/
std2Q_XYCNOT.py
512 lines (492 loc) · 23 KB
/
std2Q_XYCNOT.py
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from __future__ import division, print_function, absolute_import, unicode_literals
#*****************************************************************
# pyGSTi 0.9: Copyright 2015 Sandia Corporation
# This Software is released under the GPL license detailed
# in the file "license.txt" in the top-level pyGSTi directory
#*****************************************************************
"""
Variables for working with the 2-qubit gate set containing the gates
I*X(pi/2), I*Y(pi/2), X(pi/2)*I, Y(pi/2)*I, and CNOT.
"""
import numpy as _np
from . import gatestringconstruction as _strc
from . import gatesetconstruction as _setc
from ..tools import gatetools as _gt
description = "I*X(pi/2), I*Y(pi/2), X(pi/2)*I, Y(pi/2)*I, and CNOT gates"
gates = ['Gix','Giy','Gxi','Gyi','Gcnot']
fiducials16 = _strc.gatestring_list(
[ (), ('Gix',), ('Giy',), ('Gix','Gix'),
('Gxi',), ('Gxi','Gix'), ('Gxi','Giy'), ('Gxi','Gix','Gix'),
('Gyi',), ('Gyi','Gix'), ('Gyi','Giy'), ('Gyi','Gix','Gix'),
('Gxi','Gxi'), ('Gxi','Gxi','Gix'), ('Gxi','Gxi','Giy'), ('Gxi','Gxi','Gix','Gix') ] )
fiducials36 = _strc.gatestring_list(
[ (), ('Gix',), ('Giy',), ('Gix','Gix'), ('Gix','Gix','Gix'), ('Giy','Giy','Giy'),
('Gxi',), ('Gxi','Gix'), ('Gxi','Giy'), ('Gxi','Gix','Gix'), ('Gxi','Gix','Gix','Gix'), ('Gxi','Giy','Giy','Giy'),
('Gyi',), ('Gyi','Gix'), ('Gyi','Giy'), ('Gyi','Gix','Gix'), ('Gyi','Gix','Gix','Gix'), ('Gyi','Giy','Giy','Giy'),
('Gxi','Gxi'), ('Gxi','Gxi','Gix'), ('Gxi','Gxi','Giy'), ('Gxi','Gxi','Gix','Gix'), ('Gxi','Gxi','Gix','Gix','Gix'),
('Gxi','Gxi','Giy','Giy','Giy'), ('Gxi','Gxi','Gxi'), ('Gxi','Gxi','Gxi','Gix'), ('Gxi','Gxi','Gxi','Giy'),
('Gxi','Gxi','Gxi','Gix','Gix'), ('Gxi','Gxi','Gxi','Gix','Gix','Gix'), ('Gxi','Gxi','Gxi','Giy','Giy','Giy'),
('Gyi','Gyi','Gyi'), ('Gyi','Gyi','Gyi','Gix'), ('Gyi','Gyi','Gyi','Giy'), ('Gyi','Gyi','Gyi','Gix','Gix'),
('Gyi','Gyi','Gyi','Gix','Gix','Gix'), ('Gyi','Gyi','Gyi','Giy','Giy','Giy') ] )
fiducials = fiducials16
prepStrs = fiducials16
effectStrs = _strc.gatestring_list(
[(), ('Gix',), ('Giy',),
('Gix','Gix'), ('Gxi',),
('Gyi',), ('Gxi','Gxi'),
('Gxi','Gix'), ('Gxi','Giy'),
('Gyi','Gix'), ('Gyi','Giy')] )
legacy_effectStrs = _strc.gatestring_list(
[ (), ('Gix',), ('Giy',), ('Gxi',), ('Gyi',),
('Gix','Gxi'), ('Gxi','Giy'), ('Gyi','Gix'),
('Gyi','Giy'), ('Gxi','Gxi') ] )
germs = _strc.gatestring_list(
[('Gxi',),
('Gyi',),
('Gix',),
('Giy',),
('Gcnot',),
('Gxi', 'Gyi'),
