Compiling Quantum Lambda-Terms into Circuits via the Geometry of Interaction
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911457293107200 |
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| author | Chardonnet, Kostia Lago, Ugo Dal Hoshino, Naohiko Pistone, Paolo |
| author_facet | Chardonnet, Kostia Lago, Ugo Dal Hoshino, Naohiko Pistone, Paolo |
| contents | We present an algorithm turning any term of a linear quantum $λ$-calculus into a quantum circuit. The essential ingredient behind the proposed algorithm is Girard's geometry of interaction, which, differently from its well-known uses from the literature, is here leveraged to perform as much of the classical computation as possible, at the same time producing a circuit that, when evaluated, performs all the quantum operations in the underlying $λ$-term. We identify higher-order control flow as the primary obstacle towards efficient solutions to the problem at hand. Notably, geometry of interaction proves sufficiently flexible to enable efficient compilation in many cases, while still supporting a total compilation procedure. Finally, we characterize through a type system those $λ$-terms for which compilation can be performed efficiently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compiling Quantum Lambda-Terms into Circuits via the Geometry of Interaction Chardonnet, Kostia Lago, Ugo Dal Hoshino, Naohiko Pistone, Paolo Logic in Computer Science We present an algorithm turning any term of a linear quantum $λ$-calculus into a quantum circuit. The essential ingredient behind the proposed algorithm is Girard's geometry of interaction, which, differently from its well-known uses from the literature, is here leveraged to perform as much of the classical computation as possible, at the same time producing a circuit that, when evaluated, performs all the quantum operations in the underlying $λ$-term. We identify higher-order control flow as the primary obstacle towards efficient solutions to the problem at hand. Notably, geometry of interaction proves sufficiently flexible to enable efficient compilation in many cases, while still supporting a total compilation procedure. Finally, we characterize through a type system those $λ$-terms for which compilation can be performed efficiently. |
| title | Compiling Quantum Lambda-Terms into Circuits via the Geometry of Interaction |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2602.17482 |