Quantum Computing Foundations and Programming

This course aims to introduce the principles of quantum computing, laying a solid foundation for further advanced courses or research in quantum information.

Topics include the basic concepts and axioms of quantum information; qubits and entanglement; quantum gates and measurement; quantum communication protocols such as teleportation and superdense coding; and quantum algorithms including Simon’s algorithm, the quantum Fourier transform, phase estimation, Shor’s factoring algorithm, Grover search, and amplitude amplification. Advanced topics may include quantum complexity, cryptography, and error correction.

The course takes a theoretical computer science perspective on quantum computing. No background in quantum physics is required.

Students must be comfortable with:

• Abstract linear algebra, including complex vector spaces, inner products, matrices, eigenvectors, unitary transformations, and tensor products
• Probability, including conditional probability, random variables, expectation, and normalization
• Mathematical reasoning and proof
• Basic programming concepts

Familiarity with algorithms and asymptotic analysis is strongly recommended. Prior experience with Python or Qiskit is helpful but not required.

The Start Here module includes an ungraded prerequisite self-check and refresher resources. These resources are intended for review rather than as substitutes for the prerequisites.

• Announcements: Coursera is the official source for course announcements and deadline changes.
• Course questions: Use Piazza so other students can benefit from the discussion.
• Private matters: Send a private Piazza message or contact the instructor at dakshita@illinois.edu.
• Office hours: Tuesdays, 2:00–3:00 p.m. Central Time, beginning September 1
• Platform problems: Use Coursera’s Learner Help resources.
• Course-specific notebook problems: Post privately on Piazza when the question includes code or assignment details.

Students should not post assignment solutions, code, grades, autograder details, or personal information publicly on Piazza.

The instructional team will ordinarily respond to course questions within two business days. Responses may take longer on weekends and University holidays.

By the end of the course, students will be able to:

1. Represent quantum states and operations using bra–ket notation, complex vector spaces, tensor products, and unitary matrices.
2. Compute measurement outcome probabilities and normalized post-measurement states for full and partial projective measurements.
3. Distinguish global phase from relative phase and explain how interference affects quantum measurement outcomes.
4. Identify entangled states and analyze EPR and CHSH correlations produced by local measurements.
5. Derive the correctness and resource requirements of quantum teleportation and superdense coding.
6. Prove and apply limitations on quantum information, including the no-cloning theorem and bounds on extracting classical information.
7. Construct and analyze reversible circuits, oracle constructions, ancilla qubits, uncomputation, and universal gate sets.
8. Analyze Deutsch–Jozsa, Simon’s algorithm, Grover search, the quantum Fourier transform, phase estimation, period finding, and Shor’s algorithm.
9. Use density matrices, reduced states, quantum channels, and elementary error-correcting codes to analyze mixed states and noise.
10. Evaluate claims of quantum advantage using appropriate resource measures and complexity models, distinguishing asymptotic speedups from present-day hardware performance.
11. Implement and test quantum circuits and algorithms in Qiskit using simulation; evaluate their correctness, resource use, and robustness.

This course follows a flipped-classroom format. New asynchronous course material will be released each Monday. The course will use a rolling two-week window: the current module and the following module will ordinarily be available, allowing students to adjust their pace based on their backgrounds and schedules.

Students are expected to complete the current week’s Core module, including its assigned videos, readings, and short checks, before the Quantum Studio on Thursday. The Studio will assume familiarity with this material and will focus on applying, discussing, and extending it rather than presenting it for the first time.

Live Online Meetings

All live online meetings use the course Zoom room.

The first class meeting will be held on Tuesday, August 25, from 2:00–3:30 p.m. Central Time. Beginning Tuesday, September 1, the instructor will hold optional office hours on Tuesdays from 2:00–3:00 p.m. Central Time.

A weekly Quantum Studio will meet on Thursdays from 2:00–3:00 p.m. Central Time. Studios will emphasize guided problem solving, discussion, clarification of difficult concepts, and occasional previews or extensions of the asynchronous material. They will not repeat the recorded lectures.

For students enrolled in QC1, participation in the weekly Quantum Studio is expected as part of the scheduled course experience, although attendance is not separately graded. Students who cannot attend a particular meeting should complete the posted asynchronous Studio activity.

For students enrolled in QC2, the Quantum Studio is available but is not required.

Studio main-room activities will ordinarily be recorded and posted. Breakout-room conversations will not be recorded. A worksheet, solution or recap, and an equivalent asynchronous activity will be provided so that essential course content is accessible to students who cannot attend synchronously.

