A product of its own
Is there real evidence for this quantum claim?
Every claim dated, sourced, statused and linked to its seal — including the ones we published against ourselves. Search the tracked claims, the algorithm catalogue and the sealed runs at once.
certified randomnessWillow error correctionQAOA portfolioSycamore supremacyfraud detection kernel
74
algorithms catalogued
625
references indexed
16
advantage claims tracked
3
still surviving
Catalogue: Quantum Algorithm Zoo snapshot 2026-09-09 · sha256 dee7e76b… · every number links to its source · /v1/algorithms · /v1/claims
The catalogue
Four classes, 74 algorithms.
The classes are the Quantum Algorithm Zoo's own. Re-cutting them into commercial classes is a product decision we have not taken.
31
Oracular Algorithms
18
Optimization, Numerics, and Machine Learning
14
Algebraic and Number Theoretic Algorithms
11
Approximation and Simulation Algorithms
Built for AI agents: our MCP server exposes this archive — 9 tools, no key. /mcp · llms.txt
The Survival Registry
What happens to quantum claims after the press release.
Sixteen tracked advantage claims, each with the date it was made, the date it was first challenged, and how much of its life it survived unchallenged.
The catalogue, in full
All 74, with their class and their source.
Every algorithm in the catalogue, written on this page — not behind a call. Each description is the sealed Quantum Algorithm Zoo snapshot; what Rosetta measured, and where, lives in the ledger.
Oracular Algorithms · 31
Find a hidden subgroup of a commutative group by querying a function that is constant on each coset. This is the shared pattern behind Shor: factoring, discrete log and Pell all reduce to it.
Superpolynomial · 6 refs
Recover a secret string hidden inside a linear function with as few queries as possible.
Polynomial Directly, Superpolynomial Recursively · 5 refs
Locate the centre of a radially symmetric function by querying it pointwise.
Polynomial · 1 refs
Find two inputs with the same output, or decide whether all elements of a list are distinct.
Polynomial · 14 refs
Identify fake coins in as few weighings as possible: the classic puzzle, in query form.
Polynomial · 2 refs
Decide whether a boolean function is constant or balanced in a single query. The first historical separation between quantum and classical.
Exponential over P, none over BPP · 3 refs
Compute the effective resistance between two nodes of a graph whose edge weights are read as resistances.
Exponential · 3 refs
Compute the structure of finite rings and of their ideals.
Superpolynomial · 3 refs
Evaluate the value of a boolean formula (AND/OR/NOT) with oracle access to its inputs.
Polynomial · 13 refs
Decide whether some pair of adjacent vertices is labelled 1, given oracle access to the labelling.
Polynomial · 5 refs
The same, but reaching the graph through neighbour lists: the model changes the cost.
Polynomial · 3 refs
Decide graph properties (connectivity, bipartiteness, cycles) by querying the adjacency matrix.
Polynomial · 21 refs
Decide whether a group given by its generators is commutative.
Polynomial · 1 refs
Decide whether two finite groups given by oracle and generators are the same group under different names.
Superpolynomial · 3 refs
Compute the order of a group and decide whether an element belongs to it.
Superpolynomial · 3 refs
Find hidden structures that are not subgroups but nonlinear objects such as spheres or cones.
Superpolynomial · 3 refs
Given two functions that differ by an unknown shift, find that shift.
Superpolynomial · 12 refs
Decide whether a function depends on at most k of its n input bits. Closely related to group testing.
Polynomial · 4 refs
Multiply matrices over semirings (min-plus, for instance), the core of several shortest-path problems.
Polynomial · 5 refs
Compute maximum flow, or minimum-cost flow, on a network with capacities on its edges.
Polynomial · 1 refs
The same problem over non-commutative groups. Solving it in general would attack graph isomorphism and lattices, and it remains open.
Superpolynomial · 24 refs
Search a sorted list. The quantum margin here is only a constant factor, not a change of order.
Constant factor · 5 refs
Reconstruct a polynomial's coefficients by querying it at points.
Varies · 7 refs
Recover a hidden string when queries may leave positions unspecified.
Polynomial · 1 refs
Find the needle in an unstructured haystack: locate a marked item among N with only a yes/no oracle. This is Grover.
Polynomial · 32 refs
Estimate how far apart two probability distributions are, with sampling access only.
Polynomial · 3 refs
Traverse two binary trees welded at the leaves. The clean example of exponential separation by quantum walk.
Superpolynomial · 1 refs
Optimization, Numerics, and Machine Learning · 18
Solve a problem by starting from an easy Hamiltonian and deforming it slowly into one whose ground state encodes the answer. The model behind quantum annealing.
