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Glossary

Quantum glossary

Variational quantum eigensolver

Also: vqe

A hybrid algorithm that estimates a Hamiltonian’s ground-state energy by optimising a variational circuit.

The quantum computer prepares a trial state and measures its energy; a classical optimiser updates the parameters. By the variational principle, the measured energy can never be below the true ground state — noise and shot error aside.

E(θ) = ⟨ψ(θ)|H|ψ(θ)⟩ ≥ E₀

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Related terms

  • Variational circuit — A circuit with tunable rotation angles that a classical optimiser adjusts to minimise a cost.
  • Hamiltonian — The operator for a system’s total energy; it determines how the state evolves in time.
  • Expectation value — The average result you would get measuring an observable on many copies of the same state.