Temporal-Angular Quantum Addressing (TAQA)
A Coordination Layer for Distributed Quantum Systems via Cycle-Anchored Phase Windows
Abstract
Temporal-Angular Quantum Addressing (TAQA) is a practical coordination layer for distributed quantum systems that operationalizes cycle-anchored phase-window execution. Quantum actions are bound to a shared cyclic phase context using classical metadata (Q-Address-style addressing) and executed when a node’s locally estimated phase enters an agreed wrap-safe acceptance window within an intended cycle. For interoperability and verification, TAQA adopts tick-canonical semantics (fixed-point integers), not floating-point boundary checks. TAQA supports phase-aligned scheduling of remote operations, bounded coordination windows for entanglement attempts, and temporal labels for routing/scheduling workflows. Cryptography and anti-replay policy are externalized to Security Profiles; TAQA fields are public context, not secrets.
Normative dependencies (DOIs)
- Conventions (canonical (t₀, Tcycle, n, ϕ); modulo; wrap-safe windows; ticks): 10.5281/zenodo.18068999
- Q-Address (tick-canonical macro window + micro slot): 10.5281/zenodo.18068997
Security plug-in (DOI)
- Timeverse Security Profile: 10.5281/zenodo.18069423
1. Scope
Principle 1.1 (Control-plane only): TAQA is a classical control-plane / metadata layer. It does not introduce a quantum time operator and does not modify the Hilbert space.
Principle 1.2 (What TAQA does not define): TAQA does not define bootstrapping/estimation methods for clock parameters, hardware timing implementations, or cryptographic algorithms. Bootstrapping is handled by external layers (e.g., QBP), and security is handled by Security Profiles.
Remark 1.1 (Context papers): The long-horizon coordination limitation motivating phase windows is formalized in [4]. An initialization method compatible with cycle anchoring is given in QBP [5].
2. Conventions and windows
Remark 2.1 (Canonical conventions are defined externally): This document uses Conventions [1] as the normative source for: (i) the arithmetic time variable requirement (autonomous monotone time for computations), (ii) canonical (t₀, Tcycle, n(t), ϕ(t)) on S¹ with a negative-safe modulo convention, (iii) wrap-around-safe windows using circular distance on S¹, and (iv) tick-canonical encodings and boundary semantics.
Definition 2.1 (Phase-window coordination objective):
A TAQA instruction specifies an intended cycle index and a phase acceptance window within that cycle. Nodes execute when their local phase estimate enters the agreed window in the intended cycle.
Remark 2.2 (Tick-canonical verification): For verification/gating, window membership MUST be checked using tick fields and tick-distance membership as defined in Conventions, not by comparing floating-point phase values.
3. Core constructs
Definition 3.1 (Execution primitive: tick-canonical Q-Address minimal view):
TAQA expresses execution instructions using a tick-canonical Q-Address minimal view:
(qaddr_schema, convention_id, scope, cycle_index, resolution = 𝑅, phi_ticks, deltaPhi_ticks, slot).
This document recommends the machine-facing compatibility tag qaddr_schema=TV-QADDR-2025-12. Full schema, canonical encoding rules, and slot semantics are normatively defined in [2].
Definition 3.2 (T-Qubit (systems container)):
A T-Qubit is a systems-level container:
T-Qubit ≡ (|ψ⟩, M),
where |ψ⟩ is the quantum state and M is classical coordination metadata (e.g., Q-Address context, policy fields, audit hooks). This metadata does not introduce a new physical degree of freedom.
Remark 3.1 (Derived displays are UI-only): Human-facing displays such as HS◦deg (degrees) and HSidx(12-segment index), SWT labels, etc., are derived-only and MUST NOT drive verification.
4. TAQA coordination protocol
Protocol 4.1 (TAQA coordination)
Phase 1: Agreement (planning)
- Nodes negotiate a joint operation O (remote gate, entanglement attempt, measurement window).
- They agree on a cycle-anchored macro window encoded by tick fields: cycle_index, resolution, phi_ticks, deltaPhi_ticks, and an optional micro slot.
- The agreement is communicated via authenticated classical channels (authentication mechanisms are provided by the security layer).
Phase 2: Execution (triggering)
- Each node computes a locally available time variable t̂ᵢ(t) (implementation-dependent) and derives the corresponding tick-canonical phase context under the active convention_id.
- The node triggers its part of O when it detects both: (i) the intended cycle index, and (ii) tick-window membership for the intended window, computed using Conventions-defined tick distance.
- Fine sequencing inside the window uses slot and local hardware timing.
Remark 4.1 (Cycle anchoring is mandatory): Because phase is cyclic, “same phase” can refer to different cycles. TAQA therefore requires an intended cycle index in every executable instruction.
5. Applications
Application 5.1 (Phase-aligned distributed gate execution):
Distributed gates across nodes are scheduled for the same cycle-anchored window; micro-timing inside the window is local.
Application 5.2 (Entanglement distribution scheduling):
Photon emissions and Bell-state measurement windows can be scheduled for coincident phase windows, reducing dependence on continuous absolute-time synchronization.
Application 5.3 (Temporal routing labels):
Cycle-anchored Q-Address contexts can serve as temporal labels for routing/prioritization in repeater networks and distributed workflows.
6. Security plug-in interface
Remark 6.1 (Security scope): TAQA does not define cryptographic algorithms. TAQA/Q-Address/TSAE fields are public context (not secrets). Security (signatures, nonces, anti-replay policy, canonical encoding) is defined by the active security_profile_id as specified by the Timeverse Security Profile [3].
Definition 6.1 (Optional audit hook: TSAE receipt):
An implementation MAY produce a signed TSAE receipt after executing a step. A minimal TSAE record uses tick-canonical context:
(tsae_schema, convention_id, scope, cycle_index, resolution = 𝑅, phi_ticks, action_hash, signer_id)
This document recommends tsae_schema=TV-TSAE-2025-12 as a machine-facing compatibility tag. Signature format, canonical encoding, and anti-replay policy are defined by the active Security Profile.
7. Conclusion
TAQA provides a practical coordination layer for distributed quantum systems using cycle-anchored phase windows and local micro slots. It references tick-canonical Q-Address metadata for interoperability and supports optional signed audit receipts via Security Profiles, without relying on continuous external timing infrastructure by design.
References
- [1] T. Ouardi, Phase-Coordination Series Conventions, Zenodo (2025). DOI: 10.5281/zenodo.18068999.
- [2] T. Ouardi, Q-Address: Macro Phase + Micro Slot, Zenodo (2025). DOI: 10.5281/zenodo.18068997.
- [3] T. Ouardi, Timeverse Security Profile, Zenodo (2025). DOI: 10.5281/zenodo.18069423.
- [4] T. Ouardi, Theorem of Temporal Resolution Limitation and the Phase-Coordination Principle (v1.1), Zenodo (2025). DOI: 10.5281/zenodo.17955430.
- [5] T. Ouardi, Quantum Bootstrapping Protocol (QBP): Autonomous Initialization for Phase-Coordinated Quantum Networks (v1.2), Zenodo (2025). DOI: 10.5281/zenodo.18064435.