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Glossary

Quantum glossary

Hamiltonian

The operator for a system’s total energy; it determines how the state evolves in time.

Its eigenvalues are the allowed energies and its lowest eigenvalue is the ground-state energy that VQE hunts for. Time evolution under a Hamiltonian H for time t is the unitary e^{−iHt/ħ}.

iħ ∂|ψ⟩/∂t = H|ψ⟩

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Related terms

  • Schrödinger equation — The equation that governs how a quantum state changes in time.
  • Variational quantum eigensolver — A hybrid algorithm that estimates a Hamiltonian’s ground-state energy by optimising a variational circuit.
  • Unitary — A reversible, probability-preserving transformation; every quantum gate is a unitary matrix.