代做COMP2K、代写Python程序设计

日期：2024-05-20 07:55

Computing

Instructions

Recommended you complete this part by the end of Week 12.

You should demo this lab in your Week 13 practical session.

[You must demonstrate it to the instructor in one of your practical sessions BEFORE the due date in

order to be awarded marks. Please check the ECP for the correct due date. Note that sections are

‘complete’ and marks are awarded by attempting each task AND correctly answering related

questions to the satisfaction of the instructor.]

Quantum computing is a form of computation that uses quantum phenomena such as superposition

and entanglement that forms an essential part of quantum mechanics. Quantum mechanics describes

physics of matter at the extraordinarily small scale surprisingly accurately and is the most successful

physical theory of the universe we currently have being able to predict outcomes to an accuracy of up

to 10-11 decimal places! See for example Chapter 15 of (Moore and Mertens, 2011) for an

introduction. Quantum computing’s pervasiveness will only increase as it comes out of infancy and

there continues to be major advancements as now there are known to be several quantum computers

in existence. It is expected to become prominent part in computing and algorithms of the future by

creating a new series of quantum algorithms that surpass the computational power of classical

supercomputers by “harnessing” the power of quantum computation and is one of the 21st century’s

biggest challenges.

Quantum computers uses quantum bits or ‘qubits’, bits that are in superposition of between states

instead of being either on or off and being in one or the other state (like a classical binary bit). Qubits

still collapse into binary bits, but its actual final state has a probabilistic outcome given by a probability

density as opposed to a deterministic one.

In this laboratory we’ll be using Qiskit, an open-source framework for quantum computing that allows

you to simulate and use real quantum bits on IBM’s quantum computers. There are a few different

ways of using Qiskit:

• You can use Qiskit through IBM’s online environment, accessible here.

• You can install Qiskit as a Python library through here.

This laboratory will allow you to explore qubits and the different classical and quantum operations

you can use to manipulate qubits in a quantum circuit. Qiskit’s documentation can be found here.

Section I – Microsoft Seminar

Microsoft released an extremely useful, self-contained seminar on quantum computing that is a very

valuable resource if you find the concepts in this laboratory difficult to follow:

Seminar on Quantum Computing for Computer Scientists – https://youtu.be/F_Riqjdh2oM

Try getting a handle of quantum computing concepts from the video and playing with the mathematics

of the quantum mechanical operators before you start the following section. See for example

equations (6.23) to (6.46) from Shakes’ book. Chapter 15 of (Moore and Mertens, 2011) also provides

a great introduction to the area, including all the necessary quantum mechanical preliminaries.

Although you do not receive marks for this section and you do not have to complete the entire video,

there is significant overlap with the video and the requirements of the next section that do award

marks.

COMP2048 Theory of Computation S. S. Chandra

2

Section II – Qiskit (10 Marks)

Complete the following exercises using your knowledge of quantum computing, quantum algorithms

and quantum circuits using Qiskit or IMB Composer. All documentation including circuits, code,

results and accompanying notes must be submitted as a zip file as part of your submission on

Blackboard.

-------------------------------

[See the relevant sections of Shakes’ book, Chapter 15 of (Moore and Mertens, 2011) and the

Microsoft Seminar video for hints]

1. What does a Hadamard gate do?

(1 mark)

2. Draw and simulate a simple quantum circuit with three qubits that returns |111> with certainty.

(0.5 mark)

3. Draw and simulate a quantum circuit with three qubits that returns |111⟩ or |101⟩ with 50%

probability each.

(0.5 mark)

4. Draw and simulate a quantum circuit with three qubits that returns |000⟩, |001⟩, |010⟩, |011⟩,

|100⟩, |101⟩, |110⟩, or |111⟩ with equal probability.

(0.5 mark)

5. Make and simulate a quantum circuit whose final Bell state is

1

√2

(|01⟩− |10⟩).

(2.5 marks)

6. Simulate a coin toss using qubit(s) in a quantum circuit. Why does this lead to better ‘randomness’

than a normal/classical coin toss? How could you extend this to be a random number generator?

(2 marks)

7. Implement a solution to the 1-bit Deutsch oracle problem as discussed in lectures (using the

Deutsch-Jozsa Algorithm). Description in section 15.4.1 in (Moore and Mertens, 2011) may also

be useful.

(3 marks)

For Interest Only

One can break RSA encryption ‘easily’ using quantum computers and Shor’s algorithm in section 15.5

of (Moore and Mertens, 2011)!

References

Moore, C., Mertens, S., 2011. The Nature Of Computation. Oxford University Press.

End of Laboratory