Index

A

average - Appendix 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 Appendix B

of a matrix C.3.1

complex number Appendix B

computational basis 2.2

controlled NOT 2.6.1, 2.6.2, 5.4, 5.5

controlled phase gate

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 Appendix 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

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

Kronecker delta C.4

Kronecker product

L

local operations

local unitarty transformations

M

matrix exponentiation 3.2

maximally entangled states

maximally mixed state

two qubits

mean

median

mixed state density matrix 3.5

modulus squared Appendix B

O

open quantum systems 1.4

open-system evolution 1.4

operator-sum decomposition

orthogonal

vectors

P

partial trace

of a Bell state

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

Q

Qbit (see qubit)

quantum bit 1.3

quantum dense coding (see dense coding)

quantum gates

qubit 1.3

R

reduced density operator 4.3.1

of a Bell state 4.3.1

reduced density matrix

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