Contents of the course:
Today's computers---both in theory (Turing machines) and practice (PCs and smart phones)---are based on classical physics. However, modern quantum physics tells us that the world behaves quite differently. A quantum system can be in a superposition of many different states at the same time, and can exhibit interference effects during the course of its evolution. Moreover, spatially separated quantum systems may be entangled with each other and operations may have "non-local" effects because of this. Quantum computation is the field that investigates the computational power and other properties of computers based on quantum-mechanical principles. Its main building block is the qubit which, unlike classical bits, can take both values 0 and 1 at the same time, and hence affords a certain kind of parallelism. The laws of quantum mechanics constrain how we can perform computational operations on these qubits, and thus determine how efficiently we can solve a certain computational problem. Quantum computers generalize classical ones and hence are at least as efficient. However, the real aim is to find computational problems where a quantum computer is much more efficient than classical computers. For example, Peter Shor in 1994 found a quantum algorithm that can efficiently factor large integers into their prime factors. This problem is generally believed to take exponential time on even the best classical computers, and its assumed hardness forms the basis of much of modern cryptography (particularly the widespread RSA system). Shor's algorithm breaks all such cryptography. A second important quantum algorithm is Grover's search algorithm, which searches through an unordered search space quadratically faster than is possible classically. In addition to such algorithms, there is a plethora of other applications: quantum cryptography, quantum communication, simulation of physical systems, and many others. The course is taught from a mathematical and theoretical computer science perspective, but should be accessible for physicists as well.
This is a theory course, no programming is involved.
This course will complement Maris Ozols and Michael Walter's course on Quantum Information Theory that's taught on Monday afternoon. Neither course requires the other, but students interested in writing a thesis in quantum computation/information are encouraged to follow both.
Familiarity with basic linear algebra, probability theory, discrete math, algorithms, all at the level of a first Bachelor's course. Also general mathematical maturity: knowing how to write down a proof properly and completely.
Ronald's lecture notes.
Lectures and location:
February 3 - May 25, 2019. Every Monday 10:00-12:45, at Amsterdam Science Park, D1.111.
Each Monday block consists of 2 hours of lectures followed by a 1-hour exercise session.
Video recordings can be found on
Due to the corona virus, the later lectures will be from video recordings from 2019, see course schedule below.
This is an 8 ECTS course over 14 weeks, plus a final exam, which comes to roughly 14 hours of work per week.
There will be weekly or biweekly sets of homework exercises.
- The homework needs to be handed in at or before the start of the lecture when it's due, i.e., Monday 10:00, in person or by email to email@example.com. This is a hard deadline: if you arrive late for the lecture, then you cannot hand in homework anymore, similarly if you send it by an email that arrives after 10:00.
- The answers should be in English. Handwritten solutions or emailed scans thereof are fine, as long as they are clearly readable. If you're emailing your solutions, please send a moderately-sized pdf attachment, not separate images (nor a url); the contrast should be sufficient so that it's still readable after printing ("CamScanner" is a decent app for this).
- Cooperation among students is allowed, but everyone has to hand in their own solution set in their own words. Do not share files before the homework deadline, and never ask the questions online or put the solutions online. Plagiarism will not be tolerated.
- To get some idea of the level of detail required for your homework solutions, you can have a look at the solutions to the 2015, 2017, 2018, 2019 exams, near the bottom of this page.
- Appendix C has hints for some of the exercises, indicated by (H). If the hint gives you some facts (for instance that there exists an efficient classical algorithm for testing if a given number is prime) then you can use these facts in your answer without proving/deriving these facts themselves.
- If you use LaTeX and want to draw circuits, you could consider using
which is the package used for the Nielsen-Chuang book.
- If you have questions about the homework or the lectures, email Ronald (firstname.lastname@example.org; don't use the above gmail addrie which is only for homework submission).
- You can pick up your graded homework in subsequent lectures, or ask a fellow student to pick them up for you.
- Here are our notes with general feedback, incl. on the homework. These notes will be updated after every homework set, so check them regularly.
Exam and grading:
Each homework set will get a grade between 1 and 10;
if you don't hand it in you'll score a 1 for
that set. When determining the average grade for the homework,
we will ignore your two lowest scores.
This is also meant to cover cases of illness etc.; in general we won't allow extensions for homework submission.
The final exam (June 8) will be open book, meaning you can bring the lecture notes, your own notes, homework, and any other papers you want, but no electronic devices.
