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Equation 4 · Part 9 · How Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute Actually Works

Symbol V

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
VV

What this part means

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

Its job in the formula

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

The passage around this formula

…almost universally used is the parameterized (or variational) quantum circuit, and its mechanism has four concrete steps. First, classical input data x is encoded into a quantum state by applying a data-dependent 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,…

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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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