Quirk — drag-and-drop quantum circuit simulator
Craig Gidney
Drag gates onto wires and watch amplitudes, Bloch spheres and probabilities update live. Nothing else builds gate intuition this fast, and it needs no install or account.
Beginner · 10 resources
Quantum gates
Reversible operations that rotate qubit states. X flips, H creates superposition, Z flips a sign, and CNOT lets one qubit control another — that small set already gets you a long way.
Learn first:Qubits
Why it matters
Gates are the instruction set of a quantum computer. You cannot read a circuit diagram, let alone write one, without knowing what half a dozen gates do.
After this you will be able to
- Name what X, Z, H, S, T and CNOT do
- Explain why every quantum gate must be reversible
- Build a Bell pair with H followed by CNOT
Read it here first
The plain-language version
Every quantum gate is a rotation of the state, and every rotation can be undone by rotating back. There is no quantum AND gate and no quantum erase, because those destroy information and cannot be reversed.
Analogy
Rotating a globe. Any spin you apply can be exactly undone. Contrast a classical AND gate: told the output is 0, you cannot recover which inputs produced it.
Common misconception
Quantum computers cannot do irreversible logic, so they cannot compute what classical computers can.
What is actually true
Any classical circuit can be rewritten reversibly at modest extra cost. Quantum computers can do everything classical ones can — the interesting question is only where they are faster.
The thing to remember
Reversibility is why circuits are drawn as wires that never merge or terminate. Qubit count stays constant from left to right, unlike a classical circuit that funnels many inputs to one output.
Start here
3 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
Free accounts get a graphical circuit composer and a monthly allowance of runtime on genuine superconducting quantum processors. Your first noisy histogram from real hardware is a rite of passage.
Basics of Quantum Information
IBM Quantum Learning (John Watrous)
A rigorous but genuinely well-taught course by John Watrous covering single systems, multiple systems, quantum circuits and the core protocols. The cleanest bridge from intuition to real notation.
Also covering this
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Grok the Bloch Sphere
James Weaver
An interactive Bloch sphere where you apply gates and watch the state vector rotate in real time, with the amplitudes and angles shown alongside. The fastest way to make the sphere click.
IBM's free structured course platform and the successor to the old Qiskit Textbook. Mixes written lessons, videos and runnable notebooks, and takes you from 'what is a qubit' to running jobs on real hardware.
A free, complete undergraduate textbook with worked exercises. Uniquely, it teaches classical computing alongside quantum, so the comparison is always concrete rather than hand-waved.
PennyLane Codebook
Xanadu
Learn by writing code in the browser, exercise by exercise, from single qubits up to variational algorithms. The best option if you retain things by typing rather than reading.
A hands-on Jupyter-based workshop run worldwide by a volunteer community. Strong on doing rather than watching, and the free live cohorts give you people to get stuck with.
Quantum Computing course
Brilliant
Interactive, visual and gentle, built in collaboration with quantum researchers. Worth it if you learn best by poking at widgets; everything it covers is available free elsewhere with more effort.
Quantum Computing for the Very Curious
Andy Matuschak & Michael Nielsen
The single best starting point in existence. An essay built on spaced-repetition flashcards embedded in the text, so you actually remember it a month later. Assumes nothing but curiosity, and gets you honestly to quantum teleportation.
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Topics that list Quantum gates as a prerequisite.