Measurement-based Majorana gate g_mbq

Braiding is replaced by a schedule of projective joint fermion-parity measurements. Bonderson, Freedman and Nayak showed in 2008 that an anyonic teleportation identity lets topological-charge measurements produce the braiding transformations S[475]; Karzig et al. made it hardware in 2017 — Cliffords read as differential-capacitance shifts of dots tunnel-coupled to Majorana zero modes (MZMs) S[421]. Every published measurement here is single-wire (Z-type); the two-wire joint measurement that is the gate has never been reported D[21].
a fabricated (1.0) · b gate time unmeasured, deterministic by intent · c no readout of its own
d static · e low-frequency control at room temperature · f error structure unknown · g MBE wire stack

Fidelity is joint-measurement time over the lifetime of the basis projected, and that ratio is where the mechanism fails. The tetron's Z-loop parity lives 12.4 ms, the X loop, which a gate repeatedly projects, 14.5 µs, ~1000× shorter D[20], attributed to the larger quasiparticle-capture cross-section of the two-loop configuration: poisoning, not dephasing. At SNR 1 in 3.6 µs D[13] one X projection eats a fifth of that window, so a Clifford sequence has no margin. Operation is adaptive (next basis from last outcome), so feed-forward must close inside the same window; none has been published. Over trivial Andreev levels, meanwhile, a measurement sequence implements no braid at all D[23].

No row is a gate: the 2026 result measured one nanowire of a multi-tetron array: no braid, no joint parity, no two-qubit operation, no entanglement, no T1/T2 D[21].

The arXiv HTML of [20] also gives an X loop of ~4 µs and a Z loop of ~9.3 ms for other tunings; the ~1000× ratio holds for both readings, the 14.5 µs / 12.4 ms point values do not. Not published: a dollar figure for DARPA's US2QC award to Microsoft, and any feed-forward latency, dot–wire coupling switching time or projected gate time for this mechanism.

Nothing is fabricated for this mechanism alone: it consumes the InAs–Pb stack and the readout below it. The unbuilt part is control: per-tetron tunable dot–wire couplings, an rf loop per measurable parity, and a demodulator-to-bias path that must resolve inside the X window. At 10³ tetrons the line budget resembles transmon readout; the wall is latency, unquantified because no adaptive sequence has been attempted.

Requires the Majorana-parity carrier (two wires per tetron) and quantum-capacitance readout; it would supply the topological architecture's entire Clifford layer. The only substitute is braiding in T-junction networks, geometry nobody is building. No derived clock: with no gate operated and no code on the architecture, sum of the syndrome round: gate layers + transport + readout + reset reduces to its readout term, ~3.6 µs D[13], reset unpublished. Verification is telegraph statistics, not benchmarks: no randomised benchmarking, tomography or Bell test exists. QuTech's independent single-shot parity readout (Nature 650, 2026-02-11) replicates the method on InSb dot chains, limited protection stated D[216]; Legg's Matters Arising (2026-06-24) argues the readout regions are disordered and gapless, so the signals may be trivial, and Microsoft's same-day reply concedes nothing D[23].

Who.
| Organisation | Role | Country | What they do | Evidence |
|---|---|---|---|---|
| Microsoft Quantum | developer | US | Sole builder; tetrons, no gate | D[21] |
| DARPA | investor | US | US2QC final Validation & Co-Design stage since 2025-02-06, AFRL and Johns Hopkins APL evaluating; not a QBI Stage B performer | fact |
| QuTech | research | NL | Independent parity readout, not this gate | D[216] |

Money. 2025-02-06 · Microsoft · US2QC advances to its final Validation & Co-Design stage · undisclosed · DARPA · announced fact. 2026-01-23 · Microsoft · Quantum Pioneers Program · ≤ USD 200,000 per academic proposal for measurement-based topological computing · announced Pfact.

Market & supply chain. No market and no unit economics; only G3/G4 fault tolerance would pay, and only after a two-qubit result. Supply is internal to one company: concentration risk is total.

IP & standards. Microsoft's own published lineage S[421]; no dated patent count specific to this gate found as of 4 Sep 2026.

Roadmaps & track record. ("years not decades", promised 2025-02, for fault tolerance → restated as 2029 in 2026-06; status 4 Sep 2026: no joint measurement, no gate) C[215]; DARPA's utility-scale horizon is 2033 fact. Every annual Microsoft result has been readout; 2029 carries no X-measurement milestone.

Strategic reading. If measurement-only Cliffords work, Microsoft skips T-junction fabrication and owns the architecture; if not, the encoding, readout and epitaxy nodes below lose their only consumer.

Falsifiable in 12–24 months: a first joint (X-basis) parity measurement with a stated assignment error; any operation or entanglement between two tetrons; a published X/Z ratio below 100×. Confirm on the first two; demote to theory if none lands by end-2027. Best case 2029, measurement-only Cliffords on a small array; worst case, X-basis poisoning is intrinsic to the two-loop geometry and the line closes. Open: is the asymmetry geometric or material; does anyone outside Microsoft attempt a joint measurement.