Quantum Process Realization of LDPC Code Dualities and Product Constructions

• URL: http://arxiv.org/abs/2603.13538v1
• Date: Fri, 13 Mar 2026 19:21:05 GMT
• Title: Quantum Process Realization of LDPC Code Dualities and Product Constructions
• Abstract summary: We realize a broad class of code constructions, including Kramers-Wannier duality, tensor product, and check product, as quantum processes.<n>Using ZX-calculus, we represent these transformations diagrammatically and provide a systematic algorithm for extracting quantum circuits.
• Score: 4.632879289405095
• License: http://creativecommons.org/licenses/by/4.0/
• 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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