CS 150: Quantum Computer Science (Spring 2023)
Course description:
The universe at the sub-atomic scale is governed by quantum mechanical laws, which fundamentally differ from classical laws of motion. What is the nature of computation in such scales? Can we use quantum mechanical particles to perform computations? These are the core questions of the field of quantum computing. In this course, we present an elementary-level introduction to the computer science foundations of quantum computing. Topics include Hilbert spaces, quantum entanglement, quantum measurements, quantum circuits, quantum protocols and algorithms, Hamiltonians and the ground state problem, and quantum error-correcting codes. Students from different areas of engineering and sciences, such as computer science, physics, electrical engineering, mathematics, or chemistry, who wish to learn about the computer science foundations of quantum computers can benefit from this class. The main focus of this course is on the theoretical foundations of quantum computing; mathematical enthusiasm and knowledge in areas such as linear algebra, algorithms, discrete mathematics, and calculus are required.
General Information
Class Information:
- Class schedule: Mon/Wed 1:30-2:45pm
- Class location: JCC 265
- Office hours: Tuesdays 10 am - 11 am. JCC 465 or by appointment.
- Recitations: TBA
- TA office hours: Wednesday 12:00 pm - 1:15 pm.
- Piazza: https://piazza.com/tufts/spring2024/cs151
Instructors Information:
- Instructor's name: Saeed Mehraban
- Email: Firstname.Lastname@tufts.edu
- Office: JCC-465
- TA: Dale Jacobs
- TA Email: Firstname.Lastname@tufts.edu
Special dates:
- Midterm exam: Monday, March 3/11, same time and location as class
- Final exam: TBA
- Deadline to Drop: February 21 is the last day for AS&E students to DROP Full Term courses without
record of enrollment.
- Deadline to withdraw for a grade of W:
- April 29 is the last Day for graduate students to WITHDRAW from Full Term and Receive a Grade of W.
- April 3 is the last Day for Undergraduate AS&E Students to WITHDRAW from Full Term Courses and Receive a Grade of W.
- Last day of classes: April 29, 2024
- Scheduled class cancellations and special lectures:
- No lecture on Monday, 2/19. President’s day
- Special lecture on Thursday, 2/22 is a Monday schedule
- The week of Monday March 18 is the Spring break
- No classes the week of Apr 15. (April 15 and 17). April 15 is the Patriot’s day. April 17 is a planned make-up day
Quick Links:
Course Logistics:
Grading Policy
Course Material:
Rules, Accomodations, & Resources
Course Logistics
Prerequisites:
Calculus 2 (Math 34) and Linear Algebra (Math 70) and one of (CS 61 or Math 61 or Math 65)
Textbook:
Students are encouraged to consult the following textbooks as a basis for learning:
Tufts has kindly provided a digital version for the book by Mermin (see the link above);
we are working to do the same for the book by Nielsen and Chuang.
You are not required to purchase these textbooks in order to complete this class.
The below schedule is an approximation of what we will cover during the class.
Overview and Introduction
Digital computation:
- Boolean formula and Boolean circuits
- Reversible circuits and matrix representation of computations
The formalism of quantum mechanics:
- Quantum states, unitary operations, and the Borne rule
- Special features: Interference, no-cloning theorem, uncertainty principle, Entanglement
Quantum computations:
- Single qubit gates and Multi-qubit-systems
- Quantum circuits and quantum computing
- Simple quantum protocols: Hadamard-test, Swap test
- Quantum Teleportation and super-dense coding
Black box formulation
- Black box formulation and Deutsch-Josza
- Bernstein-Vazirani
- Simon’s algorithm
Simulating quantum physics on quantum computers
- Hamiltonians and observables
- Hamiltonian simulation
Shor’s algorithm
- Overview of Factoring and quantum Fourier transform
- Shor’s algorithm
- Phase estimation
Other Algorithms
- Phase estimation
- Grover's search
- Quantum algorithm for linear systems
Quantum Error Correction
- Basics of Error correction
- Shor's 9-qubit code
- Stabilizer Formalism
Assignments
Grading rules:
There are 6-8 problem sets, a midterm exam and a final exam. 10% of the overall is class participation;
participation also includes Piazza, office hours and recitations. Please let us know in advance if you will miss a class.
Please consult with the instructor if you have missed or will miss more than three classes.
- 10%. Class participation.
- 20%. Midterm exam
- 30%. Final exam
- 40%. Problem sets
No late submission is allowed. Your lowest grade problem set will be dropped.
How to submit the assignments:
Please submit your problem sets via gradescope by the prescribed deadline;
please contact us in advance if you need special arrangements. Please join gradescope via the entry code ZW8E3Y.
