Basics

Question 1

What does the Fredkin Gate do?

Answer 1

Controlled Swap

Question 2

What does the Toffoli Gate do?

Answer 2

Controlled Controlled Not

Question 3

What are the differences between evolution and measurement?

Answer 3

Evolution: Reversible, Deterministic, Continuous
Measurement: Irreversible, probablistic, discontinuous

Question 4

What are the Pauli Gates?

Answer 4

Flips X-Axis ( 0 1 | 1 0)
Flips Y-Axis ( 0 -i | i 0)
Flips Z-Axis ( 1 0 | 0 -1)

Question 5

What is the Hadamard Gate?

Answer 5

Induces entanglement
1 / sqrt(2) * ( 1 1 | 1 -1 )

Question 6

What are width and depth in a quantum circuit?

Answer 6

width = # of qubits
depth = # of steps needed (parallelism excluded)

Question 7

What does Shor’s Algorithm do?

Answer 7

Solves Abelian Hidden Subgroup problem
Can be used for Factorization and Discrete Logarithm

Question 8

What does Simon’s Algorithm do?

Answer 8

Finds period in functions

Question 9

What does Grover’s Algorithm do?

Answer 9

Find entries in database

Question 10

What are the properties of density matrices?

Answer 10

trace(d) = 1
probability to measure state |x> = <x|d|x>
states with same density matrix are indistinguishable

Question 11

When does a density matrix represent a pure state?

Answer 11

If trace(d ^ 2) = 1

Question 12

Given a state s1, what is the probability to measure s2?

Answer 12

(<s2||s1>) ^ 2

Question 13

How do you calculate the trace distance between two density matrices?

Answer 13

1/2 * trace(|d1 - d2|)

Question 14

How do you calculate the fidelity of two density matrices?

Answer 14

trace(sqrt(d1 ^ 1/2 * d2 * d1 ^ 1/2))
probability d1 passes for d2