('Gix', 'Giy'),
('Giy', 'Gyi'),
('Gix', 'Gxi'),
('Gix', 'Gyi'),
('Giy', 'Gxi'),
('Giy', 'Gcnot'),
('Gyi', 'Gcnot'),
('Gxi', 'Gcnot'),
('Gix', 'Gcnot'),
('Gxi', 'Gxi', 'Gyi'),
('Gix', 'Gix', 'Giy'),
('Gxi', 'Gyi', 'Gyi'),
('Gix', 'Giy', 'Giy'),
('Giy', 'Gxi', 'Gxi'),
('Giy', 'Gxi', 'Gyi'),
('Gix', 'Gxi', 'Giy'),
('Gix', 'Gyi', 'Gxi'),
('Gix', 'Gyi', 'Giy'),
('Gix', 'Giy', 'Gyi'),
('Gix', 'Giy', 'Gxi'),
('Giy', 'Gyi', 'Gxi'),
('Giy', 'Gcnot', 'Gxi'),
('Gix', 'Gix', 'Gcnot'),
('Gxi', 'Gcnot', 'Gcnot'),
('Giy', 'Gyi', 'Gcnot'),
('Gyi', 'Gcnot', 'Gcnot'),
('Gix', 'Giy', 'Gcnot'),
('Giy', 'Gcnot', 'Gcnot'),
('Gcnot', 'Gix', 'Gxi', 'Gxi'),
('Gyi', 'Gix', 'Gxi', 'Giy'),
('Gix', 'Giy', 'Gxi', 'Gyi'),
('Gix', 'Gix', 'Gix', 'Giy'),
('Gxi', 'Gyi', 'Gyi', 'Gyi'),
('Gyi', 'Gyi', 'Giy', 'Gyi'),
('Gyi', 'Gix', 'Gix', 'Gix'),
('Gxi', 'Gyi', 'Gix', 'Gix'),
('Gcnot', 'Gyi', 'Gcnot', 'Gxi'),
('Gcnot', 'Gix', 'Gcnot', 'Giy'),
('Gix', 'Gxi', 'Gcnot', 'Giy'),
('Gix', 'Giy', 'Gxi', 'Gcnot'),
('Giy', 'Gyi', 'Gxi', 'Gxi', 'Giy'),
('Gxi', 'Gxi', 'Giy', 'Gyi', 'Giy'),
('Giy', 'Gix', 'Gxi', 'Gix', 'Gxi'),
('Gyi', 'Giy', 'Gyi', 'Gix', 'Gix'),
('Giy', 'Gxi', 'Gix', 'Giy', 'Gyi'),
('Giy', 'Giy', 'Gxi', 'Gyi', 'Gxi'),
('Gyi', 'Gcnot', 'Giy', 'Giy', 'Gxi'),
('Gxi', 'Gix', 'Giy', 'Gxi', 'Giy', 'Gyi'),
('Gxi', 'Giy', 'Gix', 'Gyi', 'Gix', 'Gix'),
('Gyi', 'Giy', 'Gxi', 'Gyi', 'Gxi', 'Gcnot'),
('Gxi', 'Gxi', 'Gyi', 'Gxi', 'Gyi', 'Gyi'),
('Gix', 'Gix', 'Giy', 'Gix', 'Giy', 'Giy'),
('Gyi', 'Gxi', 'Gix', 'Giy', 'Gxi', 'Gix'),
('Gyi', 'Gxi', 'Gix', 'Gxi', 'Gix', 'Giy'),
('Gxi', 'Gix', 'Giy', 'Giy', 'Gxi', 'Gyi'),
('Gix', 'Giy', 'Giy', 'Gix', 'Gxi', 'Gxi'),
('Gyi', 'Giy', 'Gxi', 'Giy', 'Giy', 'Giy'),
('Gyi', 'Gyi', 'Gyi', 'Giy', 'Gyi', 'Gix'),
('Giy', 'Giy', 'Gxi', 'Giy', 'Gix', 'Giy'),
('Giy', 'Gix', 'Gyi', 'Gyi', 'Gix', 'Gxi', 'Giy'),
('Gyi', 'Gxi', 'Giy', 'Gxi', 'Gix', 'Gxi', 'Gyi', 'Giy'),
('Gix', 'Gix', 'Gyi', 'Gxi', 'Giy', 'Gxi', 'Giy', 'Gyi')
])
germs_lite = _strc.gatestring_list(
[('Gxi',),
('Gyi',),
('Gix',),
('Giy',),
('Gcnot',),
('Gxi', 'Gyi'),
('Gix', 'Giy'),
('Gxi', 'Gxi', 'Gyi'),
('Gix', 'Gix', 'Giy'),
('Gcnot', 'Gix', 'Gxi', 'Gxi'),
('Gxi', 'Gix', 'Giy', 'Gxi', 'Giy', 'Gyi'),
('Gxi', 'Giy', 'Gix', 'Gyi', 'Gix', 'Gix'),
('Gyi', 'Giy', 'Gxi', 'Gyi', 'Gxi', 'Gcnot'),
('Gyi', 'Gxi', 'Giy', 'Gxi', 'Gix', 'Gxi', 'Gyi', 'Giy')
])
legacy_germs = _strc.gatestring_list(
[('Gxi',), ('Gyi',), ('Gix',), ('Giy',), ('Gcnot',),
('Gxi', 'Gyi'), ('Gix', 'Giy'), ('Giy', 'Gyi'), ('Gix', 'Gyi'),
('Gyi', 'Gcnot'), ('Giy', 'Gcnot'),
('Gxi', 'Gcnot', 'Gcnot'),
