Index

A

average - A

B

basis vectors (real) C.2.1

Bell states 4.4.1

binary numbers F.2

bit 1.3

bit-flip operation 2.3.2

Bloch Sphere 3.5.4

bra C.4

bracket A, C.4

C

check-sum F.3.1

closed-system evolution 1.4

CNOT gate(see controlled NOT)

Code F.3.4

Code word F.3.4

Code distance F.3.4

commutator 2.3.2,

complex conjugate 2.7.1, B

of a matrix C.3.1, C.3.3

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

d-tensor components D.8.3

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

disjointness condition F.5

distance (see also, code distance F.3.4)

DiVencenzo's requirements 2.1

Dirac notation C.2.1, C.2.2, C.4

dot product 2.4, C.2.1, E

dual code F.8.1

dual matrix F.4.2

E

eigenvalue decomposition C.6

eigenvalues C.6

eigenvectors C.6

epsilon tensor (see Levi-Civita Tensor)

entangled states (see entanglement)

entanglement 4, 5.4, 1.2.5

pure state 4.2

mixed state 4.3

error syndrome F.4.2

expectation value 3.6

F

field F.2

 

G

generator matrix F.4.1

group D.2

H

Hadamard gate 2.16

Hamiltonian 3.2

Hamming distance F.3.3

Hamming weight, or weight F.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 2.5, C.2.2

Kraus operators 8.3

Kronecker delta C.4

Kronecker product C.7

L

Levi-Civita Tensor C.3.6

Generalized C.3.6

linear code F.3.8

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 (see Average)

median A

minimum distance of a code (also code distance) F.3.5

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 2.4, 3.5.4, 5.2, E

vectors C.4, C.5

P

parity check F.3.1

parity check matrix F.4.2

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 2.7.2

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 4.3.1

requirements for scalable quantum computing 2.1

S

scalability

Schrodinger Equation 3.2

for density matrix 3.3

separable state 4.3

simply separable 4.3

similar matrices C.5

similarity transformation C.5

singular values C.6

special unitary matrix 3.4

spectrum C.6

standard deviation A

SU C.3.8

syndrome measurement F.4.2

T

teleportation 5.5

tensor product C.7

trace C.3.5

partial(see partial trace)

transformation 1.3, 2.3, 2.3.1, 2.3.2, 2.4, 2.6, 2.6.1, 2.6.2, 2.7.1, 2.7.2, 3.2, 3.3, 3.4, 3.5.3, 4.2, 4.2, 4.2.1, 4.2, 4.2, 8.3, 8.3.2, 8.4.1, 8.4.2, C.5, D.1

active C.5

passive C.5

transpose C.3.2

U

uncertainty principle 5.3

unitary matrix 2.3, C.3.8, D.7.2

universal set of gates 2.6

universality 2.6

V

variance 5.3

W

weight, or Hamming weight F.3.2

X

X-gate 2.3.2

Y

Y-gate 2.3.2

Z

Z-gate 2.3.2