Index

A

average - Appendix A

B

basis vectors real - Appendix C

bit - Chapter 1

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

controlled NOT 2.6.1, 2.6.2, 5.4, 5.5

controlled phase gate

controlled unitary operation2.6.1

D

decoherence

degenerate

delta

Kronecker

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

determinant C.3.6

DiVencenzo's requirements 2.1

dot product

E

eigenvalue decomposition

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

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

modulus squared

O

open quantum systems

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

phase-flip

Planck's constant

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

standard deviation

SU

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

universal set of gates 2.6

universality 2.6

V

variance

X

x-gate

Y

y-gate

Z

z-gate