quant feature map — two observables into a projected/seed kernel

Primitives used: observable · quant

// A `quant` FEATURE MAP. Each `quant` block yields ONE scalar expectation
// ⟨ψ(carrier)|M|ψ⟩ of ONE observable. To build a k-dimensional quantum
// feature vector φ(x) = [⟨M₁⟩, …, ⟨Mₖ⟩], declare k observables and run one
// quant block per observable; the projected/seed kernel k(x,y)=sim(φ(x),φ(y))
// is then assembled CLASSICALLY. The grammar below is the exact form that
// passes `axon check`:
//
//   • `observable Name { qubits: n  term: <coeff> * "<Pauli>" }`  (term is
//     repeatable; the Pauli is a STRING LITERAL, one letter per qubit, MSB-first)
//   • `quant(encoding: …, observable: …, qubits: …) { … }`  (attributes in
//     PARENTHESES; the braces hold flow steps)
//   • `yield <reference>`  (a let-bound name or flow param — NO ⟨⟩ brackets)
//   • the carrier must be a continuous type (Tensor), else axon-E0782.

observable EnergyZ {
    qubits: 2
    term: 1.0 * "ZI"
    term: 1.0 * "IZ"
}

observable CorrelationZZ {
    qubits: 2
    term: 1.0 * "ZZ"
}

flow QuantFeatureMap(carrier: Tensor) -> String {
    // Feature 1 — ⟨EnergyZ⟩ over the carrier (amplitude encoding).
    quant(encoding: amplitude, observable: EnergyZ, qubits: 2) {
        let surrogate = carrier
        yield surrogate
    }
    // Feature 2 — ⟨CorrelationZZ⟩ over the same carrier (angle encoding).
    quant(encoding: angle, observable: CorrelationZZ, qubits: 2) {
        let surrogate = carrier
        yield surrogate
    }
    return "features computed"
}