('Giy', 'Gxi', 'Gcnot'),
('Giy', 'Gcnot', 'Gyi'),
('Giy', 'Gyi', 'Gcnot'),
('Gix', 'Gxi', 'Gcnot'),
('Giy', 'Giy', 'Gcnot'),
('Giy', 'Gcnot', 'Gxi'),
('Gix', 'Giy', 'Gcnot'),
('Giy', 'Gxi', 'Gyi'),
('Gix', 'Giy', 'Gyi'),
('Gyi', 'Gyi', 'Gyi', 'Gxi'),
('Giy', 'Giy', 'Giy', 'Gix'),
('Gxi', 'Gyi', 'Gix', 'Giy'),
('Gcnot', 'Gix', 'Gyi', 'Gyi'),
('Gcnot', 'Gix', 'Gix', 'Gcnot'),
('Gxi', 'Gcnot', 'Gyi', 'Gyi'),
('Gyi', 'Gyi', 'Gyi', 'Gix'),
('Gix', 'Gix', 'Giy', 'Gcnot', 'Gcnot'),
('Gcnot', 'Giy', 'Giy', 'Gix', 'Giy'),
('Gyi', 'Gcnot', 'Gix', 'Giy', 'Gyi'),
('Giy', 'Gxi', 'Gcnot', 'Gxi', 'Gcnot'),
('Gyi', 'Gcnot', 'Gxi', 'Gcnot', 'Gxi'),
('Gyi', 'Gxi', 'Gyi', 'Gxi', 'Gxi', 'Gxi'),
('Gyi', 'Gxi', 'Gyi', 'Gyi', 'Gxi', 'Gxi'),
('Gyi', 'Gyi', 'Gyi', 'Gxi', 'Gyi', 'Gxi'),
('Gxi', 'Gxi', 'Gyi', 'Gxi', 'Gyi', 'Gyi'),
('Giy', 'Gix', 'Giy', 'Gix', 'Gix', 'Gix'),
('Giy', 'Gix', 'Giy', 'Giy', 'Gix', 'Gix'),
('Giy', 'Giy', 'Giy', 'Gix', 'Giy', 'Gix'),
('Gix', 'Gix', 'Giy', 'Gix', 'Giy', 'Giy'),
('Gcnot', 'Gyi', 'Giy', 'Gxi', 'Gix', 'Gcnot'),
('Gxi', 'Giy', 'Gxi', 'Gcnot', 'Gyi', 'Gix'),
('Gxi', 'Giy', 'Giy', 'Giy', 'Gcnot', 'Gxi'),
('Gcnot', 'Gxi', 'Gcnot', 'Gxi', 'Giy', 'Gix'),
('Gyi', 'Gix', 'Gyi', 'Gix', 'Gxi', 'Gxi'),
('Gix', 'Gcnot', 'Gxi', 'Gix', 'Gxi', 'Gcnot'),
('Gxi', 'Giy', 'Gyi', 'Gxi', 'Gcnot', 'Gcnot'),
('Gix', 'Gix', 'Giy', 'Gcnot', 'Giy', 'Gcnot', 'Gxi'),
('Giy', 'Gxi', 'Gcnot', 'Gix', 'Gix', 'Giy', 'Giy'),
('Gxi', 'Gcnot', 'Giy', 'Gyi', 'Gxi', 'Gix', 'Giy'),
('Gcnot', 'Gcnot', 'Gix', 'Gxi', 'Giy', 'Gxi', 'Gxi'),
('Gxi', 'Gix', 'Giy', 'Gyi', 'Gix', 'Gix', 'Gix'),
('Gxi', 'Gix', 'Gyi', 'Gix', 'Gyi', 'Giy', 'Gyi'),
('Gix', 'Gix', 'Gix', 'Gix', 'Gxi', 'Gxi', 'Gyi'),
('Giy', 'Gcnot', 'Gxi', 'Gyi', 'Gyi', 'Gcnot', 'Gix', 'Gcnot'),
('Gxi', 'Gyi', 'Gxi', 'Giy', 'Gxi', 'Giy', 'Gix', 'Giy'),
('Giy', 'Giy', 'Gyi', 'Gix', 'Gcnot', 'Gxi', 'Gyi', 'Gyi'),
('Gxi', 'Gix', 'Gcnot', 'Gyi', 'Gix', 'Gcnot', 'Gix', 'Giy'),
('Gix', 'Gxi', 'Gxi', 'Giy', 'Gxi', 'Gyi', 'Gix', 'Gcnot'),
('Gix', 'Gix', 'Gyi', 'Gxi', 'Giy', 'Gix', 'Gcnot', 'Gyi'),
('Gix', 'Giy', 'Gix', 'Gxi', 'Gix', 'Giy', 'Gxi', 'Gxi'),
('Giy', 'Gix', 'Gcnot', 'Gxi', 'Gcnot', 'Gxi', 'Gcnot', 'Gyi'),
('Gxi', 'Giy', 'Gix', 'Gix', 'Gxi', 'Giy', 'Gxi', 'Gcnot'),
('Gyi', 'Gyi', 'Gyi', 'Gyi', 'Gix', 'Giy', 'Gix', 'Gyi')
])
#Construct the target gateset
gs_target = _setc.build_gateset(
[4], [('Q0','Q1')],['Gix','Giy','Gxi','Gyi','Gcnot'],
[ "I(Q0):X(pi/2,Q1)", "I(Q0):Y(pi/2,Q1)", "X(pi/2,Q0):I(Q1)", "Y(pi/2,Q0):I(Q1)", "CNOT(Q0,Q1)"],
effectLabels=['00','01','10','11'], effectExpressions=["0","1","2","3"])
