Tutorial Webpage for
Lecture Quantum Computing
Loading...
Welcome to the tutorial page of the Quantum Computing lecture held by Sven Groppe at the University of Lübeck
All tutorials contain the exercise descriptions, all necessary data and example solutions, such that the students have the possibility to compare their solutions.
The following tutorials are available:
This is the start page for the introduction exercises with the Silq programming language.
The lecture slides are a good starting point to solve the following exercises. Additional information from the internet can you find on the website https://silq.ethz.ch/!
Please choose your silq introduction tutorial from the tabs below:
The following exercieses cover some of the basics of Silq.
Create a qubit, a classical bit, an unsigned integer, and a list of qubits. Return them as a tuple in the given order.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
This exercise should introduce the use of some basic gates. The identity HXH = Z is one of the most used identities. You should implement the method indetityHXH, which gets one qubit as an argument. Duplicate this qubit and then apply the gates H, X, and H to one qubit and Z to the other. Return them as a tuple. You will see that the values are the same. You can play with the input qubit in the main method.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
One of the unique features of Silq is the use of annotations to avoid errors and allow safe uncomputation. You will find here some code that has some missing and maybe some wrong-placed annotations. Try to fix it.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
The following exercieses are about creating different superpositions.
Given a quantum register as an unsigned integer. Set this in a superposition such that all possible outcomes have equal probability. Try to do this for variable input sizes.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
The bell states are four different states of two qubits. They are the maximum entangled states. So you have four methods, each of which should create one bell state.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
We want an equal probability of choosing out of three options. So create a method that produces the state 1/sqrt(3)*(|00>+|01>+|10>).
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
This is the start page for the exercises covering algorithms in the Silq programming language.
The lecture slides are a good starting point to solve the following exercises. Additional information from the internet can you find on the website https://silq.ethz.ch/!
Please choose your silq introduction tutorial from the tabs below:
Oracles are an essential concept in Quantum Computation. They are used in algorithms and to prove things about Quantum complexity classes. You should now implement a few of them.
You get an n-dimensional vector of bits. Your oracle should decide if the bit values alternate. Output true if you detect this pattern. Otherwise false.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
You get an n-dimensional vector of bits. Your oracle should decide if the number of bits equal to one is divisible by three.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
You get an n-dimensional vector of bits. Your oracle should decide if the string has a period. A period p is that for all bits in X: x[i] = x[i+p], where p is in [1..n-1]. You should not output the period. Just detect if there is a period.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
Your challenge is to implement the given algorithms.
The Deutsch-Jozsa Algorithm was the first discovered algorithm where a quantum computer performs better than a classical computer. Implement the Deutsch-Jozsa Algorithm, which gets a function f and returns 0 if f is balanced and one if f is constant.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
Quantum teleportation sounds a bit magic but is possible with a relatively simple protocol. You should implement the algorithm which performs this protocol. For more information on this protocol, consider the link above.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
We will now tackle some of the advanced topics like cryptography, and machine learning/optimization on Quantum computer
The lecture slides are a good starting point to solve the following exercises. Additional information from the internet can you find on the website https://silq.ethz.ch/!
Please choose your silq introduction tutorial from the tabs below:
In this section we will cover error correction and Shor's algorithm.
Error correction is an essential part of communication. You will get an easy example: a qubit is encoded in a three-qubit state and sent to another person. During this process, one of the qubits could get flipped. Try to detect if there was a qubit flip and correct it if necessary.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
The quantum Fourier Transformation is the essential underlying algorithm that speeds up Shor's algorithm such that we can break cryptosystems like RSA with a reasonable amount of qubits and time. Despite this importance, you can implement this algorithm in 10-20 lines of code. Try to do this.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |
In the exercise before, you implemented the quantum Fourier Transformation, which is the heart of Shor's algorithm. Unfortunately, implementing the complete algorithm would take too long. But you will find here one possible implementation. Feel free to try it out and play with it.
| Exercise: | Start | ||
| Solution: | Output | In Editor | Page |