memorise

Question 1

|0>

Answer 1

[1,0]

Question 2

|1>

Answer 2

[0,1]

Question 3

given qubit |- + > = 1/2 ( |00> -|01> - |10> + |11>. what is the result of applying a cnot gate to them

Answer 3

Cnot |- + > = 1/2( |00> +|01> - |10> - |11>. The phase of the second and last qubits are flipped

Question 4

What effect do 4 hadamard gates surrounding a cnot gate have

Answer 4

It reverses the control and target qubits

Question 5

What is the definition of the Hilbert space

Answer 5

a real or complex inner product space.
-It has an inner product which is conjugate symmetric
-inner product is linear in first argument for all complex sums
-inner product of an element with itself is positive definite

Question 6

What is a hermititian operator

Answer 6

its conjugate transpose is equal to the original matrix

Question 7

what is a unitary operator

Answer 7

any operator U where U^TU= UU^T = identity

Question 8

what is eulers formula

Answer 8

For any real number x, e^ix = cos x + i sin x

Question 9

Postulate 1 of quantum mechanics

Answer 9

Any isolated physical system is a vector space of complex numbers with inner product. subspace of hilbert space

Question 10

Postulate 2 of qm

Answer 10

Time evolution of quantum systems is described by unitary transformations

for a closed system this is described by the schrodinger equation

Question 11

Postulate 3 of qm

Answer 11

Quantum measurements are described by the measurment operators {M_m}

Question 12

if state just before measurement is |𝛙>. What is probability of getting some result m and what is the state after measurement according to the Copenhagen interpretation

Answer 12

P(m) = <𝛙|M^T_m M_m |𝛙>

state after measurement:

(1/sqrt( <𝛙|M^T_m M_m |𝛙>)) x M_m |𝛙>