Variational Quantum Eigensolver (VQE)

VQE finds the lowest energy of a quantum system using a hybrid loop — a parameterized quantum circuit tuned by a classical optimizer — and is a leading near-term algorithm.

Type

hybrid quantum-classical, variational

Goal

ground-state energy

Hardware

NISQ-friendly (shallow ansatz)

What it does

A parameterized ansatz circuit prepares a trial state; the quantum computer measures the expected energy ⟨ψ(θ)|H|ψ(θ)⟩; a classical optimizer updates θ to lower it. The variational principle guarantees the estimate never dips below the true ground-state energy.

Circuit sketch

Where it's used

Quantum chemistry, materials, and — relevant to Kronos — small-scale simulation of strongly-correlated systems where classical methods struggle.

In code (Qiskit)

from qiskit.circuit.library import TwoLocal
ansatz = TwoLocal(4,'ry','cx',reps=2)
# classical optimizer minimizes <H> over ansatz parameters