#Wrong CNOT (bad 1Q phase factor)
legacy_gs_target = _setc.build_gateset(
[4], [('Q0','Q1')],['Gix','Giy','Gxi','Gyi','Gcnot'],
[ "I(Q0):X(pi/2,Q1)", "I(Q0):Y(pi/2,Q1)", "X(pi/2,Q0):I(Q1)", "Y(pi/2,Q0):I(Q1)", "CX(pi,Q0,Q1)" ],
effectLabels=['00','01','10','11'], effectExpressions=["0","1","2","3"])
global_fidPairs = [
(0, 1), (0, 5), (1, 3), (2, 4), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6), (15, 0),
(15, 5)]
pergerm_fidPairsDict = {
('Gyi',): [
(3, 1), (4, 1), (4, 2), (5, 0), (5, 1), (5, 7), (6, 0),
(6, 8), (7, 2), (7, 4), (7, 9), (8, 0), (8, 7), (9, 2),
(9, 3), (10, 9), (10, 10), (14, 7), (14, 9), (15, 10)],
('Gix',): [
(0, 5), (1, 0), (1, 1), (2, 2), (2, 5), (2, 9), (3, 3),
(3, 4), (3, 8), (4, 0), (4, 2), (4, 7), (4, 8), (4, 10),
(5, 0), (5, 1), (5, 2), (5, 6), (5, 8), (6, 7), (6, 8),
(6, 9), (7, 0), (7, 4), (8, 5), (8, 9), (9, 5), (10, 8),
(10, 10), (12, 2), (12, 4), (12, 7), (13, 2), (13, 3),
(13, 9), (14, 0), (14, 5), (14, 6), (15, 5), (15, 8),
(15, 9)],
('Giy',): [
(0, 0), (0, 7), (1, 1), (3, 5), (3, 6), (4, 2), (4, 4),
(4, 5), (5, 3), (5, 7), (7, 1), (7, 8), (8, 5), (9, 4),
(9, 5), (9, 9), (10, 5), (11, 5), (11, 6), (11, 8), (11, 10),
(12, 0), (12, 3), (13, 10), (14, 0), (14, 5), (14, 6),
(14, 7), (15, 0), (15, 6), (15, 9)],
('Gcnot',): [
(0, 7), (1, 0), (2, 4), (4, 3), (5, 5), (5, 10), (6, 1),
(6, 10), (7, 8), (8, 2), (8, 5), (8, 6), (9, 0), (9, 4),
(9, 6), (9, 9), (10, 2), (10, 4), (10, 5), (11, 5), (12, 2),
(13, 7), (14, 1), (14, 2), (14, 3), (14, 6), (15, 8),
(15, 10)],
('Gxi',): [
(0, 7), (1, 1), (1, 7), (2, 7), (3, 3), (4, 9), (5, 4),
(7, 2), (7, 10), (8, 2), (9, 2), (9, 8), (9, 9), (10, 1),
(10, 10), (11, 2), (11, 5), (11, 6), (13, 2), (14, 7),
(15, 2), (15, 3)],
('Giy', 'Gyi'): [
(0, 6), (0, 8), (0, 10), (1, 0), (1, 1), (1, 3), (2, 9),
(3, 8), (4, 4), (4, 7), (5, 7), (6, 1), (7, 0), (7, 8),
(9, 10), (10, 5), (11, 5), (12, 5), (12, 6), (14, 0),
(15, 0), (15, 6), (15, 8)],
('Gix', 'Gxi'): [
(0, 0), (1, 5), (2, 4), (3, 3), (3, 5), (5, 2), (6, 1),
(6, 8), (6, 10), (8, 6), (10, 2), (10, 8), (10, 10),
(11, 8), (12, 1), (13, 1), (13, 4), (13, 6), (13, 10),
(14, 8), (15, 3)],
('Giy', 'Gcnot'): [
(0, 2), (1, 0), (1, 4), (1, 9), (3, 10), (4, 3), (5, 7),
(7, 4), (7, 7), (7, 8), (8, 7), (8, 9), (9, 2), (9, 6),
(10, 3), (14, 10), (15, 4)],
('Gxi', 'Gyi'): [
(0, 1), (0, 2), (0, 5), (1, 3), (1, 9), (2, 4), (2, 10),
(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
('Giy', 'Gxi'): [
(1, 1), (2, 8), (3, 0), (3, 2), (3, 6), (4, 7), (7, 2),
