wk3

Question 1

What is the Hadaamard Gate

Answer 1

Entangles a qubit:
|0> -> |+>
|1> -> |->

Question 2

What is the value of the two Hadamard basis states

Answer 2

|+> = ( |0> + |1> ) / root ( 2 )
|-> = ( |0> - |1> ) / root ( 2 )

Question 3

What is the Schrodinger Equation, and what does it do

Answer 3

describes the time evolution of the state of a closed quantum system
Note: H is not the Hadamard gate but the hamiltonian operator

Question 4

What is the Hamiltonian operator used for

Answer 4

describes the specific closed system. Since the Hamiltonian operator is Hermitian it has a spectral decomposition

Question 5

what are quantum measurements described by

Answer 5

a collection of measurement operators {M}_m

There are operators acting on the state space of the system. Index m refers to the measurement outcomes that could occur in the experiment

Question 6

Given a quantum state |ѱ> immediately before a measurement. What is the probability that the result m occurs

Answer 6

p(m) = <ѱ|M^T M |ѱ>
= |M_m|ѱ>|^2

Question 7

What is the state of the quantum system after the measurement. And what is the name of this interpretation

Answer 7

( 1 / sqrt ( <ѱ|M^T M |ѱ> ) ) * M_m|ѱ>

Also known as the Copenhagen interpretation

Question 8

What properties to do the measurement operators satisfy

Answer 8

Complete and law of total probability (see image)