Every quantum algorithm worth knowing about, written down the same way: what it takes, what it returns, what it costs, and who proved it.
The Map draws our corpus as one connected structure: Open the Map
Every source behind both surfaces: See the papers
A speedup class on a record is quoted: See whose claim it is
Every record is classified by how it was verified. The badge shows the strongest tier of evidence; the chips list each method that applies.
The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
The design was verified by construction plus measured evidence: statistical re-execution, small-instance analytic agreement, sub-block, echo, or invariant checks. Scale-specific bugs can still survive.
The record rests on external authority: peer-reviewed papers, standard textbooks, expert review, or evidence carried over from related verified entries. Nothing here was re-executed by this catalog.
Only automated (LLM-assisted) review or an unreviewed community submission backs this record so far. Treat it as a starting point, not evidence.
15 public entries
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Sample from the final limiting distribution πₙ of a slowly varying sequence of Markov chains, where πₙ is chosen to concentrate on good solutions of a combinatorial optimization problem.
Given oracle access to the m × n payoff matrix of a zero-sum game with bounded entries, compute a classical representation of an ε-approximate Nash equilibrium of that game.
Given a set of constraints over a finite field, such as a max-XORSAT instance or the task of finding a degree-n polynomial over 𝔽ₚ that approximates a given data set as well as possible, produce an assignment that satisfies as many constraints as possible.
Given a hard combinatorial problem, rewrite it as an Ising spin model whose lowest-energy spin configurations are exactly that problem's solutions, so that a machine which minimizes energy can be pointed at the problem at all.
Given a network's vulnerabilities and how their connectivity creates kill-chains — paths to security compromise — decide which vulnerabilities to prioritize for patching, so that those paths are removed.
Schedule a workflow of tasks — an instance of the workflow scheduling problem, a known NP-hard class of scheduling problems — for an industrial use case, in a way that can be represented and solved by quantum, classical, and hybrid quantum-classical algorithms.
Given a list of m + 1 Hermitian n × n matrices C, A_1, A_2, …, A_m and m numbers b_1, …, b_m, find the positive semidefinite n × n matrix X that maximizes tr(CX) subject to the constraints tr(A_j X) ≤ b_j for j = 1, 2, …, m, approximately, to within ± ε of the optimum. The Zoo states that semidefinite programming has many applications in operations research, combinatorial optimization, and quantum information, and that it includes linear programming as a special case. All three papers reduce that optimization to a feasibility question by binary search on a guess for the optimal value, but not to the same feasibility question, and the difference carries a parameter that the runtimes below then depend on. Brandão and Svore add the constraint tr(X) ≤ R, with R a measure of the size of the optimal solution, and test the dual: they sample from the distribution y divided by the 1-norm of y for a dual feasible vector y. Van Apeldoorn, Gilyén, Gribling and de Wolf likewise test membership in a dual polytope induced by the current primal candidate, with R bounding the trace of an optimal primal X. Brandão, Kalev, Li, Lin, Svore and Wu instead normalise the primal to tr(X) = 1 and test it directly, deciding whether the constraints tr(A_i X) ≤ a_i + ε admit a positive semidefinite X of unit trace; Chia, Gilyén, Li, Lin, Tang and Wang adopt that same trace-one form for the dequantized version.
An optimization pattern that slowly deforms an easy ground state into the ground state of a problem Hamiltonian.
Given a target position for a robot manipulator's end effector, find joint angles that reach it — the inverse kinematics problem, which has no analytical solution for a general 6-degree-of-freedom arm and admits many joint configurations at once for a redundant one.
Find a better parameterized ansatz for the quantum approximate optimization algorithm (QAOA) applied to combinatorial optimization problems such as Max-Cut, where the standard, fixed-form QAOA ansatz is not known to be optimal and no systematic method exists for improving on it.
Evaluate candidate designs for a simplified cooling system within an engineering design process that normally requires numerous computationally intensive numerical simulations, in a way that avoids the data input/output overhead that otherwise erodes any quantum speedup on such simulation tasks.
Given the low autocorrelation binary sequences (LABS) problem, an optimization problem that is classically intractable even for moderately sized instances, determine whether QAOA can act as an algorithmic component that provides an advantage over the best classical exact solvers.
A quantum algorithm that produces approximate solutions for combinatorial optimization problems, tunable by a positive integer p.
Solve large-scale Maximum Cut (MaxCut) problems on near-term quantum hardware by decomposing the graph into many subgraph problems that can be solved in parallel, and determine how such a decomposition compares to a purely classical alternative for the same task.
A p=1 QAOA circuit with a classical MaxCut comparison and reproducible simulation evidence.