Individual welcome conversations

During the first week of the course, students are invited to an informal, individual 15-minute Zoom conversation with the instructor.

Please use Calendly to book one of the available Zoom slots on Wednesday, August 26, or Friday, August 28.

The purpose of the conversation is to learn about each student’s background, interests, goals, and initial questions. No preparation is needed. The conversation is optional, ungraded, and will not be recorded. Students unable to meet during the listed times may contact the instructor to arrange another time.

Course platforms

• Coursera: Lectures, readings, assignments, grades, announcements, and official deadlines
• Coursera Resources: The course syllabus, policies, and course-wide reference materials
• Piazza: Course questions, discussion, clarifications, private communication, and peer interaction
• Coursera notebooks: Qiskit programming activities and programming-assignment submissions
• Office hours: Optional live questions and additional explanation on Tuesdays from 2:00–3:00 p.m. Central Time, beginning September 1
• Quantum Studio: Weekly guided problem solving and discussion on Thursdays from 2:00–3:00 p.m. Central Time

Students should check Coursera announcements and Piazza regularly.

Students should complete the Start Here module before beginning the first content module. It contains:

1. How This Course Works
2. Prerequisite Self-Check
3. Linear Algebra Refresher
4. Probability Refresher
5. Instructions for joining the course Piazza
6. Course Syllabus

The prerequisite self-check is ungraded.

There is no required textbook. All required course materials will be provided through Coursera.

The following are recommended references. They are not required purchases or readings unless a particular section is assigned in a module:

• Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information
• Scott Aaronson, Introduction to Quantum Information Science
• Ronald de Wolf, Quantum Computing: Lecture Notes
• Ryan O’Donnell and John Wright, Quantum Computation lecture notes

Programming work uses Python, Jupyter notebooks, and Qiskit in a managed course environment. Assignments use simulated quantum computers; physical quantum hardware and a separate IBM Quantum account are not required.

The course includes three written problem sets. Each problem set is worth 10% of the course grade.

1. Quantum States, Measurement, and EntanglementQubits, measurement, interference, tensor products, entanglement, EPR and CHSH correlations, no-cloning, and quantum communication protocols.
2. Quantum Circuits and Hidden StructureReversible computation, oracle constructions, ancillas, uncomputation, phase kickback, Deutsch–Jozsa, and the foundations of Simon’s algorithm.
3. Quantum AlgorithmsThe quantum Fourier transform, phase estimation, period finding, Shor’s algorithm, Grover search, amplitude amplification, and limits of quantum search.

Problem sets may contain calculations, circuit analysis, mathematical derivations, and short proofs.

The course includes three substantial autograded programming assignments. Each assignment is worth 10% of the course grade.

1. Reversible Oracles and Hidden StructureConstruct reversible oracles and implement Deutsch–Jozsa and Simon’s algorithm, including classical post-processing.
2. Fourier Methods and Period FindingImplement the quantum Fourier transform, phase estimation, and small instances of order or period finding.
3. Search, Noise, and Error CorrectionImplement Grover search, study its behavior under noise, and construct elementary error-detection or error-correction circuits.

Students receive starter notebooks and visible tests. Hidden tests may assess correctness on additional inputs, output format, circuit resources, reproducibility, and robustness.

The assignments will be autograded. Grading will not depend on access to external quantum hardware.

The prerequisite self-check and practice activities are ungraded.

There is no midterm examination.

No graded work is due during Fall Break.

The cumulative final examination is worth 40% of the course grade. Its format, permitted materials, and exact date or availability window will be announced after the Fall 2026 examination schedule is confirmed. The University currently plans to publish the schedule on October 14.

The schedule follows the current Fall 2026 UIUC academic calendar. University dates remain subject to revision.

Students should plan for approximately 10–12 hours of course work per week. Workload may be higher during programming assignments and final-exam preparation.

Students requiring substantial review of linear algebra, probability, or programming should budget additional time early in the semester.

Discussion of course concepts and high-level approaches is encouraged. Unless an assignment explicitly states otherwise, all submitted mathematical work and code must be produced independently.

Students may not exchange complete solutions, notebooks, code, hidden-test information, or examination content. External sources and permitted assistance must be acknowledged as directed in the assignment.

Students must write the names of all collaborators on each assignment submission. If there were no collaborators, students should write “No collaborators.”

AI tools may be used as study aids and for limited programming support, including:

• Asking for explanations of course concepts
• Reviewing Python or Qiskit syntax
• Interpreting error messages
• Suggesting tests for code the student has written

Students may not use an AI system to generate or substantially rewrite an assignment solution, mathematical proof, or required program. Students may not use AI tools during the final examination.

