The Quantum Atlas

About the Atlas

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

Search the Atlas

Verification legend

Every record is classified by how it was verified. The badge shows the strongest tier of evidence; the chips list each method that applies.

Exact & formal

The defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.

Direct mathematics: An analytic identity or closed-form derivation proves the defining property (e.g. H² = I, Y = iXZ).
Unitary / matrix equivalence: The circuit's unitary was computed and compared against the reference matrix.
Exact statevector simulation: A full statevector simulation reproduced the exact expected state or distribution.
Stabilizer simulation: Clifford structure allowed exact verification with stabilizer methods beyond statevector limits.
Basis-state truth table: Reversible classical logic was checked exhaustively (or at edge cases) on computational-basis inputs.

Strong empirical

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.

Statistical re-execution: Measured counts from independent executions agreed within statistical tolerance (e.g. TVD bounds).
Small-instance agreement: The same generator matched analytic results at tractable sizes; large instances are inferred.
Sub-block verification: Reusable modules (oracle, QFT block, Trotter step, adder…) were verified independently.
Echo / inverse test: U followed by U† returned the input exactly, catching wiring, phase, and ancilla bugs.
Invariant & structural checks: Scale-independent invariants held: qubit counts, unitarity, symmetry, conservation laws, ancilla cleanup.
Verified by construction: The circuit follows a specification whose correctness argument is standard; the construction was audited against it.

Attested & literature

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.

Peer-reviewed paper: The record's claims trace to one or more peer-reviewed publications cited on the entry.
Textbook / standard citation: The behavior is standard material (e.g. Nielsen & Chuang, OpenQASM spec) and is cross-referenced, not re-derived.
Expert review: A named human reviewer with domain expertise checked the record.
Tangential evidence: Correctness is supported indirectly through related verified entries (e.g. a gate verified inside a verified algorithm).

Automated & unreviewed

Only automated (LLM-assisted) review or an unreviewed community submission backs this record so far. Treat it as a starting point, not evidence.

LLM-assisted review: An LLM checked the record for internal consistency. Useful screening, not evidence of correctness.
Community submission: Submitted by the community and not yet through the review pipeline.

6 public entries

Atlas stars stay in this public list. Saving an entry to your workspace starts an unstarred private copy.

Attested & literatureAlgorithmsAlgorithmHamiltonian simulation · model systems2026-08-12

Quantum algorithms to simulate many-body physics of correlated fermions

Simulate strongly correlated fermionic systems — notoriously hard for classical computers — on a quantum computer with 2D or linear (1D) nearest-neighbor qubit-qubit couplings, of the kind typical of superconducting transmon qubit arrays, including preparing the relevant quantum states and evolving the system in time, with the Fermi-Hubbard model as a worked example.

correlated fermionsfermionic gaussian statefermionic fourier transform

View ↗

Strong empiricalAlgorithmsAlgorithmHamiltonian simulation · product formula2 shown · chain generalizes to n q2026-07-16

Transverse-field Ising simulation

A compact Hamiltonian-simulation pattern for spin chains: alternate local field rotations with entangling ZZ evolution.

hamiltonian simulationising modeltrotter

View ↗

Attested & literatureAlgorithmsAlgorithmOptimization · Ising encoding2026-08-12

Ising formulations of NP-complete and NP-hard problems

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.

ising modelnp-completecombinatorial optimization

View ↗

Attested & literatureAlgorithmsAlgorithmTopological invariants2026-08-12

Additive approximation of the Jones polynomial at a primitive root of unity

Given a braid on n strands with m crossings and an integer k, compute a certain additive approximation to the Jones polynomial of the link obtained by closing the braid, evaluated at the primitive root of unity e^(2πi/k).

jones polynomialknot invariantsbraid

View ↗

Attested & literatureAlgorithmsAlgorithmHamiltonian simulation · model systems2026-08-12

Quantum simulation of the kicked rotator model

Simulate the quantum kicked rotator model — used to study quantum chaos, localization and the Anderson transition — with a quantum algorithm that scales better than classical simulation of the same model.

quantum chaoskicked rotatorlocalization

View ↗

Attested & literatureAlgorithmsAlgorithmTopological invariants2026-08-12

Additive approximation of Turaev-Viro 3-manifold invariants

Given a compact, orientable three-manifold presented by a Heegaard splitting, compute a certain additive approximation to its Turaev-Viro invariant, the scalar topological invariant that takes the same value on homeomorphic manifolds.

turaev-viro3-manifoldtopological invariants

View ↗

The Quantum Atlas

What it is

Technique

Problem domain75 of 284 entries

In a pipeline71 of 284 declare ports · 57 meet another entry

Not a pipeline stage

Order by

Quantum algorithms to simulate many-body physics of correlated fermions

Transverse-field Ising simulation

Ising formulations of NP-complete and NP-hard problems

Additive approximation of the Jones polynomial at a primitive root of unity

Quantum simulation of the kicked rotator model

Additive approximation of Turaev-Viro 3-manifold invariants