Qubit ZooCurated map of Zoo entries in the Majorana / Topological family.
Entries
| Entry | Type | Status |
|---|---|---|
| majorana-topological-qubit | qubit | proposed |
| planar-josephson-junction-qubit | qubit | proposed |
| tetron-qubit | qubit | proposed |
| topological-qubit | qubit | demonstrated |
Composition
- qubit: 4
Four-note map
- topological-qubit is the anyon-algebra umbrella and the processor-demonstration branch: fusion spaces, braid representations, and digitally synthesized non-Abelian order. These experiments validate computational primitives without showing that the processor’s physical gates are intrinsically protected.
- majorana-topological-qubit is the materials-physics note: nonlocal fermion-parity encoding, Majorana zero modes, and the requirement that splitting fall exponentially with separation.
- planar-josephson-junction-qubit is the fabrication-layer route: a lithographically defined InAs/Al-style junction where spin-orbit-coupling-for-qubit-control and phase bias near create a tunable topological channel.
- tetron-qubit is the architecture-layer proposal: four Majorana modes arranged for parity measurement and measurement-only braiding, with the long-term promise judged against threshold-theorem rather than spectroscopy alone.
What unifies this family
Topological notes in the Zoo form two evidence branches, not one uniform device stack. The digital-anyon branch in topological-qubit asks whether fusion and braid algebra can be prepared, manipulated, and read on programmable hardware. The materials-native Majorana branch climbs from majorana-topological-qubit through planar-josephson-junction-qubit to tetron-qubit, asking whether a nonlocal parity degree of freedom can become a protected computational architecture.
The branches share fusion-space language, but protection claims do not transfer automatically between them. A circuit-compiled braid can demonstrate the target logical algebra while inheriting ordinary physical-gate errors; a materials platform can show increasingly persuasive topological-channel evidence without demonstrating a controlled logical braid. Both ultimately face the divincenzo-criteria scorecard: prepare a protected state, read its logical information reliably, and execute useful operations without erasing the advantage.
Digital anyons versus materials-native protection
| Evidence branch | Primary notes | What would count as progress | Category error to avoid |
|---|---|---|---|
| Digital anyon / code-space realization | topological-qubit | Higher-fidelity state preparation, fusion/charge measurement, and braid-generated logical operations in a synthesized non-Abelian code space | Treating successful compiled braids as evidence that the underlying processor gates gained passive topological protection |
| Materials-native Majorana route | majorana-topological-qubit, planar-josephson-junction-qubit, tetron-qubit | Nonlocal parity control, poisoning-lifetime and splitting measurements, four-mode encoding, then operations whose errors improve with a protection knob | Treating spectroscopy or gap reopening alone as an operational qubit, much less a fault-tolerance advantage |
Use topological-qubit when the object being manipulated is an emergent anyon in a digitally prepared many-body state. Enter the Majorana stack when the claim depends on a native topological superconducting medium and nonlocal fermion parity. Compare either branch with threshold-theorem only after its physical error model and logical protection mechanism have been stated explicitly.
Protection-claim ladder
The easiest way to misread this family is to collapse three different claim levels into one bucket called “topological qubit.”
- majorana-topological-qubit is the protection primitive: the important content is nonlocal fermion parity, end-mode splitting, and the evidence ladder from spectroscopy to controllable parity.
- planar-josephson-junction-qubit is the materials-platform route: it asks whether a lithographic Josephson geometry can reliably enter the topological regime at all.
- tetron-qubit is the computing architecture claim: four Majorana modes in a fixed-parity layout, repeated parity measurements, and the possibility of turning protection into an actual logical resource.
A useful guardrail is that a two-end-mode device can demonstrate the ingredients of topological protection without yet constituting a full logical qubit. In this family, the graph should climb from topological-channel evidence, to parity control, to fixed-parity four-mode encoding, and only then to protected computational primitives judged against divincenzo-criteria and threshold-theorem.
