Flashcards

Week 4 QUAN INF

Elliot Bryce English 26 cards

List the truth tables and symbol for the following gates: NOT AND OR XOR

Cards in this deck (26)

1What is a universal gate?Universal if you can use it to make any other boolean operation. Like 3 CNOTs make a SWAP.
2List the truth tables and symbol for the following gates: NOT AND OR XOR
3How many functions are there from using N bits?
4What makes a gate reversible?If you apply the gate twice, you get the input functions back out. (Think like U* U =Identity matrix, so it does fuck all)
AND This implicity means that you need for any output, y, a unique input, x. (1-1 mapping)
5Which of these gates are reversible? AND CNOTAND - NO (its not even N->N)
CNOT - YES
6Which of these gates are universal? CNOT {CNOT, H} One Qubit gates ( Paulis, Rotations..) {CNOT, Single Qubit gates}CNOT - NO (can't support the superpositions mapping.)
{CNOT,H} - NO Not a universal set (doesn't have complex factors, only real elements)
One qubit gates (pauli gates) - NO (can't create entanglement between two qubits)
{CNOT, SingleQubitGates} - YES
7What is the Solovay - Kitaev theorem?The number of gates needed with the of order:
8It just popped up during the lecture but useful maths term to know. What is 'mod A' Where A is any number?Mod, moduli, "with respect to the modulus". Its basically a recurrence idea, like 3=15 (mod 12) since its the same number after the cycle of 12 (this is clock (12-24 hour) mod).
It tapers a cylic set i suppose.
9How do you do a Boolean to unitary transformation? (use this 'recipe' throughout the course he says)
10Do what you must
11—
12Every function that a classical computer can compute can be represented by...A function that sends bit strings to bit strings. So in state 0101101 -f->1100111 as an example.
I.e each bit string represents a state, and the function remaps it to a new state This is a boolean function.
13—
14What formula type is this? How do you describe it with a table? How do you represent it with a circuit?
15What is the Quantum Analogy of a boolean function?A Unitary operation is the quantum analogy of the classical boolean function
However the unitary operation has an arbitrary small error
16What is the requirements of a set of gates to be universal?Universal if you can always:
- Specify some unitary U on n qubits for some arbitrary small error epsilon>0
-Then there exists a circuit C where:
-- C only consists of gates from the V set
-- On every input states |phi>
C|phi> and U|phi> differ by at most Epsilon.
Ex. Set{CNOT, H, T} is universal.
17What does the 'arbitrary small error' arise from?Can calculate it by finding the inner product (overlap integral) of two states, the input and output.
18What is the quantum sum gate?
19What is the Quantum carry gate?
20—
21What is quantum paralism?Its the ability of a quantum computer to compute the function for all outputs with one 'crank' of the function. Note that the output shows that despite all solutions being made at once, when we measure, we collapse it into one of the states randomly.
We can useful information out of the properties of a system though. I.e. find out if a system is balanced
22What is Deutsch's problem?basically asks, is the function fair or not? Does it favour an output value?
23What is the Classical method to answer Deutsch's problem?Need to make calls into the blackbox with each different input, to measure the output. No shortcut.
24What is the quantum approach to Deutsch's problem?Can rearrange then this into a superposition of phases.
On another card.
25Continued from the Deutsch's problem, quantum solution, what is the combined state?
26What is the method to implement quantum algorythms?