Quantum Computing: Algorithms and Limitations Through the Query Model

By Prof. Rajat Mittal | IIT Kanpur

Learners enrolled: 3874 | Exam registration: 19

ABOUT THE COURSE:

Quantum Computation captured the imagination of computer scientists with the discovery of efficient quantum algorithms for factoring and fast algorithm for search. With the recent advances in quantum hardware, quantum computing has once again grabbed the limelight.

This course will primarily focus on the mathematical and computer science aspect of it. After covering the motivation and basics for quantum computing, we will move to the circuit model and take lots of examples. The main part of the course will look at quantum algorithms and the advantage they offer over classical counterparts.

Our focus will be to learn these algorithms and lower bounds as an extension to already known techniques in classical and randomized computation. The course will focus on giving computer science perspective to this interdisciplinary field.

INTENDED AUDIENCE: Computer scientist and mathematicians who would like to understand the basics of quantum algorithms

PREREQUISITES: Linear Algebra and Probability

INDUSTRY SUPPORT:

Quantum Technology Companies & Startups
Government & Research Labs
Software consulting firms

Summary

Course Status :	Upcoming
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Computer Science and Engineering
Credit Points :	3
Level :	Postgraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	26 Jan 2026
Exam Registration Ends :	13 Feb 2026
Exam Date :	24 Apr 2026 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: What is quantum computing? Quantum weirdness: Mach-Zehnder interferometer.

Week 2: Linear algebraic formulation of states: deterministic, randomized and quantum, qubits, composite systems

Week 3: Operations in quantum computing, basics gates and circuits, Mach-Zehnder in terms of quantum operations.

Week 4: Semidefinite matrices, projectors, measurements in quantum computing, principle of deferred measurement

Week 5: Classical and quantum circuits, Deutsch (from Mach-Zehnder) and Deutsch-Jozsa, swap circuit

Week 6: Randomized computation with examples

Week 7: Simon’s algorithm, Quantum Fourier transform, its applications: phase estimation and Shor’s algorithm

Week 8: Grover search, amplitude amplification and variants

Week 9: Random walks and discrete time quantum walks

Week 10: Query model: classical and quantum, approximate degree, optimality of Grover search

Week 11: Total functions: at most polynomial separation between deterministic and quantum query complexity

Week 12: Super-quadratic separation: cheatsheet model, partial functions, Aaronson-Ambainis conjecture and Forrelation problem (depending on time).

Books and references

M.A.Nielsen and I.L.Chuang, Quantum Computation and Quantum Information.

P. Kaye, R. Laflamme, M. Mosca, An Introduction to Quantum Computing

Instructor bio

Prof. Rajat Mittal

IIT Kanpur

Prof. Rajat Mittal is an associate professor at IIT Kanpur. He finished his PhD from Rutgers University and worked as a postdoctoral fellow at the Institute for Quantum Computing (Waterloo, Canada) for three years. He is interested in exploring the advantages as well as limits of quantum computing over classical computers using tools like linear/semidefinite programming and Fourier analysis.

He has received “1989 Batch faculty teaching award for innovation in teaching 2021” and “Excellence in teaching award 2019, IIT Kanpur”.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: April 24, 2026 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team