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arXiv · 2603.13538

Quantum Process Realization of LDPC Code Dualities and Product Constructions

Shuhan Zhang·Deepak Aryal·Yi-Zhuang You
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Abstract

We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes consisting of ancilla initialization, local unitaries, and projective measurements. Using ZX-calculus, we represent these transformations diagrammatically and provide a systematic algorithm for extracting quantum circuits. Central to our framework is the observation that the physical content of a classical LDPC code is captured by the operator algebra associated with its Tanner graph, and that code transformations correspond to maps between such algebras. Kramers-Wannier duality then admits a natural interpretation as gauging, while tensor and check products correspond to coupled-layer constructions in which interlayer coupling and projection implement a quotient on stacked operator algebras. Together, these results establish a unified framework connecting code transformations, quantum circuits, and mappings between distinct quantum phases of matter.

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Shuhan Zhang, Deepak Aryal, Yi-Zhuang You. 2026-03-13. Quantum Process Realization of LDPC Code Dualities and Product Constructions. https://arxiv.org/abs/2603.13538

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