dwavesystems / dwavesystems/dwave-system
DWaveSampler does not return desired result
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Description
I have the following coefficient matrix which I pass to DwaveSampler as QUBO:
```
-1000 1002 1000 1002 1024 1022 1024 1022 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 2 0 2 24 22 24 22 1000 2 0 2 24 22 24 22 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 0 0 0 0 0 0 0
0 -998 1002 1000 1022 1020 1022 1020 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 2 1002 2 0 22 20 22 20 2 1002 2 0 22 20 22 20 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 0 1000 0 0 0 0 0 0
0 0 -1000 1002 1024 1022 1024 1022 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 2 1000 2 24 22 24 22 0 2 1000 2 24 22 24 22 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 0 1000 0 0 0 0 0
0 0 0 -998 1022 1020 1022 1020 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 2 0 2 1002 22 20 22 20 2 0 2 1002 22 20 22 20 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 0 0 0 1000 0 0 0 0
0 0 0 0 -976 1002 1000 1002 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 24 22 24 22 1024 2 0 2 24 22 24 22 1024 2 0 2 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 0 0 0 0 1000 0 0 0
0 0 0 0 0 -978 1002 1000 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 22 20 22 20 2 1022 2 0 22 20 22 20 2 1022 2 0 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 0 0 0 0 0 1000 0 0
0 0 0 0 0 0 -976 1002 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 24 22 24 22 0 2 1024 2 24 22 24 22 0 2 1024 2 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 0 0 0 0 0 0 1000 0
0 0 0 0 0 0 0 -978 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 22 20 22 20 2 0 2 1022 22 20 22 20 2 0 2 1022 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 0 0 0 0 0 0 0 1000
0 0 0 0 0 0 0 0 -1000 1004 1000 1004 1048 1044 1048 1044 1000 0 0 0 0 0 0 0 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 5 0 5 60 55 60 55 1000 5 0 5 60 55 60 55 1000 2 0 2 24 22 24 22
0 0 0 0 0 0 0 0 0 -996 1004 1000 1044 1040 1044 1040 0 1000 0 0 0 0 0 0 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 5 1005 5 0 55 50 55 50 5 1005 5 0 55 50 55 50 2 1002 2 0 22 20 22 20
0 0 0 0 0 0 0 0 0 0 -1000 1004 1048 1044 1048 1044 0 0 1000 0 0 0 0 0 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 5 1000 5 60 55 60 55 0 5 1000 5 60 55 60 55 0 2 1000 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 -996 1044 1040 1044 1040 0 0 0 1000 0 0 0 0 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 5 0 5 1005 55 50 55 50 5 0 5 1005 55 50 55 50 2 0 2 1002 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 -952 1004 1000 1004 0 0 0 0 1000 0 0 0 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 60 55 60 55 1060 5 0 5 60 55 60 55 1060 5 0 5 24 22 24 22 1024 2 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 -956 1004 1000 0 0 0 0 0 1000 0 0 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 55 50 55 50 5 1055 5 0 55 50 55 50 5 1055 5 0 22 20 22 20 2 1022 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -952 1004 0 0 0 0 0 0 1000 0 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 60 55 60 55 0 5 1060 5 60 55 60 55 0 5 1060 5 24 22 24 22 0 2 1024 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -956 0 0 0 0 0 0 0 1000 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 55 50 55 50 5 0 5 1055 55 50 55 50 5 0 5 1055 22 20 22 20 2 0 2 1022
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1004 1000 1004 1048 1044 1048 1044 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 5 0 5 60 55 60 55 1000 5 0 5 60 55 60 55 1000 2 0 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -996 1004 1000 1044 1040 1044 1040 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 5 1005 5 0 55 50 55 50 5 1005 5 0 55 50 55 50 2 1002 2 0 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1004 1048 1044 1048 1044 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 5 1000 5 60 55 60 55 0 5 1000 5 60 55 60 55 0 2 1000 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -996 1044 1040 1044 1040 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 5 0 5 1005 55 50 55 50 5 0 5 1005 55 50 55 50 2 0 2 1002 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -952 1004 1000 1004 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 60 55 60 55 1060 5 0 5 60 55 60 55 1060 5 0 5 24 22 24 22 1024 2 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -956 1004 1000 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 55 50 55 50 5 1055 5 0 55 50 55 50 5 1055 5 0 22 20 22 20 2 1022 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -952 1004 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 60 55 60 55 0 5 1060 5 60 55 60 55 0 5 1060 5 24 22 24 22 0 2 1024 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -956 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 55 50 55 50 5 0 5 1055 55 50 55 50 5 0 5 1055 22 20 22 20 2 0 2 1022
