Control the dynamics
Select a system, adjust its available Hamiltonian parameters and choose the time interval.
MIXFUNN · QUANTUM DYNAMICS
Explore quantum dynamics
with MixFunn.
Follow the evolution of one or two qubits, change Hamiltonian parameters and compare neural predictions with exact solutions.
Physics informed neural networks (PINNs) commonly use multilayer perceptrons with fixed activation functions. MixFunn learns mixtures of elementary functions; its second order formulation also includes interactions between inputs. These components expand the flexibility of the neural representation [1]. The Schrödinger equation guides training, while a temporal FNO extends selected trajectories [2].
Three experiments. Adjustable parameters. Downloadable results.
A FIRST LOOK
InteractiveOne qubit in motion
h = (0.10, 0.08, 0.20)
Exact evolutionMixFunn
02
Probability of |0⟩—
State fidelity—
Move the time slider or choose a field. The sphere represents the qubit state; the curves compare its predicted and exact evolution.
Loading the MixFunn preview…
Open the full one qubit experimentCompare the predictions
Inspect probabilities, spin observables and fidelity against the exact quantum evolution.
Take the results further
Customize the curves and download figures and numerical data for your own analysis.
THE EXPERIMENTS
From a single qubit to interacting qubits
Explore three complementary tests of neural quantum dynamics.
EXPERIMENT 01
One qubit.
A family of Hamiltonians.
Vary the field components and compare MixFunn with exact dynamics, including training with and without supervised data.
Vary hx, hy, hz · Select time
Explore one qubit →
EXPERIMENT 02
Two qubits.
Temporal continuation.
Follow interacting qubits under a fixed Hamiltonian and assess how a temporal FNO extends MixFunn trajectories.
Fixed Hamiltonian · Select time
Explore two qubits + FNO →
EXPERIMENT 03
Variable couplings.
Changing quantum trajectories.
Adjust the three diagonal interactions and examine the accuracy of MixFunn and FNO across Hamiltonians.
Vary Jxx, Jyy, Jzz · Select time
Explore variable couplings →
THE SCIENTIFIC FRAMEWORK
The physics behind the curves.
Qubit states, Bloch geometry, interacting spin Hamiltonians and the neural methods used to approximate their evolution. The scientific background brings together the equations, assumptions and references.