Index

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A
average - A
B
basis vectors real C.2.1
bit 1.3
bit-flip operation 2.3.2
Bloch Sphere 3.5.4
bra
bracket
C
closed-system evolution 1.4
CNOT gate(see controlled NOT)
commutator 2.3.2,
complex conjugate '''B'''
of a matrix C.3.1
complex number '''B'''
computational basis 2.2
controlled NOT 2.6.1, 2.6.2, 5.4, 5.5
controlled phase gate 6.1
controlled unitary operation 2.6.1
D
decoherence 2.1
degenerate C.6
delta
Kronecker C.4
dense coding 5.4
density matrix 3.3,3.5
for two qubits 3.5.2, 3.5.3, 3.5.4
mixed state 3.5
pure state 3.3
density operator E
determinant C.3.6
DiVencenzo's requirements 2.1
dot product
E
eigenvalue decomposition C.6
eigenvalues C.6
eigenvectors C.6
entangled states (see entanglement)
entanglement 4, 5.4, 1.2.5
pure state 4.2
mixed state 4.3
expectation value 3.6
F
G
group D.2
H
Hadamard gate 2.16
Hamiltonian 3.2
Hermitian matrix 2.4, 3.2, 3.4, 3.5, 8.2, 8.3, C.3.3, C.6.1, E
Hilbert-Schmidt inner product 2.4
I
inner product
for real vectors C.2.1
for complex vectors C.4
inverse of a matrix C.3.7
K
ket C.2.2
Kraus operators 8.3
Kronecker delta C.4
Kronecker product C.7
L
local operations 4.2
local unitary transformations 4.2, 4.2.1
M
matrix exponentiation 3.2
maximally entangled states 4.3.1
maximally mixed state 3.5.3
two qubits
mean
median
mixed state density matrix 3.5
modulus squared B
O
open quantum systems 1.4
open-system evolution 1.4
operator-sum decomposition 8.4
orthogonal
vectors C.4, C.5
P
partial trace
of a Bell state 4.3.1
Pauli matrices 2.4, 3.4, 3.5.4
phase gate 2.3.2
phase-flip 2.3.2
Planck's constant 3.2
projection operator
pure state 3.3, 4.2, E


Q
Qbit (see qubit)
quantum bit 1.3
quantum dense coding (see dense coding)
quantum gates 2.1, 2.3, 2.6
qubit 1.3
R
reduced density operator 4.3.1
of a Bell state 4.3.1
reduced density matrix 4.3.1
see reduced density operator
reduced density operator
requirements for scalable quantum computing 2.1
S
scalability
Schrodinger Equation 3.1
for density matrix 3.3
separable state
simply separable
similar matrices
similarity transformation
singular values
special unitary matrix
spectrum C.6
standard deviation
SU C.3.8
T
teleportation 5.5
tensor product C.7
trace C.3.5
partial(see partial trace)
transpose C.3.2
U
uncertainty principle 5.3
unitary matrix D.7.2, Chapter 2
universal set of gates 2.6
universality 2.6
V
variance
X
X-gate
Y
Y-gate
Z
Z-gate