Hamiltonian Simulation

Simulating how a quantum system evolves under its Hamiltonian is the original motivation for quantum computing — and where a fusion company's physics interest is sharpest.

Goal

apply e^{-iHt}

Methods

Trotter, qubitization, LCU

Feynman

'simulate nature with a quantum machine'

What it does

Time evolution e^{-iHt} is decomposed into implementable pieces — Trotter–Suzuki splitting for local Hamiltonians, or modern qubitization/LCU methods with near-optimal scaling. It lets a quantum computer model quantum dynamics that are exponentially hard classically.

Where it's used

Quantum chemistry, materials, and — long term — strongly-correlated and kinetic plasma physics that resist classical simulation.

In code (Qiskit)

from qiskit.synthesis import SuzukiTrotter
# Trotterize exp(-iHt) into gate layers