(8, 6), (9, 1), (9, 7), (9, 9), (10, 2), (10, 10), (11, 8),
(12, 6), (13, 2), (13, 7), (14, 2), (15, 5)],
('Gix', 'Gcnot'): [
(2, 2), (3, 1), (4, 5), (4, 7), (4, 8), (5, 3), (5, 4),
(8, 5), (9, 4), (9, 6), (10, 10), (12, 0), (13, 0), (14, 5),
(15, 1), (15, 7), (15, 10)],
('Gyi', 'Gcnot'): [
(0, 2), (1, 0), (1, 4), (1, 9), (3, 10), (4, 3), (5, 7),
(7, 4), (7, 7), (7, 8), (8, 7), (8, 9), (9, 2), (9, 6),
(10, 3), (14, 10), (15, 4)],
('Gxi', 'Gcnot'): [
(0, 1), (0, 5), (1, 3), (2, 4), (2, 10), (3, 8), (5, 5),
(7, 0), (9, 3), (9, 9), (9, 10), (10, 8), (12, 2), (12, 6),
(14, 6), (15, 0), (15, 5)],
('Gix', 'Giy'): [
(1, 0), (1, 10), (4, 0), (4, 4), (4, 7), (4, 8), (5, 5),
(7, 6), (8, 9), (9, 9), (10, 2), (10, 8), (11, 10), (12, 6),
(12, 9), (13, 9), (15, 1)],
('Gix', 'Gyi'): [
(0, 5), (0, 9), (1, 6), (3, 1), (3, 2), (5, 0), (5, 4),
(6, 0), (6, 8), (9, 7), (10, 9), (11, 1), (11, 4), (14, 4),
(14, 9), (15, 5), (15, 7)],
('Gix', 'Gxi', 'Giy'): [
(0, 6), (3, 0), (5, 0), (6, 7), (7, 1), (8, 3), (9, 9),
(10, 4), (10, 9), (12, 9), (13, 2), (14, 5), (14, 8),
(14, 10), (15, 6)],
('Giy', 'Gxi', 'Gyi'): [
(0, 9), (1, 1), (1, 9), (2, 7), (3, 4), (4, 4), (4, 10),
(6, 0), (6, 3), (7, 0), (9, 4), (11, 5), (12, 4), (13, 7),
(14, 0)],
('Giy', 'Gyi', 'Gxi'): [
(0, 9), (1, 1), (1, 9), (2, 7), (3, 4), (4, 4), (4, 10),
(6, 0), (6, 3), (7, 0), (9, 4), (11, 5), (12, 4), (13, 7),
(14, 0)],
('Gix', 'Gix', 'Gcnot'): [
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(10, 4), (10, 9), (12, 9), (13, 2), (14, 5), (14, 8),
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('Gxi', 'Gyi', 'Gyi'): [
(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
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(9, 2), (9, 6), (10, 3), (14, 10), (15, 4)],
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(10, 0), (10, 4), (10, 5), (11, 2), (11, 9), (14, 6),
(14, 8), (15, 3)],
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(10, 8), (12, 2), (12, 6), (14, 6), (15, 0), (15, 4),
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(14, 6), (15, 0), (15, 5)],
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(9, 3), (10, 9), (10, 10), (14, 7), (14, 9), (15, 10)],
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(10, 8), (11, 10), (12, 6), (12, 9), (13, 1), (13, 9),
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('Giy', 'Gxi', 'Gxi'): [
(1, 7), (2, 2), (4, 8), (7, 2), (7, 10), (8, 6), (9, 8),
(9, 9), (10, 1), (11, 4), (11, 9), (12, 8), (12, 9),
(13, 0), (13, 1), (13, 9)],
('Gix', 'Giy', 'Giy'): [
