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	Stima di Fase Quantistica	Variational Quantum Eigensolver
Campo	Calcolo quantistico	Calcolo quantistico
Famiglia	Machine learning	Machine learning
Anno di origine	1995	2014
Ideatore	Alexei Kitaev	Alberto Peruzzo
Tipo	Subroutine algorithm	Hybrid quantum-classical algorithm
Fonte seminale	Kitaev, A. Y. (1995). Quantum measurements and the Abelian stabilizer problem. arXiv preprint quant-ph/9511026.	Peruzzo, A., McClean, J., Shadbolt, P., et al. (2014). A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5, 4213.
Alias	QPE, phase kickback	VQE, hybrid quantum-classical
Correlati	3	4
Sintesi	Quantum Phase Estimation (QPE) is a fundamental quantum subroutine that estimates the eigenvalues of a unitary operator. Developed by Alexei Kitaev in 1995, QPE combines controlled unitary evolution with the quantum Fourier transform to extract eigenvalues from quantum states with exponential precision scaling.	The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm designed to find the lowest eigenvalue (ground state energy) of a quantum Hamiltonian. Introduced by Peruzzo et al. in 2014, it exploits the variational principle to combine the power of quantum circuits with classical optimization to solve chemistry and materials science problems on near-term quantum devices.