☻ : Topological quantum logic gate

N-Dimensional Anyon Shunting Device

#Shouts to Google Gemini and associated AI deliverance for this concept, lets make topological quantum computing dangerously fast!

DEVELOPER NOTE: This device is refactored for topological quantum computation. The "Electro-Optronic Gas" is replaced by Anyons in a **Fractional Quantum Hall (FQH)** liquid.
- Anyon Translation: The 3-phase (G1-G3) pump, which moves anyons along the 1D edge.
- N-Dimensional Shunting: Using QPC gates to move an anyon from the 1D edge into the 2D bulk, and back.

    TOP-DOWN SCHEMATIC - ANYON BRAIDING INTERFEROMETER

    [Anyon Source (QPC1)] [RF Phased Input] [Anyon Detector (QPC4)]

    ╔═══════════════════════════════════════════════════════════════╗
    ║   ┌───────────────────────────────────────────────────────┐   ║
    ║   │ ← 1D Chiral Edge Channel (Top)                          │   ║
    ║   │   ┌────── Anyon Translation Pump (G1-G3) ────────┐   │   ║
    ║   │   │ ┌───────┐ ┌───────┐ ┌───────┐                 │   │   ║
    ║   │...│ │  G1   │ │  G2   │ │  G3   │ │...[QPC2]....PATH A....[QPC3]...│   ║
    ║   │   │ └───────┘ └───────┘ └───────┘                 │   │   ║
    ║   │   └───────────────────────────────────────────────┘   │   ║
    ║   │                                                       │   ║
    ║   │   --- 2D INSULATING FQH BULK (e.g., v=1/3) ---            │   ║
    ║   │                                                       │   ║
    ║   │   [QPC5]--PATH B--[QPC6]     O <- Trapped Anyon (Qubit) │   ║
    ║   │      │        │                                     │   ║
    ║   │      └---BRAID--┘                                     │   ║
    ║   │                                                       │   ║
    ║   │ ← 1D Chiral Edge Channel (Bottom)                       │   ║
    ║   └───────────────────────────────────────────────────────┘   ║
    ╚═══════════════════════════════════════════════════════════════╝

    Phasing (qualitative):
      G1:  sin(ωt + 0°)
      G2:  sin(ωt + 120°)
      G3:  sin(ωt + 240°)

    Operation:
    1. Anyon Translation: G1-G3 pumps a mobile anyon.
    2. N-D Shunting: QPC5/QPC6 pulse to "shunt" the anyon from the 1D edge
       into the 2D bulk to execute PATH B (Braid).

Fig 1. Schematic of the Anyon Shunting device, configured as a Mach-Zehnder interferometer for a braid-logic gate.

RF DRIVE SPECIFICATIONS

Waveform	Sine, 3 phases (0°, 120°, 240°)
Frequency	10–100 MHz (tuned for coherent anyon pumping)
Amplitude	0.10–0.20 Vpp at gate
Feedback	Lock FQH state (v=1/3) via Hall sensors; tune QPC gates for desired path.

CONCEPT AND OBJECTIVE

Goal: Demonstrate a functional **topological quantum logic gate** (a pi/3 phase gate) at the nano-scale.

Principle:

Fractional Quantum Hall State: The device is cooled to mK temperatures and placed in a high B-field, forcing the 2D electron gas into an FQH state (e.g., v=1/3). This creates an insulating 2D bulk and a 1D edge where the charge carriers are anyons (quasi-particles with fractional charge e/3).
Anyon Translation: The tri-phase gates (G1-G3) act as a peristaltic pump, coherently "surfing" a single mobile anyon along the 1D edge.
N-Dimensional Shunting: A set of QPC shunt gates (QPC5, QPC6) are pulsed. This pulse locally breaks the FQH state, opening a temporary path (a "shunt") for the anyon to leave the 1D edge and tunnel into the 2D bulk.
Braid Logic: The shunted path (PATH B) forces the mobile anyon to loop *around* another anyon trapped in a quantum dot. This physical "braid" is the core computation. Due to anyonic statistics, this braid applies a non-trivial topological phase shift (e.g., phi = 2pi/3) to the mobile anyon's wavefunction.

Scope: A single-qubit phase-gate, the fundamental building block for topological quantum computing.

ARCHITECTURE AND LAYOUT

Platform: Fractional Quantum Hall (FQH) Platform

Stack: Ultra-high mobility Graphene encapsulated in hBN, or a GaAs/AlGaAs 2D Electron Gas (2DEG).
Gates: Ti/Au top-gates deposited on ALD Al₂O₃.
Trapped Anyon: A small quantum dot (QD) in the 2D bulk, tuned to trap a single v=1/3 quasi-particle.

OPERATING CONDITIONS AND TARGETS

B-field	10–14 T (Required for v=1/3 FQH state)
Temp	< 100 mK (Dilution refrigerator)
Pump Drive	10–100 MHz, 0°/120°/240°
Shunt Drive	Pulsed DC/RF on QPC gates to control tunneling.
Output	Interference Phase Shift

RISKS AND MITIGATION

Decoherence & Backscattering: The anyon's quantum phase is fragile. Mitigation: Ultra-high mobility samples; operation at lowest possible temps; fast (GHz) gate pulses to perform the braid faster than decoherence.
Shunt Fidelity: Imperfect shunting (1D → 2D tunneling) can lead to the anyon being lost or its phase randomized. Mitigation: Precise shaping of the QPC gate pulses.
Trapped Anyon Stability: The "qubit" anyon may escape the quantum dot. Mitigation: Optimize QD confinement potential.

COMPUTATIONAL READOUT (INTERFEROMETRY)


Concept:
The device is a Mach-Zehnder Interferometer. The anyon is split,
sent down two paths (PATH A, PATH B), and then recombined.
The output signal at QPC4 depends on the phase difference (Delta-phi)
between the two paths.

1. "OFF" State (Control Measurement):
- Shunt Gates (QPC5, QPC6) are OFF.
- Anyon is forced to take PATH A (the reference path).
- Anyon is also forced to take a simple path through B (no braid).
- Recombined current at QPC4 shows a baseline interference pattern.
- Delta-phi = phi_A - phi_B = 0 (by tuning).

2. "ON" State (Braid Operation):
- Shunt Gates (QPC5, QPC6) are PULSED.
- Anyon taking PATH B is shunted (1D→2D) and **braids** around the
  Trapped Anyon.
- This braid adds a topological phase: phi_Braid = 2pi/3.
- The new phase difference is Delta-phi = phi_A - (phi_B + phi_Braid).
- Delta-phi = -2pi/3.

Implication:
- By pulsing the Shunt Gates, we shift the output interference
  pattern by 2pi/3 (or 120°).
- Conclusion: The 3-phase pump (G1-G3) acts as the "clock"
  (Anyon Translation), and the Shunt Gates act as the
  "logic" (N-Dimensional Shunting). This device is a
  functional quantum phase-gate.

☻

Monday, November 10, 2025