Quantum Process Realization of LDPC Code Dualities and Product Constructions

Abstract:We realize a broad class of code transformations, 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 formulate these code transformations diagrammatically and develop a systematic algorithm for extracting their quantum-process realizations. 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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2603.13538 [quant-ph]

(or arXiv:2603.13538v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.13538 Focus to learn more arXiv-issued DOI via DataCite

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