Quantum Information Science II (MIT Open Learning Library)

Quantum Information Science II (8.371x) is the graduate-level continuation of MIT’s QIS I series, assuming familiarity with the material in 8.370x. Where QIS I builds from quantum mechanics through the major quantum algorithms, QIS II turns to the deeper questions of what quantum information fundamentally is, how it degrades, and how to protect it.

Like QIS I, the full series is freely available on MIT’s Open Learning Library with automatic grading on problem sets.

What you’ll learn

QIS II is organized into three parts:

Part 1: Quantum States, Noise and Error Correction covers the mathematical description of noise in quantum systems. Topics include quantum operations as completely positive maps, the operator-sum (Kraus) representation, decoherence models for realistic quantum hardware, quantum error-correcting codes including the Knill-Laflamme conditions, and the stabilizer formalism for constructing and analyzing quantum codes.

Part 2: Efficient Quantum Computing, Fault Tolerance, and Complexity addresses how to perform reliable computation despite physical errors. Topics include fault-tolerant gate sets, the threshold theorem for fault-tolerant computation, universal quantum computation with limited gate sets, and quantum computational complexity including BQP and its relationship to the polynomial hierarchy.

Part 3: Advanced Quantum Algorithms and Information Theory covers quantum information theory and the information-theoretic analysis of quantum algorithms. Topics include the quantum Fourier transform over non-abelian groups, the hidden subgroup problem, quantum walks and their algorithmic applications, von Neumann entropy, quantum mutual information, and the capacity of quantum channels.

Course structure

Three parts, each containing video lectures, reading materials, and graded problem sets. The series is permanently available on MIT’s Open Learning Library at no cost, with no enrollment deadlines.

Completing all three parts represents a substantial fraction of a graduate quantum information science curriculum. The mathematical level is significantly higher than QIS I.

Who is this for?

• Students who have completed QIS I and want to continue to graduate-level material
• Researchers in quantum computing who need a rigorous treatment of error correction and information theory
• Anyone preparing for research in quantum algorithms, quantum error correction, or quantum communication

Prerequisites

Completion of MIT QIS I (8.370x) or equivalent mastery of quantum mechanics, quantum circuits, and the major quantum algorithms. Graduate-level mathematical maturity is required: comfort with proofs, abstract linear algebra, and probability theory.

Why take this course?

Error correction and fault tolerance are the central unsolved engineering challenges in quantum computing. Grounding in these topics is increasingly necessary for anyone who wants to work on real quantum systems rather than idealized theoretical models.

The combination of Chuang and Shor as instructors, together with MIT’s rigorous problem sets and free availability, makes QIS II one of the best freely accessible paths to graduate-level quantum information science.