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.
4 public entries
Atlas stars stay in this public list. Saving an entry to your workspace starts an unstarred private copy.
The two-site Fermi-Hubbard dimer Hamiltonian, mapped to qubits via the Jordan-Wigner transformation: nearest-neighbor hopping competing with on-site Coulomb repulsion.
The anisotropic Heisenberg (XXZ) spin-chain Hamiltonian: exchange-coupled spins with tunable easy-axis/easy-plane anisotropy Δ, U(1)-symmetric under total-Sz rotation.
The classical (longitudinal-field) Ising Hamiltonian expressed as a diagonal SparsePauliOp: a foundational Z-only spin model with no quantum superposition dynamics of its own.
The transverse-field Ising model (TFIM): the standard minimal Hamiltonian exhibiting a quantum (zero-temperature) phase transition driven by competing Z-Z order and X-field disorder.