The Quantum Atlas

Explore quantum algorithms and circuits, with resource estimates, verification evidence, and sources.

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.

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Toffoli (CCX) gate

Exact & formal

Multi-controlled gate

The three-qubit doubly-controlled NOT gate that implements reversible classical AND/NAND logic and is universal for classical reversible computation.

q[0]

CCX

q[1]

CCX

q[2]

CCX

Basic gate

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The Quantum Atlas

Explore quantum algorithms and circuits, with resource estimates, verification evidence, and sources.

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

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.

Search the Atlas

Toffoli (CCX) gate

Exact & formal

Multi-controlled gate

The three-qubit doubly-controlled NOT gate that implements reversible classical AND/NAND logic and is universal for classical reversible computation.

q[0]

CCX

q[1]

CCX

q[2]

CCX

Basic gate

View ↗

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

The Quantum Atlas

What it is

Technique

Problem domain75 of 285 entries

In a pipeline72 of 285 declare ports · 58 meet another entry

Not a pipeline stage

Order by

Toffoli (CCX) gate

The Quantum Atlas

What it is

Technique

Problem domain75 of 285 entries

In a pipeline72 of 285 declare ports · 58 meet another entry

Not a pipeline stage

Order by

Toffoli (CCX) gate