Explore quantum algorithms and circuits, with resource estimates, verification evidence, and sources.
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.
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 minimal-basis (STO-3G) H₂ electronic Hamiltonian after Jordan-Wigner/parity mapping and two-qubit tapering: the canonical small-molecule target for variational quantum eigensolver (VQE) demonstrations.
The Jordan-Wigner-encoded fermionic number operator n = c†c = (I-Z)/2, whose eigenvalues count mode occupation exactly.
Removes a fermion from spin orbital p. Representative form: aₚ.
Adds a fermion in spin orbital p subject to antisymmetry. Representative form: a†ₚ.
Kinetic, external-potential, or orbital-rotation term. Representative form: O₁ = Σ hₚq a†ₚa_q.
Electron-electron interaction term. Representative form: O₂ = 1/2 Σ hₚqrs a†ₚa†_q a_r a_s.
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.
Generalized singles and doubles relax occupied-to-virtual restrictions to enlarge the variational manifold.
Repeated paired generalized doubles with generalized singles trade expressivity against shallower chemistry circuits.
A chemistry-inspired unitary coupled-cluster ansatz truncated to single and double excitations.
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