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engine::course reads the course from wai-quantum/course/: 21 lessons from a first circuit through superposition, entanglement, interference, the standard algorithms, noise and mitigation, error correction and fault tolerance to resource estimates, each a Markdown text in English and Simplified Chinese and an exercise.json with a schema. A check runs each case of an exercise (a generator's inputs) with its intent and the verdict, measures its constraints (the gates allowed, counts, the T count, the critique's smells, the resource estimate's counts), and says what went wrong from the diagnostics, the verdict and the critique, never from the solution. The tests hold every solution to pass by proof, every known wrong answer to fail for its stated reason, and every locale to every text and message. wai-quantum learn shows, starts, checks, hints and explains a lesson, keeps progress only on this machine, and speaks the language --lang or LANG names; the command summaries and docs topics have Chinese translations held to the English they came from. The verdict gains of_diagnostic for a generator's refusal. llms.txt names the course. Co-Authored-By: Claude Opus 5.5 <[email protected]>
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A controlled gate is usually described as acting on its target. When the target is in a state the gate only multiplies by a phase, the gate changes nothing about the target, and the phase lands on the control instead. That is phase kickback.
The state |−⟩ = (|0⟩ − |1⟩)/√2 is such a state for x: X|−⟩ = −|−⟩. So cx q[0], q[1] with q[1] in |−⟩ multiplies the part of the state where q[0] is |1⟩ by −1, and leaves q[1] in |−⟩.
OPENQASM 3.0;
include "stdgates.inc";
qubit[1] q;
x q[0];
h q[0];
This prepares |−⟩. Phase kickback is how the algorithms in the next unit read a function's answer: the answer becomes a phase on the input qubits, and interference turns the phases into an outcome. The debugger shows it step by step: wai-quantum debug prints the amplitudes before any line, and the Studio's Step through pane draws each qubit's state.