Multiple-Gate Circuit: Further Details

The binary quadratic models created by dwavebinarycsp and the embeddings found on a D-Wave 2000Q system for these BQMs.

Single Comprehensive Constraint

Binary Quadratic Model:

BinaryQuadraticModel({'a': 6.0, 'c': -2.0, 'z': 6.0, 'd': 0.0, 'b': -2.0,
'aux0': 0.0, 'aux1': 0.0}, {('aux1', 'a'): -4.0, ('z', 'a'): 0.0, ('aux1', 'aux0'): 0.0,
('z', 'aux1'): -4.0, ('b', 'a'): -2.0, ('d', 'c'): 0.0, ('z', 'c'): -2.0, ('z', 'd'): 0.0,
('z', 'aux0'): -4.0, ('z', 'b'): 4.0, ('c', 'a'): -2.0, ('c', 'aux0'): 4.0, ('c', 'b'): 2.0,
('d', 'a'): -2.0, ('d', 'aux1'): 4.0, ('d', 'aux0'): -2.0, ('b', 'aux0'): 2.0,
('aux0', 'a'): -2.0, ('c', 'aux1'): 2.0, ('b', 'aux1'): 0.0, ('d', 'b'): 0.0},
-2.5, Vartype.BINARY)

Embedding 1:

{'a': [946, 951, 959],
 'aux0': [954, 957],
 'aux1': [955, 1083, 1086, 1081, 1080],
 'b': [948, 956],
 'c': [944, 958, 950],
 'd': [953, 825, 831, 824],
 'z': [952]}

Embedding 2:

{'a': [1104],
 'aux0': [1110, 1102],
 'aux1': [1107, 981, 979, 977, 976],
 'b': [1111, 1103, 1098],
 'c': [1105, 1233, 1232, 1238],
 'd': [1108, 1100, 1099],
 'z': [1106, 1109]}

Embedding 3:

{'a': [1838, 1846, 1840, 1847],
'aux0': [1839],
'aux1': [1836, 1835],
'b': [1837, 1831, 1829, 1826, 1830],
'c': [1706, 1834, 1711],
'd': [1705, 1833, 1709],
'z': [1704, 1832]}

Embedding 4:

{'a': [665, 537, 540, 539],
'aux0': [669, 661, 656],
'aux1': [664, 668],
'b': [670, 662, 659],
'c': [667],
'd': [666, 794, 798, 793, 795],
'z': [671, 663]}

Multiple Small Constraints

Binary Quadratic Model:

BinaryQuadraticModel({'a': 0.0, 'c': 2.0, 'b': 0.0, 'not1': -2.0, 'd': 2.0,
'or4': 0.0, 'or2': 4.0, 'not6': 0.0, 'and5': 8.0, 'z': 2.0, 'and3': 6.0},
{('not6', 'and5'): 2.0, ('or2', 'c'): -4.0, ('or4', 'd'): -4.0, ('or4', 'and3'): 2.0,
('and3', 'a'): -4.0, ('and5', 'and3'): -4.0, ('z', 'and5'): -4.0, ('or4', 'not6'): 4.0,
('or4', 'or2'): -4.0, ('z', 'not6'): -4.0, ('or2', 'd'): 2.0, ('or4', 'and5'): -4.0,
('c', 'b'): 2.0, ('b', 'not1'): 4.0, ('not1', 'and3'): -4.0, ('or2', 'b'): -4.0,
('not1', 'a'): 2.0}, -5.5, Vartype.BINARY)

Embedding 1:

{'a': [1870, 1737, 1862, 1856, 1865, 1609],
'and3': [1728, 1600],
'and5': [1731, 1735],
'b': [1603],
'c': [1605],
'd': [1606],
'not1': [1604, 1612],
'not6': [1730],
'or2': [1607, 1602],
'or4': [1733, 1729, 1601],
'z': [1734]}

Embedding 2:

{'a': [578, 450, 452],
'and3': [448, 576],
'and5': [447, 455],
'b': [574, 569],
'c': [572],
'd': [444],
'not1': [582],
'not6': [442, 446, 454],
'or2': [440, 568],
'or4': [441, 445, 453],
'z': [451]}

Embedding 3:

 {'a': [1051],
'and3': [1058, 1060, 1052],
'and5': [1059],
'b': [921, 924],
'c': [926],
'd': [1054],
'not1': [1049, 1055],
'not6': [1063, 1056],
'or2': [922, 1050],
'or4': [1061, 1053, 1048],
'z': [1062]}

Embedding 4:

 {'a': [1438],
'and3': [1560, 1432],
'and5': [1688, 1695],
'b': [1561, 1566],
'c': [1564],
'd': [1565],
'not1': [1439, 1433],
'not6': [1691, 1693],
'or2': [1563],
'or4': [1562, 1567, 1690],
'z': [1694]}