Linear algebra for quantum computing
Vectors and Dirac notation, matrices, eigenvalues, tensor products and the Schmidt decomposition, built from scratch with pictures.
I built this to learn quantum computing properly and to share what I learned: fourteen modules that follow a quantum computer from room temperature down to ten millikelvin, then into current research, with 226 live labs and an explained answer to every question.
Start with the math, descend through the five temperature stages of a real machine, then go inside the hardware and out into the algorithms that run on it.
Vectors and Dirac notation, matrices, eigenvalues, tensor products and the Schmidt decomposition, built from scratch with pictures.
Five modules that follow the qubits down the fridge: each stage colder, each module a little deeper.
How superconducting qubits are built and coupled, how gates become microwave pulses, and how error correction makes logical qubits.
Algorithms and their limits, simulation methods, chemistry and machine learning on qubits, and quantum information and cryptography.
A superconducting quantum processor hangs at the bottom of a dilution refrigerator, a few thousandths of a degree above absolute zero. The course is organised around the same stages: each module sits one plate further down, from 300 K to the mixing chamber at 10 mK.
Move your pointer over the machine to look around it.
Intuition first, then the formalism, with every idea backed by something you can run, poke at or check.
Bloch spheres, a 4-qubit circuit simulator, Grover and Shor, a 2,000-qubit stabilizer simulator, decoders and lattice surgery, all running in your browser.
Fourteen modules in four parts with a clear lesson path, progress for every lesson and module, and a key-ideas recap at the end of each lesson.
A ten-question check after every lesson. Write down your own reasoning, check your answer, then read why it is right.
Every simulation runs on a real state-vector engine, so the numbers you see are calculated. Your progress stays private in your browser.
Author of this course · MSc, McGill University
Sai Ganesh holds an MSc from McGill University and is passionate about AI and computational modelling. He has over four years of work experience with premier organizations including the National Institute of Ocean Technology, the University of Manitoba, Vecmocon and Siechem. He has published more than 16 research works in premier conferences and journals, cited by researchers in the field, and has 5 patents published with the Indian Patent Office. He has also received several laurels at national and international hackathons, conferences and bootcamps.
No. The course assumes high-school algebra and a little comfort with complex numbers. Module 01, the math toolkit, builds the linear algebra you need, and everything else is built up from there.
Read the lesson, try its labs, then take the ten-question check. Get seven or more right on the first try and the lesson is marked complete in your module. You can retake any check with the options shuffled.
Only in your browser. Lesson progress, quiz scores and the reasoning notes you write are stored on your device, and nothing is sent anywhere.
Students, engineers and researchers who want a real understanding of quantum computing — from first principles all the way to fault-tolerant architectures.
Begin with the math toolkit, or go straight to 300 K.