Experimental-evidence ladder
Track two claims separately: evidence for a topological phase and evidence for a useful qubit. Progress on the first ledger does not automatically advance the second.
| Rung | What would advance the claim | Best entry to inspect | What it still would not establish |
|---|---|---|---|
| Candidate topological channel | A hard induced gap plus phase-, field-, and gate-dependent closing/reopening, with trivial Andreev and disorder explanations actively excluded | planar-josephson-junction-qubit for the phase-biased 2DEG route; majorana-topological-qubit for the nanowire route | Non-Abelian statistics, a protected state space, or any qubit fidelity |
| Nonlocal parity degree of freedom | Separation-dependent suppression of mode overlap together with repeatable parity-sensitive readout and a measured poisoning lifetime | majorana-topological-qubit for the protection primitive | A fixed-total-parity four-mode encoding or a controllable logical basis |
| Operational encoded qubit | Four-mode initialization, repeated parity measurement, and calibrated single- and joint-qubit operations within the encoded subspace | tetron-qubit | That the operations inherit an error advantage from topology rather than merely using Majorana-compatible hardware |
| Hardware-level protection | Error rates that improve with separation or another protection knob under the full preparation/control/readout stack, compared with an unprotected baseline | Read all three notes as a materials-to-architecture chain | Below-threshold logical suppression or a reduced fault-tolerance overhead |
| Fault-tolerance advantage | Logical error suppression with scale and an overhead comparison under a stated decoder and noise model | threshold-theorem and the appropriate code entry | Nothing less should be treated as experimental confirmation of a system-level overhead claim |
This ladder prevents a common category error: a cleaner zero-bias or gap-reopening signature can strengthen the materials case while leaving the computing case unchanged. Conversely, parity readout becomes architecture evidence only when its fidelity, lifetime, repeatability, and role in encoded operations are measured together.
Boundary-case routing table
| Entry | Why it stays in topological-moc | What nearby family it can be confused with |
|---|---|---|
| topological-qubit | the central object is a non-Abelian fusion space and its braid/fusion operations, even when that space is digitally synthesized rather than materials-native | codes-moc because present demonstrations use active programmable processors; the routing hinge is whether the note is about the anyon model itself or the underlying error-correcting architecture |
| majorana-topological-qubit | the core claim is nonlocal fermion-parity encoding with exponentially suppressed mode overlap, even before a full four-mode computational encoding is assembled | super-semi-moc shares the same InAs/Al language, but not the topological-protection claim |
| planar-josephson-junction-qubit | phase-biased Josephson geometry is being used to open a topological channel, not just to tune a qubit frequency | super-semi-moc if the junction is being discussed as an electrostatically tunable weak link rather than a topological medium |
| tetron-qubit | the device is an architecture for repeated parity measurements and measurement-only braiding built on Majorana ingredients | cross-platform-moc at the systems level, because its real payoff is lower logical overhead if the physical protection holds |
Boundary with the super-semi family
The materials overlap with super-semi-moc on purpose, especially around InAs/Al weak links and Josephson geometries, but the classification hinge is different. A note belongs in this Majorana / Topological branch when the qubit claim depends on entering a topological superconducting regime and protecting information in nonlocal fermion parity. If the same hybrid hardware is being used mainly for gate-tunable Josephson physics, Andreev control, or protected-circuit engineering without a topological phase claim, it belongs in super-semi-moc instead.
A useful mental check is: if removing the words “topological phase” or “nonlocal parity” would leave the note conceptually intact, it probably is not a topological-family note.
Reading order
Choose the path that matches the claim:
- Anyon algebra and processor demonstrations: start with topological-qubit, then compare its digitally compiled operations with threshold-theorem to keep demonstration fidelity separate from passive protection.
- Materials-native protection: start with majorana-topological-qubit for the protection mechanism, continue to planar-josephson-junction-qubit for the scalable materials platform, and finish with tetron-qubit for the control architecture that tries to turn those ingredients into a computable qubit.