The map · problem classes by tier

Where quantum wins, where it doesn't, and where nobody has checked.

The canonical catalogue lists 74 quantum algorithms with their published references; a handful are rigorously proven. This is the map that separates them — by how real the advantage is today, not by industry. Each class: its algorithm, the vertical it touches, the classical champion it must beat, and the honest state right now.

Field state · july 2026 · sourced, re-audited before each verdict

Three things the word "problem" hides.

The distinction that orders everything below — and that most coverage blurs:

classThe problem class (industry): "optimize a portfolio", "molecular ground state", "route a fleet". A few dozen cover ~80% of the value.
algorithmThe recipe: QAOA, VQE, Shor, Grover, HHL. There are 74 catalogued.
advantageThe real question: does that recipe actually beat classical — at what size, on what hardware? Almost nobody measured this. That is the ledger.

The four tiers.

The axis is not "which industry" — it is how real the quantum advantage is today. This ordering is what a decision-maker, or a copilot, actually needs and nobody else publishes this way.

Tier AProven in theory, blocked by hardware

Wins on paper, but needs error correction / millions of qubits that don't exist yet. Not runnable fights — timing maps.

Class
Algorithm
Vertical
Honest state today
Integer factoring / cryptanalysis
Shor
Crypto
Proven (superpolynomial). Needs ~millions of physical qubits with error correction → not executable today. Its value now is timing: NIST already standardized post-quantum crypto (2024).
Unstructured search
Grover
Cross-industry
Proven but only quadratic (modest, not exponential). Needs an efficient oracle + fault tolerance; overhead makes it impractical near-term.
Linear systems
HHL
ML, engineering
Exponential with heavy fine print (state-prep and readout caveats). Frequently dequantized. Not practical near-term.
Tier BAdvantage plausible, genuinely quantum, early

The strongest case theoretically: simulate the quantum with the quantum. The bottleneck is real — where a future win is most credible, and where the baseline is hardest.

Class
Algorithm
Vertical
Honest state today
Molecular ground-state / electronic structure
VQE, QPE
Pharma, Chemistry
The strongest case that exists. VQE limited by NISQ noise; QPE needs fault tolerance. Not yet demonstrated at useful scale, but the bottleneck is genuinely quantum. RQ-0007 — see the precision note below.
Materials & battery simulation
VQE, QPE
Energy, Materials
Same family as molecular. Early. Genuine quantum bottleneck; strong industry interest (batteries, catalysts).
Quantum dynamics simulation
Hamiltonian sim.
Physics, materials
Where advantage is most natural. "Utility" demos (2023) were matched classically weeks later with tensor networks → contested. The most fertile ground, but classical answers fast.
Tier CContested — classical wins today (combinatorial optimization)

Where most of the commercial hype lives and where classical is most brutal. QAOA / annealing don't beat well-tuned classical at scale. The right terrain for the first fight — the honest "not yet" is cheap and valuable.

Class
Algorithm
Vertical
Honest state today
Portfolio optimization
QAOA, annealing
Finance
No proven advantage at scale. Champion: Gurobi, OR-Tools, tuned annealing. Projected crossover far off. RQ-0012 — first-fight candidate #1.
Vehicle / fleet routing
QAOA, annealing
Logistics, Mining
Classical dominates; OR-Tools is brutal to beat. RQ-0019 — first-fight candidate (mining, accessible data).
Grid / energy balancing
QAOA, annealing
Energy
Combinatorial optimization; classical strong. RQ-0033.
Risk / Monte Carlo
Amplitude est.
Finance, insurance
QAE needs deep circuits / fault tolerance; the quadratic speedup gets eaten by constants. No advantage at scale today.
Tier DSkeptical / largely dequantized

Where the most was promised and the least held. High-value arbiter content precisely because almost nobody says it out loud.

Class
Algorithm
Vertical
Honest state today
Quantum machine learning
Q-kernels, VQC
Cross-industry
Heavily dequantized: several celebrated claims turned out classically matchable. The most skeptical terrain — read any QML claim with maximum caution.

Where classical already won decisively

Protein structure prediction is not quantum — and shouldn't be implied to be. AlphaFold (classical deep learning) solved a 50-year problem. If Rosetta touches "drug discovery" it must be surgical: the quantum value is in electronic-structure precision (Tier B), not in replacing a discovery pipeline that classical AI now leads. Saying this out loud raises arbiter credibility.

Precision note for RQ-0007 (molecular)

A serious computational chemist reads a molecular verdict knowing AlphaFold + classical docking already work. So the claim must be narrow: plausible quantum advantage lives in electronic structure of strongly-correlated systems (transition metals, certain excited states, cases DFT approximates poorly) — not "accelerating drug discovery" broadly. The narrow, exact claim protects us; the broad one exposes us.

What this means for the first fight

Start in Tier C (portfolio or mining routing), not Tier B (molecular). Counterintuitive but correct: Tier C is cheap (QAOA simulable, free tier), the champion (OR-Tools) is brutal and free — so nobody can accuse us of a weak baseline — and the expected result, "classical wins, quantum hasn't crossed yet," is exactly the product: the first honest negative with an estimated crossover.

Molecular is tempting because advantage is more plausible — and that is why it's a bad first fight: a win there would be an extraordinary claim demanding extraordinary evidence, against a baseline that needs chemistry expertise. Credibility is built with the honest negative, not the risky win.

The archive

The algorithms, one by one, with the source attached.

Above is the map by tier: our reading. Here is the raw catalogue, served from the database rather than hand-written: every entry in the Quantum Algorithm Zoo with the speedup the source declares, the primary papers, and the public implementations that exist.

Two things this table does not say. Each row's speedup is what the cited source declares, not a measurement of ours: declaring is not measuring. And cataloguing is not implementing — this page shows and documents them, it does not offer them as a service. The only column we assert is the evidence one, and it is empty on almost every row.

74algorithms catalogued
4categories
625citations resolved
1with a sealed run of ours

Showing 74 of 74

How to check this page

Everything above comes from the same database that answers the API. Download the source, recompute its sha256 and compare it with the one declared by /v1/algorithms under procedencia.instantanea_sha256: if it matches, you are looking at the same catalogue we are. Agents read it over the API or over MCP with buscar_algoritmo_cuantico.