CS 639 · Fall 2026
Systems Architecture for Quantum Computers
Tuesday / Thursday 1:00PM – 2:15PM · MH2516 · September 3 – December 8, 2026
Course Overview
Quantum computers promise new ways to solve problems that are difficult for conventional computers, but building a useful quantum computer is fundamentally a systems challenge. This undergraduate course develops an understanding of the full stack: how quantum information works, how quantum algorithms are expressed and optimized, how programs are compiled and executed on real machines, how quantum computer architecture connects software to hardware, and how quantum error correction can make computation reliable.
Fall 2026 Lecture Schedule
Fall instruction begins Wednesday, September 2; because this course meets Tuesday/Thursday, the first class is Thursday, September 3. Thanksgiving recess is November 26–29. The final Tuesday/Thursday meeting is Tuesday, December 8.
| Week | Date | Lecture / Assessment | Main Ideas |
|---|---|---|---|
| Part I · How Quantum Computing Works | |||
| 1 | Thu, Sep 3 | 1. From Bits to Qubits | Qubits, state vectors, superposition, Bloch-sphere intuition |
| 2 | Tue, Sep 8 | 2. Quantum Gates and Circuits | X, H, phase gates, CNOT; composing simple circuits |
| 2 | Thu, Sep 10 | 3. Measurement and Entanglement | Measurement, multi-qubit states, Bell states, correlations |
| 3 | Tue, Sep 15 | 4. Quantum Teleportation and Circuit Reasoning | Teleportation as a worked example; tracing information through circuits |
| 3 | Thu, Sep 17 | 5. Noise and Decoherence | Why qubits fail, T1/T2, gate and readout errors, mixed states intuitively |
| 4 | Tue, Sep 22 | 6. Where Does Quantum Speedup Come From? | Interference, oracles, and Bernstein–Vazirani as an accessible example |
| 4 | Thu, Sep 24 | 7. Grover’s Algorithm I: Quantum Search | Unstructured search, oracles, phase marking, and the basic Grover circuit |
| 5 | Tue, Sep 29 | 8. Grover’s Algorithm II: Amplitude Amplification | Geometric intuition, repeated amplification, complexity, and worked examples |
| 5 | Thu, Oct 1 | 9. Quantum Fourier Transform I | From the classical Fourier transform to quantum states; phase and periodicity intuition |
| 6 | Tue, Oct 6 | 10. Quantum Fourier Transform II | QFT circuit construction, controlled rotations, and why QFT is useful |
| 6 | Thu, Oct 8 | In-Class Quiz 1 20% | Quantum fundamentals, Grover’s algorithm, and the Quantum Fourier Transform |
| Part II · Programming and Building Quantum Computers | |||
| 7 | Tue, Oct 13 | 11. Variational Quantum Algorithms | VQE, QAOA, parameterized circuits, and hybrid quantum-classical computation |
| 7 | Thu, Oct 15 | 12. Computing with Noisy Qubits | NISQ systems, error mitigation, ZNE, and the limits of imperfect hardware |
| 8 | Tue, Oct 20 | 13. Quantum Compilers I: From Programs to Circuits | Compilation stack, gate sets, decomposition, and circuit optimization |
| 8 | Thu, Oct 22 | 14. Quantum Compilers II: Mapping and Routing | Limited connectivity, placement, SWAPs, and routing overhead |
| 9 | Tue, Oct 27 | 15. Quantum Compilers III: Scheduling and Optimization | Parallelism, critical paths, and hardware-aware and noise-aware compilation |
| 9 | Thu, Oct 29 | 16. Quantum Computer Architecture I: The System Stack | Processor, control system, ISA, measurement, and the compiler–hardware interface |
| 10 | Tue, Nov 3 | 17. Quantum Computer Architecture II: Executing a Circuit | Control pulses, timing, connectivity, readout, feedback, and system bottlenecks |
| 10 | Thu, Nov 5 | In-Class Quiz 2 20% | Variational and noisy quantum computing, compilers, and architecture |
| Part III · How We Make Quantum Computers Reliable | |||
| 11 | Tue, Nov 10 | 18. How Do We Protect a Qubit? | Why classical redundancy is insufficient; repetition codes and syndrome intuition |
