After the exam

Regarding the grades:

The grades are decided by following central guidelines that apply for mathematics courses. Each grade also reflects the individual exam solution.

Problem 1, parts a and b. Maximum score requires complete and correct computation  of the probabilities of observing the qubits  
using inner product with the vectors from the basis.

Problem 2.a: Maximum score requires complete and correct set up of all four probabilities of seeing each qubit in its possible state, writing the resulting state of the system in each state after measurement, and proving that this is a product state, either
by writing it directly in tensor product form, or by using the criterion with products of amplitudes.  Part 2b, maximum score requires justification, either explicitly applying the Partial Measurement Rule, or using the definition of
entanglement for pure states by comparing a product of amplitudes.

Problem 3a: Maximum score requires setting up correctly a mixed state as a collection of states with positive probabilities summing to 1. Part 3b: Maximum score requires setting up the mixed state with equal probabilities 1/2, and getting the correct diagonal 2x2 matrix.

Problem 4a: Maximum score requires setting up the correct circuit for the combined 4-qubit system, not just a 3-qubit system.
Part 4b: Maximum score requires correct computation of the combined state, of the probability of observing <000>, and the resulting state of the combined system if <000>
is observed. Part 4c: Maximum score  requires setting up three more possible states observed by A with their probabilities
and resulting state of the system in case of measurement, and correct explanation of what unitary gates B must apply in each case.

Problem 5a: Maximum score requires setting up the effect of the phase gate followed by the diffusion operator as reflections, with correct  explanation of the angle, in the two-dimensional space spanned by the vectors corresponding to the marked and unmarked items.
Part 5b: Maximum score requires correct justification of the position of the initial state after iteration in t steps and correct
estimation of the probability of success.