# QILP-0: Constructing Observational Declarative Twins of Quantum Circuits

arXiv: https://arxiv.org/abs/2609.01049 · HTML: https://mlsanity.com/paper/2609.01049/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 73 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning](https://mlsanity.com/paper/2301.09138/) (2023)
- [Operationally meaningful representations of physical systems in neural networks](https://mlsanity.com/paper/2001.00593/) (2020)
- [Opportunities and limitations of explaining quantum machine learning](https://mlsanity.com/paper/2412.14753/) (2024)
- [Learning Minimal Representations of Many-Body Physics from Snapshots of a Quantum Simulator](https://mlsanity.com/paper/2509.13821/) (2025)
- [Discovering quantum phenomena with Interpretable Machine Learning](https://mlsanity.com/paper/2604.16015/) (2026)
- [Disentanglement by means of action-induced representations](https://mlsanity.com/paper/2602.06741/) (2026)
- [LQP: The Dynamic Logic of Quantum Information](https://mlsanity.com/paper/2110.01361/) (2021)
- [symQV: Automated Symbolic Verification of Quantum Programs](https://mlsanity.com/paper/2212.02267/) (2022)

## Abstract (arXiv)

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.