University of New Mexico · CS591

Quantum Computing

G. Matthew Fricke · 16 weeks · 4 quarters

Mathematical foundations, quantum foundations, computational models and algorithms, and physical quantum machines. Follow the four-quarter schedule below to find available lecture slides.

Earlier syllabus (PDF)

Assignments and grading

Weekly homework and two exams determine the final grade.

80% Weekly homework

10% Each of two exams

Class schedule

The schedule below is the current course plan; the earlier syllabus PDF retains the previous schedule. Q1 retains its existing lecture decks. Q2–Q4 have been resequenced at slide level; completed student decks will be linked here as they become ready. Instructor working drafts contain explicit development placeholders. PDFs show static slides; use PowerPoint for animations and embedded media.

Instructor working materials

The slides have been split and reordered into six Q2 foundation decks, eight Q3 meeting decks, and four Q4 physical-machine decks. Bruna’s 24 development placeholders cover Q2 and Q4 only; Matthew’s Q3 algorithm gaps are marked separately.

DRAFT lecture PowerPoints and PDFs · Slide audit and development tasks · DRAFT — Bruna’s placeholder packet

Authoring drafts, not completed student lectures. Original decks are preserved.

Q1 · Mathematical Foundations

Weeks 1–4 · Lectures 1–6. From the course introduction and complex numbers to vector spaces and matrix operators.

Week 1: Introduction and Complex Numbers

Lecture 1: IntroductionSlides not yet available
Lecture 2: Algebra of Complex NumbersPDF · 34 pages · 2.0 MB · PowerPoint

Q2 · Quantum Foundations

Weeks 5–8 · Tensor products, quantum states, waves, observables, measurement, unitary dynamics, and entanglement. Foundation slides from Lectures 7 and 9–12 have been separated from the computational models, algorithms, and Qiskit material now taught in Q3.

Week 5: Tensor Products and Quantum States

System composition, product bases, state vectors, Dirac notation, normalization, and measurement probabilities.

Revised foundation decks in development; see the instructor working materials.

Week 6: Waves, Interference, and Observables

Physical interference, observables, eigenstates, and the Born rule.

Revised foundation decks in development; Bruna’s additions are marked in the working slides.

Week 7: Measurement and Dynamics

Measurement outcomes and state updates, unitary evolution, and Hamiltonian dynamics.

Revised foundation decks in development.

Week 8: Entanglement — Review and Synthesis

Entangled states, correlations, Bell tests and their assumptions, followed by a synthesis of the Q2 foundations.

Revised foundation decks in development.

Q3 · Computational Models and Algorithms

Weeks 9–12 · Eight meetings. Begin with the conceptual introduction to quantum computation models inside M₀, then build the M-machine progression. The complete circuit model and Qiskit implementation arrive together at M_Q.

Week 9: Reversible and Probabilistic Computation

Algorithms develop alongside each computational model. Eight revised instructor decks now follow these meetings; missing derivations, examples, and lab work are explicitly marked.

Tuesday — M₀: Reversible Deterministic Computation
Introduction to computational models, followed by reversible maps, ancillas, CNOT/Toffoli/Fredkin, and the puzzle framework.Revised instructor draft available in the working materials; student lecture still in development.
Thursday — M₁: Probabilistic Computation
Probability vectors, stochastic transformations, sampling, and classical baselines.Revised instructor draft available in the working materials; student lecture still in development.

Week 10: Amplitudes and Composite Quantum Systems

Tuesday — M₂: Amplitudes and Interference
Real amplitudes, H/Z, interference puzzles, and Deutsch’s algorithm.Revised instructor draft available in the working materials; student lecture still in development.
Thursday — M₃: Composite Quantum Systems
Tensor products, CNOT, Bell states, and entanglement.Revised instructor draft available in the working materials; student lecture still in development.

Week 11: Computing with M₃

Tuesday — Computing with M₃: Multi-Qubit Interference
Oracle puzzles, Deutsch–Jozsa, and Bernstein–Vazirani.Revised instructor draft available in the working materials; student lecture still in development.
Thursday — Computing with M₃: Amplitude Amplification
Marked-item search, Grover’s algorithm, scaling, and limits.Revised instructor draft available in the working materials; student lecture still in development.

Week 12: Complex Phase and Universal Quantum Computation

Tuesday — M₄: Complex Phase
Complex amplitudes, phase gates, roots of unity, the quantum Fourier transform (QFT), and quantum phase estimation (QPE).Revised instructor draft available in the working materials; student lecture still in development.
Thursday — M_Q: Universal Quantum Computation
The complete circuit model, transition to Qiskit, and period finding/Shor’s algorithm as a capstone.Revised instructor draft available in the working materials; student lecture still in development.

Q4 · Physical Quantum Machines

Weeks 13–16 · Information, decoherence, noise, error correction, hardware, and the practical limits of quantum computation. Lecture decks are in preparation.

Week 13: Information in Classical and Quantum Systems

Lecture 34: Classical Information and Shannon EntropyLecture deck in preparation.
Lecture 35: Quantum Information and von Neumann EntropyLecture deck in preparation.

Week 14: Decoherence, Noise, and Error Mitigation

Lecture 36: Information, Decoherence, and Limits of Quantum SystemsLecture deck in preparation.
Lecture 45: Noise Models, Decoherence, and Error MitigationLecture deck in preparation.

Week 15: Error Correction and Quantum Hardware

Lecture 44: Quantum Error-Correcting Codes and Fault ToleranceLecture deck in preparation.
Lecture 46: Quantum Hardware Platforms and Architectural ConstraintsLecture deck in preparation.

Week 16: Physical Limits and Synthesis

Lecture 47: When Quantum Helps, When It Fails, and When It Is IrrelevantLecture deck in preparation.
Lecture 48: ConclusionLecture deck in preparation.