Interactive lab

Live simulations

Small, real-time versions of the physics behind my projects. Everything runs in your browser: change the parameters and watch the system respond.

Quantum computing · Gates

Qubit on the Bloch sphere

Apply quantum gates to a single qubit and watch its state rotate, then measure it.

Circuit: |0⟩

|ψ⟩ = (1.00+0.00i)|0⟩ + (0.00+0.00i)|1⟩

Bloch vector: (0.00, 0.00, 1.00)

P(0) 1.000P(1) 0.000

Try H then T then H: phase becomes amplitude. The same gate algebra, scaled up and routed onto IBM Heavy-Hex hardware, is what my quantum compilation work handles.

Gravity-Aided Navigation

Navigating without GPS

Inertial drift versus gravity-map-aided correction, the core idea behind the RelativisticQ-PNT demonstrator.

Inertial sensor bias = 0.60Gravity-fix gain = 0.08

INS-only error: 0.0 px
Gravity-aided error: 0.0 px

Faint = true path. White = unaided inertial dead reckoning, drifting as sensor bias accumulates. Gold = the same inertial solution corrected by matching against the gravity anomaly map (the shaded field). Set the gain to zero to see GPS-denied drift take over.

Symplectic Hamiltonian PINN

Energy that doesn't drift

A chaotic Duffing oscillator integrated two ways. Watch which one conserves energy.

Nonlinearity β = 1.00Time step Δt = 0.050

Explicit Euler |ΔH/H₀|: 0.00e+0
Symplectic leapfrog |ΔH/H₀|: 0.00e+0

t = 0.0

Faded = explicit Euler, which spirals outward as energy leaks in. Gold = symplectic leapfrog, which stays on its energy shell. This is the property my Hamiltonian PINN service preserves.