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E(θ)=⟨ψ(θ)∣H∣ψ(θ)⟩E(\theta) = \langle \psi(\theta) \mid H \mid \psi(\theta) \rangle

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This is the variational algorithm, and by 2026 it is not one technique among several — it is close to the entire working repertoire of near-term quantum hardware. The archetype is the variational quantum eigensolver (VQE), first demonstrated in 2014 on a photonic quantum processor, where Alberto Peruzzo and coauthors used the loop to compute the ground-state molecular energy of the helium hydride cation, HeH+, to within chemical accuracy [ 1 ] . The demonstration used only a small photonic chip, but its structural claim was the important part: instead of demanding the long coherent evolution that quantum phase estimation requires, VQE splits the work. The quantum processor’s only job is to…

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E(θ)=⟨ψ(θ)∣H∣ψ(θ)⟩.E(\theta) = \langle \psi(\theta) \mid H \mid \psi(\theta) \rangle .

Equation 2 · Evolutionary Physics

Variational Evolution: How Quantum Computers Learn Their Answers

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

This is the variational algorithm, and by 2026 it is not one technique among several — it is close to the entire working repertoire of near-term quantum hardware. The archetype is the variational quantum eigensolver (VQE), first demonstrated in 2014 on a photonic quantum processor, where Alberto Peruzzo and coauthors used the loop to compute the ground-state molecular energy of the helium hydride cation, HeH+, to within chemical accuracy [ 1 ] . The demonstration used only a small photonic chip, but its structural claim was the important part: instead of demanding the long coherent evolution that quantum phase estimation requires, VQE splits the work. The quantum processor’s only job is to…

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