Quantum foundations

Qubits, gates, and what actually makes quantum different. No prior quantum needed.

Stewart Smith
·8 December 2025

Quantum computing is easier than you might think. (Remember it’s just computing, it’s not quantum physics!) Some quick math brush-ups and few concept primers…

5 lessons · ~1 hour

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What you'll learn

Start from zero and build up the math that quantum computing actually runs on. By the end you can read qubits, gates, and circuits well enough to open the Code Playground and run your first circuit on real hardware.

  • Why quantum computers matter, and what they are actually for
  • The math they run on: complex numbers, matrices, and vectors
  • What a qubit really is: state vectors, superposition, the Bloch sphere
  • The core quantum gates and how they transform qubits

Course contents

  1. 01What’s quantum computing?Quantum computing is easier than you might think. (Remember it’s just computing, it’s not quantum physics!) Some quick math brush-ups and few concept primers are all you need to start making meaningful mistakes.
  2. 02Complex numbersComplex numbers are a key part of orchestrating quantum algorithms, and you can learn what they are in just a few minutes.
  3. 03MatricesMatrices are the mathematical building blocks for quantum bits, quantum gates, and quantum circuits.
  4. 04Qubits (quantum bits)Like bits in classical computing, qubits are the fundamental containers for storing value in a quantum circuit. These stored values can be altered by applying quantum gates to them.
  5. 05Quantum logic gatesQuantum logic gates are the means of “getting work done” on a quantum computer. They perform computation by altering the values of quantum bits (“qubits”).
Your instructor
Stewart Smith

Stewart Smith is an award-winning creative technologist, artist, writer, and speaker. He’s led innovation teams across ten time zones, and wields wisdom accrued from his years with Google, Amazon, and Unity. Educated as a graphic designer (MFA, Yale University), his work has spanned quantum computing, artificial intelligence, spatial computing, aerospace, and fine art.

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