qCompute — Operator Grammar

File: qc_OperatorGrammar.md
Layer: RTT‑Inside Compute Harness
Status: Canonical (2026)

This document defines the formal grammar, argument rules, and legality semantics for all qCompute operators.

The grammar is:

• minimal
• deterministic
• environment‑aware
• backend‑aware
• drift‑aware
• replay‑safe

qCompute computes structure, not amplitudes.

1. Operator Namespace#

Operators belong to five families:

Each operator has:

• name
• tier
• drift characteristic
• backend requirement
• environment legality

2. Formal Grammar#

2.1 Operator Invocation#

<operator> "(" <args> ")"

2.2 Arguments#

<args> ::= <arg> | <arg> "," <args>
<arg>  ::= <name> "=" <value>

2.3 Names#

<name> ::= /[a-zA-Z_][a-zA-Z0-9_]*/

2.4 Values#

<value> ::= <int> | <float> | <bool> | <string>

2.5 QuBits#

q, q1, q2 ∈ ℕ

3. Operator Legality Rules#

Each operator is validated against:

1. grammar
2. argument correctness
3. environment legality
4. tier legality
5. backend legality
6. token requirements
7. archive terminality

If invalid:

allowed: false
reason: "<canonical reason>"

Canonical reasons:

• "invalid grammar"
• "invalid arguments"
• "illegal in environment"
• "backend mismatch"
• "backend illegal in environment"
• "tier decrease inside frame"
• "token required"
• "archive terminal"
• "illegal transition"

4. Tier Semantics#

r1 (primitive)#

• allowed in sandbox + production
• low drift
• backend: local-sim
• may reuse frame

r2 (composite)#

• allowed in sandbox + production
• medium drift
• backend: hybrid-sim
• tier escalation → new frame

r3 (pulse)#

• production only
• token required
• high drift
• backend: hardware-qpu-2
• always opens new frame

measurement#

• allowed in sandbox + production
• forces tier decrease
• forces new frame

meta#

• allowed in sandbox + production
• zero drift
• always opens new frame

5. Backend Legality#

Archive is terminal and forbids all operators.

6. Environment Legality#

Transitions:

• sandbox → production (token required)
• production → archive (token required)
• archive → (forbidden)

7. Drift Semantics#

Each operator has a drift characteristic:

Drift overflow:

• closes current frame
• opens new frame
• routes operator into new frame

8. Frame Semantics#

A frame is valid if:

• tier is monotonic (no decrease)
• backend is consistent
• drift ≤ drift bound
• environment is legal

Triggers for new frame:

• first operator
• tier escalation
• tier decrease
• r3 operator
• drift overflow
• meta operator
• environment transition

9. Capture Semantics#

Each operator produces:

operator:
  op_id: "<id>"
  name: "<operator>"
  params: {...}
  validation: {...}
  routing: {...}
  drift: {...}
  timestamp: "<iso8601>"
  hash_prev: "<sha256>"
  hash_self: "<sha256>"

All fields are required.

10. Replay Semantics#

Replay verifies:

• grammar
• tier monotonicity
• backend legality
• environment legality
• drift bounds
• transition legality
• hash chain integrity
• canonical field presence

Replay is deterministic and read‑only.

11. Invariants#

1. grammar must be valid
2. arguments must be valid
3. environment must allow tier
4. backend must match tier
5. r3 requires token
6. measurement forces new frame
7. meta forces new frame
8. drift must not exceed bound
9. archive is terminal
10. hash chain must be valid

Summary#

The Operator Grammar defines:

• operator namespace
• formal grammar
• argument rules
• tier semantics
• backend legality
• environment legality
• drift + frame semantics
• capture + replay invariants

This grammar is the foundation of qCompute.