QILP-0: Constructing Observational Declarative Twins of Quantum Circuits

• URL: http://arxiv.org/abs/2609.01049v1
• Date: Tue, 01 Sep 2026 10:46:42 GMT
• Title: QILP-0: Constructing Observational Declarative Twins of Quantum Circuits
• Abstract summary: This paper introduces QXymb, a general framework for constructing observational declarative twins of quantum circuits.<n>We develop QILP-0, its first complete order-0, which constructs a finite multi-valued propositional logic program from observed circuit behaviour.<n>In every reported relation, the induced QILP-0 theory achieves complete, conflict-free reconstruction with strict accuracy equal to one.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: This paper introduces QXymb, a general framework for constructing observational declarative twins of quantum circuits, and develops QILP-0, its first complete order-0 specialization. QILP-0 constructs a finite multi-valued propositional logic program from observed circuit behaviour within a declared observational scope. The pipeline traverses a declared family of quantum observables incrementally according to a reproducible structural grading and a declared observational reference horizon. Progress is quantified through reference-relative coverage against a fixed target-independent reference. Observable responses are organized through target-independent geometry, while retained latent structure is mapped deterministically back to original observable columns before symbolic processing, preserving observational semantics and provenance. Selected observable profiles are converted into a finite relation through admissible target-independent discretization. The target is used only afterwards to audit twin-admissibility and induce the declarative theory. A theory is certified as an exact observational declarative twin when it completely and correctly reconstructs the resulting finite task-conditioned discrete relation. Logical exactness is therefore separated from numerical, backend, provider, and discretization uncertainty, which is retained as audit metadata. Validation uses two complementary QML settings. Exhaustive Bars & Stripes experiments compare product and grid-CZ embeddings from 16 to 100 qubits and exercise the native-discrete branch. Low-Depth MNIST analyses all 14,708 digit-0/1 instances before and after a trained variational quantum transformation and exercises continuous discretization. In every reported relation, the induced QILP-0 theory achieves complete, conflict-free reconstruction with strict accuracy equal to one.

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