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Equation 2 · Part 4 · Variational Evolution: How Quantum Computers Learn Their Answers

Symbol H

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

What this part means

H is an input to the expression that computes the quantity on the left.

Its job in the formula

H is an input to the expression that computes the quantity on the left.

The passage around this formula

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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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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