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1002 1000 1002 1024 1022 1024 1022 1000 0 0 0 0 0 0 0 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -998 1002 1000 1022 1020 1022 1020 0 1000 0 0 0 0 0 0 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 0 1000 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1002 1024 1022 1024 1022 0 0 1000 0 0 0 0 0 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 0 1000 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -998 1022 1020 1022 1020 0 0 0 1000 0 0 0 0 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 0 0 0 1000 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -976 1002 1000 1002 0 0 0 0 1000 0 0 0 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 0 0 0 0 1000 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -978 1002 1000 0 0 0 0 0 1000 0 0 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 0 0 0 0 0 1000 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -976 1002 0 0 0 0 0 0 1000 0 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 0 0 0 0 0 0 1000 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -978 0 0 0 0 0 0 0 1000 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 0 0 0 0 0 0 0 1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1002 1000 1002 1024 1022 1024 1022 1000 3 0 3 36 33 36 33 1000 3 0 3 36 33 36 33 1000 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -998 1002 1000 1022 1020 1022 1020 3 1003 3 0 33 30 33 30 3 1003 3 0 33 30 33 30 0 1000 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1002 1024 1022 1024 1022 0 3 1000 3 36 33 36 33 0 3 1000 3 36 33 36 33 0 0 1000 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -998 1022 1020 1022 1020 3 0 3 1003 33 30 33 30 3 0 3 1003 33 30 33 30 0 0 0 1000 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -976 1002 1000 1002 36 33 36 33 1036 3 0 3 36 33 36 33 1036 3 0 3 0 0 0 0 1000 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -978 1002 1000 33 30 33 30 3 1033 3 0 33 30 33 30 3 1033 3 0 0 0 0 0 0 1000 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -976 1002 36 33 36 33 0 3 1036 3 36 33 36 33 0 3 1036 3 0 0 0 0 0 0 1000 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -978 33 30 33 30 3 0 3 1033 33 30 33 30 3 0 3 1033 0 0 0 0 0 0 0 1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1000 1003 1036 1033 1036 1033 1000 0 0 0 0 0 0 0 1000 2 0 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1003 1000 1033 1030 1033 1030 0 1000 0 0 0 0 0 0 2 1002 2 0 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1036 1033 1036 1033 0 0 1000 0 0 0 0 0 0 2 1000 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1033 1030 1033 1030 0 0 0 1000 0 0 0 0 2 0 2 1002 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003 1000 1003 0 0 0 0 1000 0 0 0 24 22 24 22 1024 2 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967 1003 1000 0 0 0 0 0 1000 0 0 22 20 22 20 2 1022 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003 0 0 0 0 0 0 1000 0 24 22 24 22 0 2 1024 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967 0 0 0 0 0 0 0 1000 22 20 22 20 2 0 2 1022
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1000 1003 1036 1033 1036 1033 1000 2 0 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1003 1000 1033 1030 1033 1030 2 1002 2 0 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1036 1033 1036 1033 0 2 1000 2 24 22 24 22
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1033 1030 1033 1030 2 0 2 1002 22 20 22 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003 1000 1003 24 22 24 22 1024 2 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967 1003 1000 22 20 22 20 2 1022 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003 24 22 24 22 0 2 1024 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967 22 20 22 20 2 0 2 1022
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1000 1003 1036 1033 1036 1033
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1003 1000 1033 1030 1033 1030
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1000 1003 1036 1033 1036 1033
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -997 1033 1030 1033 1030
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003 1000 1003
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967 1003 1000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -964 1003
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -967
```
This matrix is 64 by 64. The 64 variables can be tiled, counting index from 0 to 63, into a 8 by 8 decision matrix in row major order, and there are two constraints on this matrix:
1. forall i from 1 to 64, sum(xik) = 1 (k runs from 1 to 64)
2. forall k from 1 to 64, sum(xik) =1 (i runs from 1 to 64)
Basically, there is exactly a 1 in each row, and exactly a 1 in each column.
I tried this matrix on both DwaveSampler and SimulatedAnnealingSampler. SimulatedAnnealingSampler returns an answer satisfying all constraints, but DwaveSampler does not. My code that engages DwaveSampler is as follows:
```
sampler = dimod.ScaleComposite(EmbeddingComposite(DWaveSampler()))
response = sampler.sample_qubo(Q, num_reads=10)
```
What is wrong here? I've also noticed that ScaleComposite matters here, because without it the answer is mostly 0, which is non-sensical.
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