| 11 | Thu, Nov 12 | 19. The Surface Code | Data and ancilla qubits, stabilizers intuitively, syndrome extraction, and logical qubits |
| 12 | Tue, Nov 17 | 20. Finding and Correcting Errors | Syndrome history, decoding, matching intuition, and real-time classical processing |
| 12 | Thu, Nov 19 | 21. Scaling Quantum Error Correction | Code distance, threshold, logical error rate, and physical-qubit overhead |
| 13 | Tue, Nov 24 | 22. Computing with Logical Qubits | Fault tolerance, logical gates, transversal gates, and lattice surgery at a high level |
| 13 | Thu, Nov 26 | No Class — Thanksgiving Recess | UW–Madison Thanksgiving recess: Nov 26–29 |
| 14 | Tue, Dec 1 | 23. From Error Correction to Fault-Tolerant Computing | Magic states, expensive T gates, and the end-to-end path from logical circuits to reliable execution |
| 14 | Thu, Dec 3 | In-Class Quiz 3 20% | Quantum error correction and fault-tolerant quantum computing |
| Part IV · Synthesis and Outlook | |||
| 15 | Tue, Dec 8 | 24. The Future of Quantum Computer Architecture | What may scale next: better qubits, new codes, modular systems, and open architectural challenges |
Weekly Practice Quizzes
There are 12 weekly practice quizzes, each worth 3 points, for a total of 36 points (36% of the course grade). These low-stakes quizzes are designed to keep students current with the material and provide regular practice before the in-class quizzes. Many will include short coding exercises that help students understand the concepts covered in class while also developing small software artifacts, such as simple circuit simulators, compiler transformations, mapping or scheduling routines, and basic error-correction tools.
Practice-quiz release dates and deadlines will be posted in Canvas. Twelve practice quizzes will be distributed across the instructional weeks of the semester.
Grading
The course uses a simple 100-point grading system. The three in-class quizzes assess conceptual understanding and the ability to reason about quantum systems. Weekly practice quizzes are low-stakes and graded for completion.
In-Class Quizzes
| Assessment | Date | Primary Scope | Points |
|---|---|---|---|
| Quiz 1 | Thu, Oct 8 | Quantum fundamentals, Grover’s algorithm, and the Quantum Fourier Transform | 20 |
| Quiz 2 | Thu, Nov 5 | Variational and noisy quantum computing, quantum compilers, and architecture | 20 |
| Quiz 3 | Thu, Dec 3 | Quantum error correction and fault-tolerant quantum computing | 20 |
Class Participation
Participation is worth 4 points. Full credit reflects consistent, constructive engagement with the course. Examples include asking or answering questions during class, contributing to in-class problem solving and discussion, helping explain concepts to peers, and participating on Piazza by asking thoughtful questions, answering classmates’ questions, or sharing useful course-related insights. Participation is evaluated on the quality and consistency of engagement rather than the sheer number of comments or posts.
Letter Grades
UW–Madison reports conventional course grades using A, AB, B, BC, C, D, and F; plus and minus grades are not used. UW–Madison specifies the letter-grade framework and GPA values, while individual course syllabi define the relationship between course performance and the final letter grade. This course uses the percentage thresholds below.
| Course Score | Letter Grade | UW Grade Points / Credit |
|---|---|---|
| 93–100 | A | 4.0 |
| 88–<93 | AB | 3.5 |
| 80–<88 | B | 3.0 |
| 75–<80 | BC | 2.5 |
| 70–<75 | C | 2.0 |
| 60–<70 | D | 1.0 |
| <60 | F | 0.0 |
Official UW–Madison grading references: Valid Grades and Student Grading and GPA. The percentage thresholds above are the grading thresholds adopted for this course.