Late submission policy:
No late submissions will be accepted.
You can discuss your ideas with your classmates during the preliminary stages of working on your problem sets,
but all assignements should be written individually using your own words. You should be able to explain your solution upon request.
If you consulted any source (classmates, friend, TA, textbook, paper, faculty member, etc.) please cite that
source in your submission.
Course Material
This section will be developed as the semester unfolds.
Thanks to Tufts libraries the digital copy of the book by Mermin is available at this link.
Problem sets
Reading
(Required) Linear Algebra Background
Please use these lecture notes for the preliminary mathematics background for this course. Your first problem set will be about the linear algebra background. You can also read 2.1-2.1 of Nielsen Chuang for a review of linear algebra.
Suggested reading for each lecture:
The notes you take from the class are the main references for this course. The "preliminary notes" which I put out for some lectures are my personal notes which I use before the classes. You can use them if you find them helpful. I do not follow exactly from a specific reference.
You are only responsible to know the topics we cover in class. You can use the textbooks to help help you understand specific
topics better. Below each lecture I will put approximate reading suggestions. If there are topics that were not covered in class
you can view them as optional reading (which would help you gain deeper understanding of the course).
Basics of quantum computing
- Lecture 1: Overview [Slides]
- Lecture 2 (01/22): Classical v.s. Quantum bits [ Lecture notes]
- Lecture 3 (01/24): Reversible computations [ Lecture notes]
- Lecture 4 (01/29): Introduction to quantum formalism [ Lecture notes]
- Reading: Section 2.2 of Nielsen Chuang
- Reading: 1.5-1.10 of Mermin's book.
- Lecture 5 (01/31): Introduction to quantum computing [ Lecture notes]
- Section 1.3 of Nielsen Chuang
- Lecture 6 (02/05): Single qubit systems [ Lecture notes]
- Section 4.2 of Nielsen Chuang
- Mermin's book 1.11-1.12
- Lecture 7 (02/07): Tensor products [ Lecture notes]
- Section 2.1.7 of Nielsen Chuang
- Lectures 8 (02/12) and 9 (02/14): Entanglement [ Lecture notes]
- Section 2.3 of Nielsen Chuang
Quantum Algorithms
The lecture notes for quantum algorithm are here
- Reading: Chapter 2 and 3 or Mermin's book.
- Reading: Read the relevant material from chapter 4.7, 5, 6 of Nielsen Chuang (only what we covered in class is required).
- Lecture 9 (02/21): The Deutsch-Josza Problem
Useful links
The following are nice introductory notes about quantum computation.
You can use the following references as encyclopeida of complexity classes or quantum algorithms
Rules, Accomodations, & Resources
Attendance rule:
If a student misses or expects to be missing more than three lectures,
they should consult with the instructor. In any situation, please contact the course staff with any concerns.
Covid-19:
If you have flu-like symptoms, please refrain from attending the class. If possible, please let us
know in advance via email. For more information regarding Tufts's resources and policies regarding Covid-19,
please visit Tufts's response to Covid-19.
Religious holy days:
In case a student is observing a religious holy
day and might have to skip a class or miss a deadline, please let us know in advance. We will accommodate such circumstances.
Equal access:
Tufts is committed to providing equal access and support to all qualified students through the provision
of reasonable accommodations. If you have a disability that requires reasonable accommodations,
contact the StAAR Center at StaarCenter@tufts.edu or 617-627-4539. Please be aware that
accommodations cannot be enacted retroactively, making timeliness a critical aspect for their provision.
Tufts's academic integrity statement:
Tufts holds its students strictly accountable for adherence to academic integrity. The consequences of violations can be severe. It is critical that you understand the requirements of ethical behavior and academic work as described in Tufts’
academic integrity handbook. If you ever have a question about the expectations concerning a particular assignment or project in this course, be sure to ask me for clarification. The Faculty of the School of Arts and Sciences and the School of Engineering are required to report suspected cases of academic integrity violations to the Dean of Student Affairs Office. If I suspect that you have cheated or plagiarized in this class, I must report the situation to the dean.
Student Support, including Mental Health:
As a student, there may be times when personal stressors or difficulties
interfere with your academic performance or well-being. The
Dean of Student Affairs Office offers support
and care to undergraduates and graduate students who are experiencing difficulties and can also aid faculty in their work
with students. In addition,
through Tufts’
Counseling and Mental Health Service (CMHS) ,
students can access mental health support 24/7, and they can provide information on additional resources.
CMHS also provides confidential consultation, brief counseling, and urgent care at no cost for all Tufts
undergraduates as well as for graduate students who have paid the student health fee. To make an appointment,
call 617-627-3360. Please visit the CMHS website
to learn more about their services and resources.