Assignment-related AI use must be disclosed in the designated notebook cell or submission statement. Students remain responsible for understanding and verifying everything they submit.

Assignment-specific instructions take precedence over this general policy.

Written problem sets and programming assignments include an automatic 24-hour grace window. No email or extension request is needed to use this window.

After the grace window closes, submissions will not ordinarily be accepted except in cases involving approved accommodations, documented emergencies, religious observances, or University-recognized activities.

The grace window does not apply to the final examination. Students anticipating an examination conflict should contact the instructor as early as possible.

Students must follow the University of Illinois Student Code and the University’s academic-integrity requirements.

Unauthorized collaboration, copied code, undisclosed use of external solutions, fabricated results, sharing examination material, or attempts to infer hidden autograder tests may constitute academic misconduct.

When uncertain about whether a resource or form of assistance is permitted, students should ask before submitting their work.

Students seeking disability-related accommodations should contact Disability Resources and Educational Services and provide the instructional team with the appropriate accommodation documentation.

Students are encouraged to begin this process early so arrangements can be implemented promptly and privately. Course videos will include captions or transcripts, and course documents will be prepared in accessible formats wherever practicable.

The intent of this section is to raise student and instructor awareness of the ongoing threat of bias and racism and of the need to take personal responsibility in creating an inclusive learning environment.

The Grainger College of Engineering is committed to the creation of an anti-racist, inclusive community that welcomes diversity along a number of dimensions, including, but not limited to, race, ethnicity and national origins, gender and gender identity, sexuality, disability status, class, age, or religious beliefs. The College recognizes that we are learning together in the midst of the Black Lives Matter movement, that Black, Hispanic, and Indigenous voices and contributions have largely either been excluded from, or not recognized in, science and engineering, and that both overt racism and micro-aggressions threaten the well-being of our students and our university community.

The effectiveness of this course is dependent upon each of us to create a safe and encouraging learning environment that allows for the open exchange of ideas while also ensuring equitable opportunities and respect for all of us. Everyone is expected to help establish and maintain an environment where students, staff, and faculty can contribute without fear of personal ridicule, or intolerant or offensive language. If you witness or experience racism, discrimination, micro-aggressions, or other offensive behavior, you are encouraged to bring this to the attention of the course director if you feel comfortable. You can also report these behaviors to the Bias Assessment and Response Team (BART). Based on your report, BART members will follow up and reach out to students to make sure they have the support they need to be healthy and safe. If the reported behavior also violates university policy, staff in the Office for Student Conflict Resolution may respond as well and will take appropriate action.

All members of the Illinois Computer Science department — faculty, staff, and students — are expected to adhere to the CS Values and Code of Conduct. The CS CARES Committee is available to serve as a resource to help people who are concerned about or experience a potential violation of the Code. If you experience such issues, please contact the CS CARES Committee. The Instructors of this course are also available for issues related to this class.

Diminished mental health, including significant stress, mood changes, excessive worry, substance/alcohol abuse, or problems with eating and/or sleeping can interfere with optimal academic performance, social development, and emotional well-being. The University of Illinois offers a variety of confidential services including individual and group counseling, crisis intervention, psychiatric services, and specialized screenings at no additional cost. If you or someone you know experiences any of the above mental health concerns, it is strongly encouraged to contact or visit any of the University's resources provided below. Getting help is a smart and courageous thing to do — for yourself and for those who care about you.

Counseling Center: 217-333-3704, 610 East John Street Champaign, IL 61820

McKinley Health Center:217-333-2700, 1109 South Lincoln Avenue, Urbana, Illinois 61801

University wellness center: https://wellness.illinois.edu

Students enrolled in QC1 are expected to participate in the weekly Quantum Studio or complete the posted asynchronous Studio activity when they cannot attend. For students enrolled in QC2, synchronous Studio participation is available but not required. Attendance is not separately graded. All students remain responsible for completing course work by the published deadlines.

Accommodations for religious observances, disability-related needs, and qualifying University activities will be handled in accordance with the Student Code absence provisions.

Information about confidential support and University reporting obligations concerning sexual misconduct is available through We Care. Emergency guidance is available in the University’s Emergency Response Guide.

For imminent danger, call 911. Students in the United States experiencing a mental-health crisis may call or text 988.

The instructional team may make reasonable adjustments to the schedule, assessments, or assigned materials. Material changes will be communicated through a Coursera announcement.