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Quantum Computing Fundamentals: a free, maths-first course

Learn the mathematics behind quantum computing, from complex numbers and linear algebra to qubits, quantum gates, entanglement and algorithms. Work through written explanations, equations and exercises at your own pace, using the notation you will encounter in textbooks and research papers.

Who is this course for?

Start with high-school mathematics; no previous quantum computing knowledge is required. The Mathematical Foundations chapter introduces the tools you will need. If you already know complex vector spaces, linear algebra and bra-ket notation, you can begin with Qubits and Gates.

What you will learn

  • Read and use bra-ket notation to describe quantum states
  • Calculate how quantum gates change single- and multi-qubit states
  • Follow entanglement, teleportation and superdense coding protocols
  • Work through Grover search, the quantum Fourier transform and Shor's algorithm

Start with the course introduction or begin the first lesson: Complex Numbers.

Course chapters and lessons

Afterword & Next Steps