Method — Algorithm library
Quantum algorithms, honestly labeled
Each algorithm page states the proven speedup and its fine print (oracle models, data-loading costs, disputed advantages), what today's hardware can demonstrate, and ships a runnable circuit you can open in the Lab.
All algorithms10 pages · every one runnable
Oracle problem · beginner · A routine demo at 5–15 qubits. Accuracy drops as n grows.Bernstein–VaziraniOne query instead of n queries. This is proven, but only in the oracle (black-box) model.Oracle problem · beginner · Runs cleanly at 2–6 qubits on any current QPU.Deutsch–JozsaExponential, but only against exact normal (deterministic) methods. One query, in the oracle (black-box) model.Search · intermediate · Demos with 2–3 qubits succeed. Useful sizes are far out of reach.Grover's searchA quadratic speedup in the number of questions: about √N instead of N. Proven, in the oracle (black-box) model.Optimization · intermediate · Runs at tens to low hundreds of qubits on real hardware. In every published head-to-head so far, normal solvers matched or beat it.QAOANone proven for any normal optimization problem. At low depth, simple normal algorithms are proven to match or beat it on known families of problems.Building block · intermediate · Clean demos with a few qubits are routine. The controlled turns get smaller by half with each added qubit, and they drop below what hardware can tune long before 50 qubits.Quantum Fourier TransformO(n^2) gates, compared with O(n·2^n) steps for a normal FFT on the same list of numbers (proven). But it works on amplitudes you can't read out, so it is a building block inside other algorithms, never a speedup on its own.Building block · advanced · Textbook demos with 3–5 counting qubits and hand-picked gates. The deep controlled circuits needed for real chemistry or factoring are beyond any current machine.Quantum Phase EstimationNot a speedup on its own. It is the building block that gives Shor's algorithm its huge advantage, and it powers proposed advantages in chemistry. (This is theory. Any useful precision needs error-corrected machines.)Protocol · intermediate · Routine in labs. Satellite links have gone beyond 1,000 km.Quantum teleportationNo speedup. It moves 1 qubit state for each Bell pair used, plus 2 normal bits.Cryptography · advanced · Numbers like 15 and 21 have been factored, mostly with circuit shortcuts that already assume the answer. Nothing comes close to breaking real encryption, which would need error-corrected (fault-tolerant) machines.Shor's AlgorithmSuperpolynomial: its cost grows far more slowly than the best known normal factoring method. The scaling is proven math, but it has never been shown beyond toy numbers.Protocol · beginner · A clean two-qubit demo on any gate-based QPU.Superdense coding2 bits for each qubit sent, as long as the two sides already share a Bell pair.Chemistry · intermediate · Small-molecule demos (H2, LiH, BeH2, roughly 2–12 qubits) run on real hardware with heavy error mitigation. A laptop gets the same energies instantly and more accurately.Variational Quantum EigensolverNone proven. It is a rule-of-thumb method for noisy hardware. Every published VQE result can be matched by a normal computer, most of them easily.