Quantum Process Realization of LDPC Code Dualities and Product Constructions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908885504229376 |
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| author | Zhang, Shuhan Aryal, Deepak You, Yi-Zhuang |
| author_facet | Zhang, Shuhan Aryal, Deepak You, Yi-Zhuang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Process Realization of LDPC Code Dualities and Product Constructions Zhang, Shuhan Aryal, Deepak You, Yi-Zhuang Quantum Physics Strongly Correlated Electrons 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. |
| title | Quantum Process Realization of LDPC Code Dualities and Product Constructions |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2603.13538 |