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PreprintarXiv licencearXiv

Quantisation of Abstract Data Types

  • Mingsheng Ying
  • Zhicheng Zhang
  • Kean Chen
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Abstract

In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstraction in quantum programming. We formally define a quantisation of classical data types and show that their equational specifications can be soundly lifted to the quantum setting. Two standard quantisation methods for classical functions, namely the bit oracle and the phase oracle, arise as special cases of this general construction. We illustrate the framework with applications to quantum arrays and quantum error-correcting codes, showing how they can be understood through the lens of data-type quantisation. We further establish conditions under which quantisation preserves structural relationships and constructions of classical data types, including embeddings, isomorphisms, and products.

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Cite

BibTeXRIS
BibTeX
@misc{ying2026quantisation,
  title = {{Quantisation of Abstract Data Types}},
  author = {Mingsheng Ying and Zhicheng Zhang and Kean Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03778},
  eprint = {2609.03778},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03778},
}
RIS
TY  - UNPB
TI  - Quantisation of Abstract Data Types
AU  - Mingsheng Ying
AU  - Zhicheng Zhang
AU  - Kean Chen
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03778
UR  - https://arxiv.org/abs/2609.03778
AB  - In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstraction in quantum programming. We formally define a quantisation of classical data types and show that their equational specifications can be soundly lifted to the quantum setting. Two standard quantisation methods for classical functions, namely the bit oracle and the phase oracle, arise as special cases of this general construction. We illustrate the framework with applications to quantum arrays and quantum error-correcting codes, showing how they can be understood through the lens of data-type quantisation. We further establish conditions under which quantisation preserves structural relationships and constructions of classical data types, including embeddings, isomorphisms, and products.
ER  -