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arXiv · 2510.07051

Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions

Gilles Barthe·Minbo Gao·Jam Kabeer Ali Khan·Matthijs Muis·Ivan Renison·Keiya Sakabe·Michael Walter·Yingte Xu·Tianshi Yu·Li Zhou
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Abstract

We present sound and complete relational program logics for infinite-dimensional quantum and classical-quantum programs. The logics model assertions as self-adjoint unbounded linear relations, which simultaneously support quantitative and qualitative reasoning. Our main theoretical results include new convergence theorems and infinite-dimensional duality theorems for infinite-dimensional quantum states, which we use to establish completeness.

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Gilles Barthe, Minbo Gao, Jam Kabeer Ali Khan, Matthijs Muis, Ivan Renison, Keiya Sakabe, Michael Walter, Yingte Xu, Tianshi Yu, Li Zhou. 2025-10-08. Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions. https://arxiv.org/abs/2510.07051

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