Notation xiii
N set of natural numbers, i.e., {0, 1, 2,... }
Z set of integers
R set of real numbers
C set of complex numbers
B classical bit (set {0, 1})
B quantum bit (qubit, space
C2
p. 53)
Fq finite field of q elements
Z/nZ ring of residues modulo n
Zn additive group of the ring Z/nZ
(Z/nZ)∗
multiplicative group of invertible elements of
Z/nZ
Sp2(n) symplectic group of order n over the field F2
(p. 165)
ESp2(n) extended symplectic group of order n over the
field F2 (p. 164)
L(N ) space of linear operators on M
L(N , M) space of linear operators from N to M
U(M) group of unitary operators in the space M
SU (M) special unitary group in the
space M
SO (M) special orthogonal group in the
Euclidean space M
Notation for matrices:
H =
1

2
1 1
1 −1
, K =
1 0
0 i
,
Pauli matrices: σx =
0 1
1 0
, σy =
0 −i
i 0
, σz =
1 0
0 −1
Notation for complexity classes:
NC (p. 23) NP (p. 28) BQP (p. 91)
P (p. 14) MA (p. 138) BQNP (p. 139)
BPP (p. 36) Πk (p. 46) PSPACE (p. 15)
PP (p. 91) Σk (p. 46) EXPTIME (p. 22)
P/poly (p. 20)
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