Advanced Quantum Computing Courses

Graduate and research-level quantum computing content from MIT, Caltech, Cambridge, and Perimeter Institute. These 22 courses cover quantum information theory, fault-tolerant computation, and the algorithms that define the frontier of the field. Most are free.

Real quantum computer hardware in a research laboratory

What advanced quantum computing covers

Advanced courses move from learning quantum computing to understanding it at a level that prepares you for research. The topics are more abstract, mathematically demanding, and less focused on immediate practical application, and that is intentional.

Quantum information theory treats information as a physical quantity and asks what the laws of quantum mechanics imply for communication, compression, and cryptography. Topics include quantum entropy, quantum channel capacity, entanglement measures, and quantum key distribution with security proofs.

Fault-tolerant quantum computation is the theory of how to build reliable quantum computers from unreliable components. The threshold theorem (if physical error rates fall below a threshold, arbitrarily long computations are possible) is a central result. Surface codes, stabilizer codes, and the Gottesman-Knill theorem are standard topics.

Quantum complexity theory asks which computational problems quantum computers can solve efficiently. The complexity class BQP (bounded-error quantum polynomial time) is the quantum analogue of P. QMA (quantum Merlin-Arthur) is the quantum analogue of NP. Understanding these classes clarifies where quantum speedups are possible and where they are not.

Advanced algorithms at this level include the HHL algorithm for linear systems, Quantum Singular Value Transformation (QSVT), which provides a unified framework for many quantum speedups, quantum walks, and amplitude estimation. These require comfort with quantum phase estimation and polynomial approximation theory.

Quantum hardware physics covers how qubits are physically implemented: superconducting transmon qubits, trapped ions, neutral atoms, photonic systems, and nitrogen-vacancy centers. Understanding the physics of decoherence, gate operations, and readout at this level requires some quantum mechanics background.

The best free advanced courses

One distinctive feature of advanced quantum computing education is that the best content is overwhelmingly free. This is the opposite of the beginner landscape, where paid platforms sometimes offer better-structured introductory courses than free alternatives.

MIT publishes lecture notes and problem sets for its quantum information courses through MIT OpenCourseWare at no cost. John Preskill's lecture notes from Caltech's PHYS 219, widely considered the most comprehensive graduate quantum computing text available, have been publicly available since the late 1990s and are still updated. The Perimeter Institute archives hundreds of hours of research-level lectures through its PIRSA platform, freely accessible to anyone.

Cambridge publishes lecture notes for its quantum information and computation courses, which are freely available online. EdX and Coursera carry some advanced content as well, though the free-to-audit versions of those are often worth less than the fully open MIT and Caltech materials.

The implication: if you are ready for advanced content, cost is not a barrier. The limiting factor is time and mathematical preparation, not access to material.

Prerequisites for advanced courses

Advanced quantum computing courses assume significant preparation. The honest list:

If the linear algebra requirement is the weak point, 3Blue1Brown's "Essence of Linear Algebra" series followed by a rigorous textbook like Axler's "Linear Algebra Done Right" is the fastest path to readiness. Comfort with the mathematics will determine whether advanced courses are productive or frustrating.

Advanced courses

22 graduate and research-level courses, ranked by rating

From advanced courses to research

Completing advanced courses puts you at the boundary of current knowledge, not inside research, but prepared to enter it. The step from coursework to research is about learning to engage with the literature rather than textbooks.

The arXiv quant-ph preprint server (arxiv.org/archive/quant-ph) is where essentially all quantum computing research appears before or alongside journal publication. Reading new preprints regularly, even if you only understand 60-70% of a given paper at first, builds familiarity with research norms, notation, and the open problems that the community cares about.

A practical approach: pick one specific area, quantum error correction, near-term algorithms, quantum complexity, or hardware, and identify five to ten landmark papers that everyone in that area cites. Work through those papers carefully, looking up every technique you do not recognize. Once you can read those papers fluently, you can read current work in that area.

For those interested in formal academic research, see our university programs guide covering PhD programs in quantum computing and quantum information.

Frequently asked questions

What is the hardest quantum computing course available online?
Caltech's PHYS 219 (Quantum Computation) taught by John Preskill and MIT's graduate quantum information courses are among the most rigorous. The Perimeter Scholars International (PSI) quantum information lectures, archived on PIRSA, are another demanding option covering the field at a research level. All of these are free.
Are MIT and Caltech quantum courses really free?
Yes. MIT makes course materials including lecture notes and problem sets freely available through MIT OpenCourseWare. Caltech's John Preskill has published his lecture notes publicly for decades, and video lectures are available online. The Perimeter Institute's lectures are available through their PIRSA archive. You do not get a credential from these free versions, but the content is identical to what enrolled students receive.
What's the difference between quantum information and quantum computing?
Quantum information is the broader field: it studies how information can be encoded, stored, transmitted, and processed using quantum systems. It includes quantum communication, quantum cryptography, quantum error correction, and quantum complexity theory alongside quantum computing. Quantum computing is the subset focused specifically on computation. Advanced courses often cover both together because the theoretical foundations overlap significantly.
How do I go from advanced courses to actual research?
Complete one or two advanced courses, then start reading recent papers from arXiv quant-ph. Pick a specific area that interests you and find three to five landmark papers to read carefully. Replicate results where you can. Then look for open problems in survey papers or follow researchers whose work interests you. Many researchers are accessible for questions through email or at conferences like QIP and TQC.