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 · routine demo at 5-15 qubits; fidelity decays with nBernstein–VaziraniOne query vs n queries; proven, oracle modelOracle problem · beginner · clean at 2-6 qubits on any current QPUDeutsch–JozsaExponential vs deterministic classical only; one query, oracle modelSearch · intermediate · 2-3 qubit demos succeed; useful sizes far out of reachGrover's searchQuadratic query speedup — √N vs N; proven, oracle modelOptimization · intermediate · Runs at tens to low hundreds of qubits on real hardware; every published head-to-head so far is matched or beaten by classical solversQAOANone proven for any classical optimization problem; at low depth, simple classical algorithms provably match or beat it on known instance familiesBuilding block · intermediate · Clean few-qubit demos are routine; the controlled rotations shrink exponentially with register size and drop below hardware precision well before 50 qubitsQuantum Fourier TransformO(n^2) gates versus O(n·2^n) classical FFT operations on the equivalent vector (proven) — but it acts on amplitudes you cannot read out, so it is a subroutine, never a standalone speedupBuilding block · advanced · Textbook demos with 3–5 counting qubits and hand-picked gates; the deep controlled-unitary circuits needed for real chemistry or factoring are beyond any current machineQuantum Phase EstimationNot a speedup by itself — the subroutine that delivers Shor's superpolynomial advantage and proposed quantum-chemistry advantages (theory; requires fault tolerance at any useful precision)Protocol · intermediate · routine in labs; satellite links beyond 1,000 kmQuantum teleportationNo speedup — moves 1 qubit per Bell pair + 2 classical bitsCryptography · advanced · Numbers like 15 and 21 factored, mostly with circuit shortcuts that presuppose the answer; nothing remotely near cryptographic scale, which requires fault toleranceShor's AlgorithmSuperpolynomial over the best known classical factoring algorithm (proven algorithmic scaling; never demonstrated beyond toy numbers)Protocol · beginner · clean 2-qubit demo on any gate-based QPUSuperdense coding2 bits per qubit sent, given a pre-shared Bell pairChemistry · intermediate · Small-molecule demos (H2, LiH, BeH2, roughly 2–12 qubits) run on real hardware with heavy error mitigation; a laptop computes the same energies instantly and more accuratelyVariational Quantum EigensolverNone proven — a heuristic for noisy hardware; every published VQE result is reproducible classically, most of them trivially