107
Index
Abelian group, 9
AND function, 3
balanced function, 4
Birkhoff’s theorem, 15
bit, 19
block-XZX decomposition, 73
block-ZXZ decomposition, 70
Boolean function, 1
bottom-up, 49
CAC decomposition, 79
Cayley table, 8
classical vector, 19
Clos network, 42
closure, 9
continuous group, 20
control function, 28
control gate, 28
controlled bit, 27, 28
controlled circuit, 27
controlled gate, 28
controlled NOT, 28, 44
controlled square root of NOT, 51
controlling bit, 27, 28
conventional computing, 10
countable, 20
cyclic group, 9, 50
cyclic permutation, 9
dimension, 20
direct product, 17
dual decomposition, 34, 73
dual partition, 19, 35
dual Young subgroups, 19
ESOP, 5
ESOP expansion, 45
Fourier transform, 61
GAP, 10
gate cost, 34
Gaussian integer, 52
generator, 9
group, 7
group aZU(n), 62, 79
group bXU(n), 72
group bZU(n), 72
group cXU(n), 63
group P
x
(n), 28, 87, 95
group P
z
(n), 27, 95
group P(n), 10
group Q
z
(n), 88
group Q(n), 65
group S(n), 65
group XU(n), 59, 61
group ZU(n), 60
Grover’s search algorithm, 62
HADAMARD gate, 57
Hadamard matrix, 21
Hermitian conjugation, 20
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