Denotational semantics for stabiliser quantum programs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914173596729344 |
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| author | Booth, Robert I. Comfort, Cole |
| author_facet | Booth, Robert I. Comfort, Cole |
| contents | The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational semantics for stabiliser operations which include measurement, classically-controlled Pauli operators, and affine classical operations, in which quantum error-correcting codes are first-class objects. The operations are interpreted as certain affine relations over finite fields. This offers a conceptually motivated and computationally-tractable alternative to the standard operator-algebraic semantics of quantum programs (whose time complexity grows exponentially as the state space increases in size). We demonstrate the power of the resulting semantics by describing a small, proof-of-concept assembly language for stabiliser programs with fully-abstract denotational semantics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Denotational semantics for stabiliser quantum programs Booth, Robert I. Comfort, Cole Logic in Computer Science Category Theory Symplectic Geometry Quantum Physics The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational semantics for stabiliser operations which include measurement, classically-controlled Pauli operators, and affine classical operations, in which quantum error-correcting codes are first-class objects. The operations are interpreted as certain affine relations over finite fields. This offers a conceptually motivated and computationally-tractable alternative to the standard operator-algebraic semantics of quantum programs (whose time complexity grows exponentially as the state space increases in size). We demonstrate the power of the resulting semantics by describing a small, proof-of-concept assembly language for stabiliser programs with fully-abstract denotational semantics. |
| title | Denotational semantics for stabiliser quantum programs |
| topic | Logic in Computer Science Category Theory Symplectic Geometry Quantum Physics |
| url | https://arxiv.org/abs/2511.22734 |