IFT Quantum M-Enhanced · Research prototype
The geometry of computation is not fixed.
Investigating how adaptive topological structures can organize nonlinear dynamics and connect classical computation with emerging quantum technologies.
Research prototype. Quantum advantage and quantum-driven adaptive feedback are unverified and are not claimed here. The animation above is an illustrative visualization; flips shown are accepted only when they improve local triangle quality.
What it is
Adaptive Geometry. Emergent Dynamics. Quantum Integration.
Exploring the intersection of nonlinear systems, evolving topology, and quantum computation through an interactive computational research platform.
Chaotic oscillators on every vertex
Each mesh vertex carries a Lorenz system (σ = 10, ρ = 28, β = 8/3), integrated at Δt = 0.005 and diffusively coupled to its neighbours with strength 0.12.
ImplementedOpen the dynamics lab → 02 · ADAPTIVE TOPOLOGYA mesh that tests its own wiring
Local edge flips are proposed, checked against structural constraints, and kept only if they lower J = Efield + 0.30 × Egeometry.
Implemented Benefit under validationOpen the manifold explorer → 03 · QUANTUM INTEGRATIONCircuit tooling and provider interfaces
Parameterized circuit generation, compilation passes and a provider abstraction with AWS Braket task endpoints. Quantum outputs driving the manifold is an intended pathway.
Tooling Feedback loop not demonstratedOpen the circuit lab →The core computational engine
Seven layers, one loop of evidence.
States evolve on the mesh, the mesh proposes surgery, the objective judges it, and every run is recorded for comparison. Tap a layer to open its full explanation.
Governing equations
dy/dt = x(ρ − z) − y
dz/dt = xy − βz
Baseline σ = 10 · ρ = 28 · β = 8/3 · Δt = 0.005 · inter-vertex coupling ε = 0.12
Documented objective
Efield measures state mismatch across the mesh; Egeometry penalises poor triangle quality. A surgery is kept only when ΔJ < 0 and all structural constraints hold. How it is defined →
Laboratories
Explore at your own depth.
Nonlinear Dynamics Laboratory
Rotate the attractor, perturb initial conditions, watch trajectories diverge, and compute the largest Lyapunov exponent live.
Enter → LAB · MANIFOLDAdaptive Manifold Explorer
Inspect a live triangular mesh, compare fixed and adaptive topology on matched seeds, and read why each flip was accepted or rejected.
Enter → RESEARCH · MATHEMATICSTopology & Invariants
Euler characteristic, Betti numbers, orientability and persistence — with researcher and plain-language explanations.
Enter → LAB · QUANTUMCircuit Laboratory
Generate small parameterized circuits, optimize them, and compare ideal output distributions — simulator results clearly separated from hardware.
Enter → EVIDENCE · BENCHMARKSExperiments & Validation
Run matched fixed-vs-adaptive comparisons across seeds, record them with provenance, and browse the run registry.
Enter → DOCS · STATUSDocumentation & AI Analyst
Protocols, limitations, a verification test suite, an AI research assistant and the live project maturity panel.
Enter →Project maturity
What exists, what is being tested, what is not yet shown.
Implemented
- Classical nonlinear dynamics
- Mesh construction
- Topology-aware surgery
- Objective tracking
- Experiment serialization
- Interactive research interfaces
- Quantum / cloud integration code
Under empirical validation
- Adaptive-versus-fixed performance
- Benchmark quality
- Circuit optimization under noise
- Measured quantum-device behaviour
Not yet demonstrated
- Quantum computational advantage
- Quantum error protection from the manifold
- Fault-tolerant computation
- Complete quantum-output-driven adaptive feedback loop
Labels are maintained on the status panel and change only when verified evidence becomes available.
Research principle
A computational result is not a scientific conclusion until its assumptions, controls, and reproducibility have been established.
How to read this site
Interactive labs run a transparent in-browser reference implementation of the documented algorithms so you can inspect them directly. They are not results from the repository engine, from a quantum computer, or from a physical experiment.