vqd

Create a VQD solver with an estimator primitive, a ComputeUncompute fidelity primitive, a parameterized ansatz like RealAmplitudes, and an optimizer such as SLSQP. Set k to the number of eigenvalues and call compute_eigenvalues with your SparsePauliOp operator.

VQE finds only the ground-state energy of a Hamiltonian, while VQD finds the lowest k eigenvalues including excited states. VQD runs VQE-style optimizations sequentially, adding overlap penalty terms that force each new state to be orthogonal to previously found states.

Betas control the strength of orthogonality enforcement between states. If excited-state energies collapse toward the ground state, increase betas starting around 1.0; if optimization fails to converge, reduce betas so the penalty does not dominate the energy term.

When convergence_threshold is set, VQD monitors the average weighted fidelity with prior states and raises AlgorithmError if overlap remains too high after optimization. Increase optimizer maxiter, adjust betas, or relax the threshold to resolve it.

The fidelity overhead grows with each additional state because every step computes overlaps against all prior states, making large k expensive. Ansatz expressibility and optimizer quality also limit accuracy, so exact diagonalization may be preferable for small systems.