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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]>
731 B
731 B
Suppose f(x) = s · x mod 2, the parity of the bits that x shares with a hidden string s. Classically, each query of f reveals one bit of s at best: asking about x = 100 gives the first bit, and so on, n queries for n bits.
The Bernstein–Vazirani algorithm finds all of s with one query, with the circuit of Deutsch–Jozsa: inputs in superposition, the target in |−⟩, the oracle, and Hadamards on the inputs. The oracle leaves the state
Σₓ (−1)^(s·x) |x⟩ / √2ⁿ,
and that pattern of signs is exactly what n Hadamards turn into the single basis state |s⟩.
Remember the bit order: the outcome is written c[2] c[1] c[0], the highest bit first. An oracle that reads q[0] and q[2] has the hidden string 101.