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observable

Since v2.19.0 · Top-level declaration

Grammar​

# Top-level declaration — a BLOCK of `key: value` fields:
observable <Name> {
    qubits: <n>                 # optional — the declared register width
    term: <coeff> * "<Pauli>"   # repeatable — one cₖ · Pₖ per line
    term: <coeff> * "<Pauli>"
}

# <coeff> is a real scalar (optional leading +/-), then `*`, then the
# Pauli string as a STRING LITERAL: one letter per qubit, MSB-first,
# from { I (identity), X, Y, Z }.  e.g. "Z", "ZZ", "XI".

observable declares a Hermitian operator as a weighted sum of Pauli strings — M = Σₖ cₖ Pₖ — the quantity a quant block measures to collapse a Hilbert-space state back to a single classical expectation ⟨ψ| M |ψ⟩.

Because every term is a real coefficient times a tensor product of Pauli matrices (each Hermitian and involutory), the sum is Hermitian by construction — so its expectation is always real, and it is a valid quantum-mechanical measurement. The compiler proves this (axon-E0785); a malformed observable never reaches the runtime.

Surface​

observable is a top-level declaration, like type or anchor — a brace block of key: value fields. It is referenced by name from a quant block's observable: attribute. The two recognised fields are qubits: (the register width) and term: (repeatable — one weighted Pauli term per line).

# A single-qubit energy observable: ⟨Z⟩.
observable Energy {
    qubits: 1
    term: 1.0 * "Z"
}

# A two-qubit correlation observable: ½⟨ZZ⟩ − 1.2⟨XI⟩.
observable Correlation {
    qubits: 2
    term:  0.5 * "ZZ"
    term: -1.2 * "XI"
}

Nota de gramática: los coeficientes y los Pauli van como campos term: <coeff> * "<Pauli>" dentro del bloque — NO como una expresión observable Name = coeff * Pauli. La cadena de Pauli es un string literal (entre comillas). Esta es la forma exacta que pasa axon check.

Anatomy​

term: — one weighted Pauli per line (repeatable)​

term: <coeff> * "<PauliString>". The coefficient is a real scalar (optional leading +/-), then *, then the Pauli string as a quoted string literal. Repeat the term: key once per cₖ · Pₖ.

Pauli strings​

Each Pauli string names one factor per qubit, most-significant qubit first:

LetterMatrixMeaning
Iidentityqubit untouched
X[[0,1],[1,0]]bit-flip basis
Y[[0,−i],[i,0]]
Z[[1,0],[0,−1]]computational basis

All term: strings must share one length = the qubit count n; a quant block measuring the observable encodes a state of that width.

qubits: + coefficients​

qubits: declares the register width (optional; defaults from the term widths). The coefficients set each term's Hermitian weight; the operator norm of the sum bounds the achievable expectation (a single Pauli string has ‖P‖ = 1, so ⟨P⟩ ∈ [−1, 1]).

Runtime behaviour​

A declared observable lowers to a PauliSum value (the closed list of (coeff, pauli_string) terms). At measurement the runtime computes ⟨ψ| M |ψ⟩ = Σₖ cₖ ⟨ψ| Pₖ |ψ⟩ — Pauli action is exact on the Q32.32 substrate (entries {0, ±1, ±i} never round), so a Pauli-sum expectation is bit-reproducible in the enterprise backend.

Static guarantees​

  • axon-E0785 — the Pauli-sum must be well-formed: every term a real coefficient times a valid Pauli string of consistent width.
  • axon-E0784 — a quant block's observable: must resolve to a declared observable (closed-catalogue resolution).
  • axon-E0786 — a declared density matrix companion must have dimension D = 2ⁿ.

What this primitive is NOT​

  • Not a type. A type declares a data shape; an observable declares a measurement operator over a Hilbert space.
  • Not an anchor. An anchor is a grounding constraint on a flow's outputs; an observable is the physical quantity a quant block reads.
  • Not executable on its own. It is inert until a quant block names it — like a type is inert until a value inhabits it.

See also​

  • axon://primitives/quant — the block that measures an observable.
  • axon://primitives/flow — the parent of every quant block.