Your grade for the exam should be at least 5.0 in order to pass the course.
There's the possibility for a re-sit of the exam on June 29.
The final grade is determined for 60% by the final exam (or the re-sit if you take it) and 40% by the homework-grade. In accordance with the Mastermath rules, the final grade will be rounded to the nearest integer, also for Master of Logic students.
Preliminary course schedule (updated because of the corona virus!):
We will start with 6 lectures about quantum algorithms, followed by 2 lectures about complexity theory and 3 lectures about distributed settings.
Then 2 lectures about Hamiltonian simulation and the HHL algorithm.
The topic of the last lecture will be decided by a student-vote midway through the semester.
- Monday February 3, 10:00-12:45
Introduction to quantum mechanics and qubits, overview of the course
Chapter 1 of lecture notes. Also make sure you know the material in Appendices A and B
- Monday February 10, 10:00-12:45
The circuit model, Deutsch-Jozsa algorithm
Chapter 2 of lecture notes
Homework set 1 due: Exercises 1,4,7,9,11 from Chapter 1
- Monday February 17, 10:00-12:45
Chapter 3 of lecture notes
- Monday February 24, 10:00-12:45
Quantum Fourier transform
Chapter 4 of lecture notes
Homework set 2 due: Exercises 3,5,8 from Chapter 2 and Exercises 1,3,4 from Chapter 3
- Monday March 2, 10:00-12:45
Shor's factoring algorithm
Chapter 5 of lecture notes
- Monday March 9, 10:00-12:45
Grover's search algorithm
Chapter 7 of lecture notes
Grover search in action
Homework set 3 due: Exercises 1,3,4 from Chapter 4 and Exercises 2,3 from Chapter 5
- Monday March 16, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 9 from 2019 (password yjD3)
Quantum query lower bounds
Chapter 11 of lecture notes
- Monday March 23, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 10 from 2019 (password yjD3)
Quantum complexity theory
Chapter 12 of lecture notes
Homework set 4 due via pdf-attachment to email: Exercises 3,4,7 from Chapter 7 and Exercises 3,7,9 from Chapter 11
- Monday March 30, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 11 from 2019 (password yjD3)
Quantum encodings, with a non-quantum application
Chapter 13 of lecture notes
- Monday April 6, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 12 from 2019 (password yjD3)
Quantum communication complexity
Chapter 14 of lecture notes
Homework set 5 due via pdf-attachment to email: Exercises 2,3 from Chapter 12 and Exercises 1,2,4 from Chapter 13
Monday April 13, no class (Easter Monday)
- Monday April 20, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 13 from 2019 (password yjD3)
Chapter 16 of lecture notes
Monday April 27, no class (King's Day)
Monday May 4, no class (Commemoration of the dead)
- Monday May 11, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 7 from 2019 (password yjD3)
Chapter 9 of lecture notes (until Sec 9.3.1)
Homework set 6 due via pdf-attachment to email: Exercises 2,5,10 from Chapter 14 and Exercises 4,5,6 from Chapter 16
- Monday May 18, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 8 from 2019 (password yjD3)
The HHL algorithm
Remainder of Chapter 9, and Chapter 10 of lecture notes
- Monday May 25, 10:00-12:45. No physical lecture due to corona. Instead watch the video of lecture 14 from 2019 (password yjD3)
Elective topic: Entanglement and non-locality
Chapter 15 of lecture notes
Homework set 7 due via pdf-attachment to email: Exercises 4,6,7,8 from Chapter 9 and Exercise 1 from Chapter 10
Note: no homework corresponding to this last lecture about Ch 15, but there will probably be a related question on the exam
- Monday June 8, 10:00-13:00
Final exam (open book: all paper is allowed, no electronics other than what is needed for downloading the questions & uploading your answers)
If you want to practice, here are the exams from 2015, 2017, 2018, and 2019, with solutions.
Here is the 2020 exam, with solutions.
- Monday June 29, 10:00-13:00
Re-sit of the exam (open book: all paper is allowed, no electronics other than what is needed for downloading the questions & uploading your answers)
If you want to take the re-sit: let Ronald know by email, at least one day in advance. If you take the re-sit, the earlier exam-grade will be nullified and replaced by the re-sit-grade. Be aware that this could actually worsen your grade, or even make you fail the course if your re-sit grade is <5.0. Your homework grade will still count for 40%.
Last update of this page: June 8, 2020