Variational Quantum Eigensolver (VQE) | Molecular Ground States
Quick Technical Answer:
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm designed for NISQ computers that finds the ground state energy of a molecular Hamiltonian by variationally updating ansatz parameters using classical optimizers.
Formula / Unitary:
E_0 \le \langle\psi(\theta)| H |\psi(\theta)\rangle = \sum_i c_i \langle\psi(\theta)| P_i |\psi(\theta)\rangle
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Rayleigh-Ritz Variational Principle
According to the variational theorem of quantum mechanics, the expectation value of a Hamiltonian H with respect to any trial wavefunction |ψ(θ)⟩ is strictly greater than or equal to the true ground state energy E_0. The quantum computer evaluates ⟨H⟩ for a given parameter set θ, and a classical optimizer (COBYLA, SPSA, Adam) updates θ iteratively to minimize the energy.
Frequently Asked Questions
Why is VQE resilient to noise on NISQ hardware?
VQE uses shallow-depth parameterized circuits and delegates optimization to classical routines, allowing coherent error mitigation techniques like Zero-Noise Extrapolation (ZNE).