A plausible example of superpolynomial speedup appears in [ 530 ] · 34 refs
Compute the principal eigenvector of a matrix, the core of PageRank-style methods.
Polynomial · 1 refs
Optimise over convex bodies and estimate their volumes, with membership-oracle access to the body.
Polynomial · 11 refs
A family based on double-bracket flows for diagonalising and preparing states. The source declares its advantage unknown.
Unknown · 6 refs
Estimate determinants, traces and other sums over a matrix's spectrum.
Superpolynomial · 2 refs
Estimate the gradient of a smooth function at a point, or learn a polynomial's coefficients, by querying an oracle.
Polynomial · 8 refs
Attack lattice problems, which are the basis of the post-quantum cryptography standardised by NIST.
Exponential · 3 refs
Solve Ax = b. This is HHL, and the asterisk matters: it returns a quantum state encoding the solution, not the answer vector.
Superpolynomial · 24 refs
Umbrella entry gathering the quantum techniques proposed for machine learning. Also the area where the most claims fell to dequantization — classical algorithms that later matched the supposed advantage.
Varies · 56 refs
Reduce certain optimisation problems to a decoding problem, and solve that instead.
Superpolynomial · 13 refs
Solve constraint satisfaction problems (SAT and family) with a polynomial improvement over the best classical backtracking.
Polynomial · 8 refs
Search for good approximate solutions to combinatorial problems with a short parameterised circuit. This is QAOA, and it is the family carrying almost the entire commercial promise of quantum optimisation.
Superpolynomial · 12 refs
Solve path-in-the-hypercube problems by dynamic programming, a family that includes the travelling salesman.
Polynomial · 1 refs
Optimise a linear objective over positive semidefinite matrices under linear constraints. The workhorse of convex relaxation.
Polynomial (with some exceptions) · 6 refs
Solve systems of linear differential equations.
Superpolynomial · 19 refs
Solve nonlinear differential equations, under strong assumptions about how nonlinear they may be.
Superpolynomial · 13 refs
Recover a signal hidden inside a high-dimensional tensor of Gaussian noise.
Polynomial (quartic) · 1 refs
Algebraic and Number Theoretic Algorithms · 14
Compute the class group of a number field, a central invariant of algebraic number theory.
Superpolynomial · 2 refs
Decode a linear error-correcting code, the hard problem that code-based cryptography rests on.
Varies · 2 refs
Given b = a^s mod N, find s. Underpins DSA, ECDSA and Diffie-Hellman key exchange.
Superpolynomial · 7 refs
Break an n-bit integer into its prime factors. This is what RSA rests on.
Superpolynomial · 13 refs
Estimate Gauss sums over finite fields, a basic object of number theory.
Superpolynomial · 2 refs
Estimate matrix elements and multiplicity coefficients of group representations, including Clebsch-Gordan coefficients.
Superpolynomial · 6 refs
Solve Pell's equation x^2 - d*y^2 = 1 over the integers. Breaking it breaks the Buchmann-Williams cryptosystem.
Superpolynomial · 1 refs
Decide whether an ideal of a number field is principal and, if so, find its generator. At least as hard as factoring.
Superpolynomial · 3 refs
Attack specific cryptographic primitives with quantum resources, beyond Shor and Grover.
Various · 23 refs
Solve congruences whose unknowns sit in the exponent.
Polynomial · 1 refs
Check whether the product of two matrices equals a third, faster than multiplying them.
Polynomial · 3 refs
Approximation and Simulation Algorithms · 11
Approximate the Jones polynomial and other knot invariants, a BQP-hard problem.
Superpolynomial · 10 refs
Estimate entries of high powers of a matrix without computing the full matrix.
Superpolynomial · 1 refs
Estimate the partition function of a classical system, from which essentially every thermodynamic quantity follows.
Superpolynomial · 10 refs
Prepare the ground state or a thermal state of a Hamiltonian, the starting point of almost all materials and chemistry simulation.
Superpolynomial · 31 refs
Sample from distributions a classical computer cannot sample efficiently.
Superpolynomial · 3 refs
Speed up simulated annealing: reach the equilibrium of a Markov chain in fewer steps.
Polynomial · 5 refs
Simulate how a quantum system evolves in time given its Hamiltonian. Feynman's original application and the strongest candidate for real utility.
Superpolynomial · 61 refs
Approximate topological invariants of three-dimensional manifolds.
Superpolynomial · 3 refs
Compute weight enumerators of codes, which describe the distance distribution of an error-correcting code.
Superpolynomial · 4 refs
Compute zeta functions of curves over finite fields, with direct use in elliptic-curve cryptography.
Superpolynomial · 2 refs
Snapshot 2026-09-09 · sha256 dee7e76b… · /v1/algorithms