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Equation 4 · Part 8 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Symbol U

C(θ)=⟨ψ0∣V†(x) U†(θ) A U(θ) V(x)∣ψ0⟩C(\theta) = \left\langle \psi_0 \right| V^{\dagger}(x)\, U^{\dagger}(\theta)\, A\, U(\theta)\, V(x) \left|\psi_0\right\rangle
UU

What this part means

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

Its job in the formula

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

The passage around this formula

…unitary V(x) to a fixed initial state — commonly done by rotating each qubit by an angle set from one feature of x, so the input vector is literally written into rotation angles. Second, an “ansatz” unitary U(θ) — a fixed sequence of parameterized single-qubit rotation gates and two-qubit entangling gates, repeated over several layers — is applied, where θ is now a set of continuously adjustable classical numbers rather than data. Third, an observable A is measured on the resulting state; because…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the surrounding passage

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