Fredkin gate¶
A reversible three-bit controlled-swap gate that preserves the control bit and swaps the other two bits exactly when the control is active.
Core Idea¶
The Fredkin gate maps (c,a,b) to (c,a,b) when c=0 and to (c,b,a) when c=1, is its own inverse, conserves Hamming weight, and is universal for conservative reversible logic with suitable resources. Control condition selects identity or transposition; the bijective mapping retains every input bit in recoverable output structure and enables circuits without logical information erasure. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Fredkin gate belongs to reversible computing and is useful where the analyst can specify the typed reversible computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate bit order, control polarity, truth table, classical or quantum realization, reversibility, conservative property, ancilla assumptions, and universality claim are explicit. The scope is broad within that domain but bounded by the need for bit order, control polarity, truth table, classical or quantum realization, reversibility, conservative property, ancilla assumptions, and universality claim are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making bit order, control polarity, truth table, classical or quantum realization, reversibility, conservative property, ancilla assumptions, and universality claim are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Fredkin gate can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Fredkin gate. Fredkin gate compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed reversible computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express bit order, control polarity, truth table, classical or quantum realization, reversibility, conservative property, ancilla assumptions, and universality claim are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of reversible computing because they reuse the typed reversible computing carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Control condition selects identity or transposition; the bijective mapping retains every input bit in recoverable output structure and enables circuits without logical information erasure., and type the carrier, state every parameter and convention in the definition, test that bit order, control polarity, truth table, classical or quantum realization, reversibility, conservative property, ancilla assumptions, and universality claim are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Fredkin gate Domain-specific
Parents (1) — more general patterns this builds on
-
Fredkin gate is a kind of Bijectivity Prime
The proposed strict upward parent is
prime:bijectivity.
Hierarchy paths (3) — routes to 1 parentless root
- Fredkin gate → Bijectivity → Function (Mapping)
- Fredkin gate → Bijectivity → Injectivity → Function (Mapping)
- Fredkin gate → Bijectivity → Surjectivity → Function (Mapping)
Neighborhood in Abstraction Space¶
Fredkin gate sits in a moderately populated region (52nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Digital Logic & Boolean Networks (9 abstractions)
Nearest neighbors
- Counterfactual quantum computation — 0.89
- Quantum circuit — 0.89
- Nondeterministic Turing machine — 0.88
- Entscheidungsproblem — 0.88
- And-inverter graph — 0.88
Computed from structural-signature embeddings · 2026-09-08