csdg", "cswap"): { (0, 1): False, (0, 2): False, (0, None): True, (1, 0): False, (1, 2): True, (1, None): False, (2, 0): False, (2, 1): True, (2, None): False, (None, 0): True, (None, 1): False, (None, 2): False, }, ("csdg", "ccz"): True, ("csdg", "rccx"): { (0, 1): True, (0, 2): False, (0, None): True, (1, 0): True, (1, 2): False, (1, None): True, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): True, (None, 1): True, (None, 2): False, }, ("csdg", "rcccx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): True, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): True, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): True, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): True, (None, 1): True, (None, 2): True, (None, 3): False, }, ("csdg", "csdg"): True, ("csdg", "swap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("csdg", "iswap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("swap", "c3sx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): False, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): False, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): False, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("swap", "ccx"): { (0, 1): True, (0, 2): False, (0, None): False, (1, 0): True, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("swap", "cswap"): { (0, 1): False, (0, 2): False, (0, None): False, (1, 0): False, (1, 2): True, (1, None): False, (2, 0): False, (2, 1): True, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("swap", "ccz"): { (0, 1): True, (0, 2): True, (0, None): False, (1, 0): True, (1, 2): True, (1, None): False, (2, 0): True, (2, 1): True, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("swap", "rccx"): False, ("swap", "rcccx"): { (0, 1): True, (0, 2): False, (0, 3): False, (0, None): False, (1, 0): True, (1, 2): False, (1, 3): False, (1, None): False, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): False, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("swap", "swap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("swap", "iswap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("iswap", "c3sx"): { (0, 1): True, (0, 2): True, (0, 3): False, (0, None): False, (1, 0): True, (1, 2): True, (1, 3): False, (1, None): False, (2, 0): True, (2, 1): True, (2, 3): False, (2, None): False, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("iswap", "ccx"): { (0, 1): True, (0, 2): False, (0, None): False, (1, 0): True, (1, 2): False, (1, None): False, (2, 0): False, (2, 1): False, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("iswap", "cswap"): { (0, 1): False, (0, 2): False, (0, None): False, (1, 0): False, (1, 2): True, (1, None): False, (2, 0): False, (2, 1): True, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("iswap", "ccz"): { (0, 1): True, (0, 2): True, (0, None): False, (1, 0): True, (1, 2): True, (1, None): False, (2, 0): True, (2, 1): True, (2, None): False, (None, 0): False, (None, 1): False, (None, 2): False, }, ("iswap", "rccx"): False, ("iswap", "rcccx"): { (0, 1): True, (0, 2): False, (0, 3): False, (0, None): False, (1, 0): True, (1, 2): False, (1, 3): False, (1, None): False, (2, 0): False, (2, 1): False, (2, 3): False, (2, None): False, (3, 0): False, (3, 1): False, (3, 2): False, (3, None): False, (None, 0): False, (None, 1): False, (None, 2): False, (None, 3): False, }, ("iswap", "iswap"): { (0, 1): True, (0, None): False, (1, 0): True, (1, None): False, (None, 0): False, (None, 1): False, }, ("sxdg", "cx"): { (0,): False, (1,): True, }, ("sxdg", "c3sx"): { (0,): False, (1,): False, (2,): False, (3,): True, }, ("sxdg", "ccx"): { (0,): False, (1,): False, (2,): True, }, ("sxdg", "dcx"): False, ("sxdg", "ch"): False, ("sxdg", "cswap"): False, ("sxdg", "csx"): { (0,): False, (1,): True, }, ("sxdg", "cy"): False, ("sxdg", "cz"): False, ("sxdg", "ccz"): False, ("sxdg", "rccx"): False, ("sxdg", "rcccx"): False, ("sxdg", "ecr"): { (0,): False, (1,): True, }, ("sxdg", "cs"): False, ("sxdg", "csdg"): False, ("sxdg", "swap"): False, ("sxdg", "iswap"): False, ("sxdg", "sxdg"): True, ("t", "id"): True, ("t", "sx"): False, ("t", "x"): False, ("t", "cx"): { (0,): True, (1,): False, }, ("t", "c3sx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("t", "ccx"): { (0,): True, (1,): True, (2,): False, }, ("t", "dcx"): False, ("t", "ch"): { (0,): True, (1,): False, }, ("t", "cswap"): { (0,): True, (1,): False, (2,): False, }, ("t", "csx"): { (0,): True, (1,): False, }, ("t", "cy"): { (0,): True, (1,): False, }, ("t", "cz"): True, ("t", "ccz"): True, ("t", "rccx"): { (0,): True, (1,): True, (2,): False, }, ("t", "rcccx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("t", "ecr"): False, ("t", "sdg"): True, ("t", "cs"): True, ("t", "csdg"): True, ("t", "swap"): False, ("t", "iswap"): False, ("t", "sxdg"): False, ("t", "t"): True, ("t", "tdg"): True, ("t", "y"): False, ("t", "z"): True, ("tdg", "cx"): { (0,): True, (1,): False, }, ("tdg", "c3sx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("tdg", "ccx"): { (0,): True, (1,): True, (2,): False, }, ("tdg", "dcx"): False, ("tdg", "ch"): { (0,): True, (1,): False, }, ("tdg", "cswap"): { (0,): True, (1,): False, (2,): False, }, ("tdg", "csx"): { (0,): True, (1,): False, }, ("tdg", "cy"): { (0,): True, (1,): False, }, ("tdg", "cz"): True, ("tdg", "ccz"): True, ("tdg", "rccx"): { (0,): True, (1,): True, (2,): False, }, ("tdg", "rcccx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("tdg", "ecr"): False, ("tdg", "cs"): True, ("tdg", "csdg"): True, ("tdg", "swap"): False, ("tdg", "iswap"): False, ("tdg", "sxdg"): False, ("tdg", "tdg"): True, ("y", "id"): True, ("y", "sx"): False, ("y", "cx"): False, ("y", "c3sx"): False, ("y", "ccx"): False, ("y", "dcx"): False, ("y", "ch"): False, ("y", "cswap"): False, ("y", "csx"): False, ("y", "cy"): { (0,): False, (1,): True, }, ("y", "cz"): False, ("y", "ccz"): False, ("y", "rccx"): False, ("y", "rcccx"): False, ("y", "ecr"): False, ("y", "sdg"): False, ("y", "cs"): False, ("y", "csdg"): False, ("y", "swap"): False, ("y", "iswap"): False, ("y", "sxdg"): False, ("y", "tdg"): False, ("y", "y"): True, ("y", "z"): False, ("z", "id"): True, ("z", "sx"): False, ("z", "cx"): { (0,): True, (1,): False, }, ("z", "c3sx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("z", "ccx"): { (0,): True, (1,): True, (2,): False, }, ("z", "dcx"): False, ("z", "ch"): { (0,): True, (1,): False, }, ("z", "cswap"): { (0,): True, (1,): False, (2,): False, }, ("z", "csx"): { (0,): True, (1,): False, }, ("z", "cy"): { (0,): True, (1,): False, }, ("z", "cz"): True, ("z", "ccz"): True, ("z", "rccx"): { (0,): True, (1,): True, (2,): False, }, ("z", "rcccx"): { (0,): True, (1,): True, (2,): True, (3,): False, }, ("z", "ecr"): False, ("z", "sdg"): True, ("z", "cs"): True, ("z", "csdg"): True, ("z", "swap"): False, ("z", "iswap"): False, ("z", "sxdg"): False, ("z", "tdg"): True, ("z", "z"): True, }