CSE622 Introduction to Quantum Computing Winter 2025

This is an introductory course about designing solutions for computation problems using the quantum computing models. It has been shown that these models allow us to solve certain problems more efficiently compared to classical platforms (like Digital circuits or Turing machines). On the other hand, there are certain scenarios where this model is siimlar or even worse than classical platforms. In this course a student will learn about the models and interesting solutions (circuits, algorithms) for some problems from the perspective of computer science. The first half of the course will introduce the postulates of quantum computing, operations and operators and basic structure of circuits and algorithms on the circuit model and the Turing machine model. We will also cover some simple but amazing solutions like quantum teleportation, super-dense coding and Deutsch-Jozsa algorithm. The second half of the course will cover important algorithmic tools like the quantum Fourier transformation, amplitude amplification and eigenvalue estimation and discuss important algorithms like Grover’s search, Shor's factoring, BB84 protocol which bring significant efficiency compared to classical algorithms. Depending upon time and interest, some recent advances will be covered. Students may have to read a recent/classical research paper and/or simulate some of their algorithms and circuits on some quantum backend (e.g., IBM quantum computer) to gain a solid understanding about the system.

Pre-requisites

All of the following are strict requirements. The course relies heavily on linear algebra and algorithms.
You are expected to be comfortable with the following prior concepts:

If you are not familiar or comfortable with these concepts, then you must do a self-study before joining the course (you are recommend to solve a few problems in those concepts from any textbook; mere reading of concepts may not provide sufficient depth); this book chapter explains the linear algebraic concepts suitable for quantum computation in one place.

Course Objectives

  1. Understand the principles of quantum computing.
  2. Understand different quantum computing models used in different applications like search, numerical algorithms, cryptography, etc.
  3. Design and/or analyse quantum algorithms and circuits.
  4. Explain and/or implement simple algorithms and circuits from research papers.

Evaluation Policy

Evaluation will be based on homeworks, closed-book proctored quiz, midsem and endsem exams, and project/survey. A student must get 20% or above in the weighted aggregate of midsem and endsem to pass the course (irrespective of the total of all components).

Course Personnel and Office Hours



Debajyoti Bera - dbera@ - Thursday 5-6pm (email me if you want meet at some other time)
Saurav Awasthi - saurava@ - TBA

Weekly Schedule

  1. Lec 1 (06/1): Single-qubit system, measurement
  2. Lec 2 (08/1): Operators of single-qubit system, B92 QKD protocol
  3. Lec 3 (13/1): Multi-qubit system
  4. Lec 4 (15/1): Multi-qubit system, Bell states
  5. Lec 5 (20/1): Multi-qubit system, Quantum teleportation
  6. Lec 6 (22/1): Density matrix representation, partial trace for subsystems
  7. Lec 7 (27/1): Expectation value of an observable, single-qubit operations, Bloch sphere representation of a qubit
  8. Lec 8 (29/1): Multi-qubit operations, how to design a unitary operator, Grover-Rudolph state preparation
  9. Lec 9 (31/1): Quiz, Implementation of controlled operations
  10. Lec 10(03/2): Data encoding, oracle gates, simple algorithms
  11. Lec 11(10/2): Phase kickback, amplitude amplification, Grover's database search algorithm
  12. Lec 12(17/2): Hamiltonian simulation, QUBO-Ising modeling
  13. Lec 13(19/2): Quantum Fourier transformation, Draper's quantum algorithm for addition
  14. Lec 14(3/3): Proof of amplitude amplification, application Grover's unordered search, O(sqrt(nt)) algorithm to retrieve all t solutions
  15. Lec 15(5/3): Amplitude amplification when probability of success is not known (paper https://arxiv.org/pdf/quant-ph/9605034)
  16. Lec 16(17/3): Quantum Algorithm for Minimum Finding(Durr, Hoyer https://arxiv.org/abs/quant-ph/9607014)
  17. Lec 17(19/3): Using Grover Search, Amplitude Amplification to design algorithms for problems such as median finding, spanning tree etc
  18. Lec 18(24/3): Quantum Fourier Transform, project discussion
  19. Lec 19(26/3/): Quantum Fourier Transform and its application to Order Finding
  20. Lec 20(2/4): Quantum Algorithm for Order Finding
  21. Lec 21(7/4): Shors Factoring Algorithm and QFT circuit implementation. Introduction to Kitaev’s Quantum Phase Estimation
  22. Lec 22(9/4): Quantum Phase Estimation and its applications for order finding.
  23. Lec 23(14/4): Quantum Circuit for QPE and error analysis for QPE.
  24. Lec 24(16/4): HHL algorithm
  25. Lec 25(21/4): HHL algorithm
  26. Lec 26(23/4): Hamiltonian simulation

Homeworks

Collaboration will be allowed in the later homeworks, but not in the initial ones. Particularly, if it is not mentioned, you should not consult any other person or any other resource for solving the questions.
  1. Homework 1
  2. Homework 2
  3. Homework 3
  4. Homework 4
  5. Homework 5
  6. Homework 6

Worksheets

Practice worksheets will be regularly announced. Students are encouraged to solve them on their own and discuss their solutions with the TA or the instructor.
  1. Worksheet 1
  2. Worksheet 2
  3. Worksheet 3
  4. Worksheet 4

Proctored Assessments