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(5, 4), (6, 8), (7, 4), (7, 10), (8, 8), (8, 9), (10, 5),
(11, 5), (11, 6), (11, 9), (13, 10), (14, 1), (14, 9)],
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(9, 5), (9, 9), (10, 5), (11, 5), (11, 6), (11, 8), (11, 10),
(12, 0), (12, 3), (13, 10), (14, 0), (14, 5), (14, 6),
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(7, 5), (7, 6), (7, 8), (8, 5), (12, 5), (13, 0), (13, 2),
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(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gxi', 'Gcnot', 'Gcnot'): [
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(10, 10), (11, 2), (11, 5), (11, 6), (13, 2), (14, 7),
(15, 2), (15, 3)],
('Gix', 'Gyi', 'Giy'): [
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(8, 7), (9, 5), (10, 3), (11, 4), (14, 0), (14, 6), (14, 9),
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('Gxi', 'Gyi', 'Gix', 'Gix'): [
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(7, 5), (7, 6), (7, 8), (8, 5), (12, 5), (13, 0), (13, 2),
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(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
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(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
('Gyi', 'Gix', 'Gix', 'Gix'): [
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(6, 0), (6, 8), (9, 7), (10, 9), (11, 1), (11, 4), (14, 4),
(14, 9), (15, 5), (15, 7)],
('Gxi', 'Gyi', 'Gyi', 'Gyi'): [
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(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
('Gyi', 'Gyi', 'Giy', 'Gyi'): [
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(5, 3), (5, 7), (6, 4), (6, 10), (8, 2), (8, 3), (9, 0),
(10, 8), (11, 1), (11, 7), (13, 1), (13, 8)],
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(8, 9), (9, 0), (9, 9), (10, 3), (10, 4), (10, 8), (11, 5),
(12, 5), (12, 9), (13, 1), (13, 9), (15, 1)],
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(7, 6), (8, 9), (9, 9), (10, 2), (10, 8), (11, 10), (12, 6),
(12, 9), (13, 9), (15, 1)],
('Gyi', 'Gix', 'Gxi', 'Giy'): [
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(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
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(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gix', 'Gxi', 'Gcnot', 'Giy'): [
(0, 1), (0, 2), (0, 5), (0, 10), (1, 3), (1, 7), (2, 1),
(2, 7), (3, 6), (5, 1), (6, 10), (7, 0), (7, 6), (9, 0),
(9, 2), (10, 4), (11, 7), (11, 9), (13, 7), (14, 3),
(14, 7), (15, 5), (15, 10)],
('Giy', 'Giy', 'Gxi', 'Gyi', 'Gxi'): [
