fin Algos

Question 1

Circuit for Deutsch algorithm

Answer 1

Question 2

Describe the intuition behined Deutsch algorithm

Answer 2

1) initalise two registers, and apply an X rotation to the second one such that the overall state is |01>
2) apply hadamard to both
3) pass both qubits ( |+-> ) through the function Uf. Since for some arbitrary state |x->, Uf will yield (-1) to the power of f(x) multiplied by the original state |x->
4) this means that for the state |+-> which expands to |0-> + |1+>. the two parts of the quibits will be to the power of f(0) and f(1) respectively. Allowing us to easily see if the function is constant or balanced as it is called with both possible parameters
5) in the end if it is constant we get state |0> on first register and if balanced we get |1>

Question 3

Deutsch Jozsa Circuit

Answer 3

Question 4

What is the difference between deutsch and deutsch jozsa

Answer 4

Deutsch is {0,1} -> {0,1}. Deutsch Jozsa is Bit string to bit

Question 5

What is the generalised way of expressing Hadamard onto an arbitrary |x> tensor n

Answer 5

Sum for each z=0 and z+1: (-1)^ (x.z) |z>

Question 6

What is the probability of seeing all 0’s after measurement in deutsch jozsa

Answer 6

absolute value squared of: 1 / 2 ^ n multiplied by ( sum over all possible values of x (0 or 1) for -1 to the power of f(x) )

This means if x is constant then p(all zeros) is certain, otherwise the function must be constant