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Question 1

What space do quantum states exist in

Answer 1

Hilber Space

Question 2

What are the properties of Hilbert space

Answer 2

Real or Complex numbers with an inner product

Question 3

Form of complex number z

Answer 3

z = x +iy

Question 4

How do you normalise a vector (ket)

Answer 4

divide it by the magnitude of the vector (for qubits its root 2)

Question 5

What makes vector set linearly dependant

Answer 5

There exists a set of complex numbers a_1,..,a_n, such that for non zero vectors v_1,v_n. and a_j is not equal to 0. There exists at least one value of j such that:

a_1(V_1)+a_2(V_2) +…_a_n(V_n)=0

Question 6

What are polar coordinates

Answer 6

An alternate coordinate system. Equivalent x and y coordinates of z complex number where (z = x+ yi) can be translated to polar by:

y = r sin (phi)
x= r cos (phi)

Question 7

Pauli 0

Answer 7

2x2 identity matrix

Question 8

pauli X

Answer 8

[ [ 0, 1 ], [ 1, 0 ] ]

Question 9

pauli y

Answer 9

[ [0 ,-i ] , [i , 0] ]

Question 10

pauli z

Answer 10

[ [ 1, 0] , [0 ,-1 ] ]