(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gyi', 'Giy', 'Gyi', 'Gix', 'Gix'): [
(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gyi', 'Gcnot', 'Giy', 'Giy', 'Gxi'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gxi', 'Gxi', 'Giy', 'Gyi', 'Giy'): [
(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Giy', 'Gyi', 'Gxi', 'Gxi', 'Giy'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Giy', 'Gix', 'Gxi', 'Gix', 'Gxi'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Giy', 'Gxi', 'Gix', 'Giy', 'Gyi'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gix', 'Giy', 'Giy', 'Gix', 'Gxi', 'Gxi'): [
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(10, 5), (11, 2), (11, 5), (12, 7), (12, 10), (13, 0),
(13, 4), (14, 5)],
('Gxi', 'Gix', 'Giy', 'Gxi', 'Giy', 'Gyi'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gxi', 'Gxi', 'Gyi', 'Gxi', 'Gyi', 'Gyi'): [
(0, 1), (0, 5), (1, 3), (3, 8), (5, 5), (7, 0), (9, 3),
(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gyi', 'Giy', 'Gxi', 'Giy', 'Giy', 'Giy'): [
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(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
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(7, 6), (8, 9), (9, 9), (10, 2), (10, 8), (11, 10), (12, 6),
(12, 9), (13, 9), (15, 1)],
('Giy', 'Giy', 'Gxi', 'Giy', 'Gix', 'Giy'): [
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(5, 3), (6, 10), (8, 2), (8, 8), (9, 4), (10, 7), (12, 1),
(13, 2), (15, 6), (15, 9)],
('Gxi', 'Gix', 'Giy', 'Giy', 'Gxi', 'Gyi'): [
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gyi', 'Gyi', 'Gyi', 'Giy', 'Gyi', 'Gix'): [
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(7, 4), (7, 7), (7, 8), (8, 1), (8, 5), (8, 7), (8, 9),
(9, 2), (9, 6), (10, 3), (14, 10), (15, 4)],
('Gxi', 'Giy', 'Gix', 'Gyi', 'Gix', 'Gix'): [
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(3, 8), (5, 5), (7, 0), (9, 3), (9, 9), (9, 10), (10, 8),
(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
('Gyi', 'Giy', 'Gxi', 'Gyi', 'Gxi', 'Gcnot'): [
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(12, 2), (12, 6), (14, 6), (15, 0), (15, 5)],
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
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(15, 0), (15, 5)],
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(9, 9), (9, 10), (10, 8), (12, 2), (12, 6), (14, 6),
(15, 0), (15, 5)],
('Gix', 'Gix', 'Gyi', 'Gxi', 'Giy', 'Gxi', 'Giy', 'Gyi'): [
(1, 1), (2, 5), (4, 3), (5, 5), (6, 3), (7, 1), (10, 2),
(10, 5), (11, 2), (11, 5), (12, 7), (12, 10), (13, 0),
(13, 4), (14, 5)],
}